Bridge cable force real-time tracking method based on peak value automatic extraction

Abstract

The invention discloses a bridge cable force real-time tracking method based on peak value automatic extraction, and aims to solve the problem that the manual extraction of real-time and batch power spectral density map peak values is tedious and difficult, and the method comprises the steps: firstly converting an acceleration signal collected by a sensor into frequency domain information through fast Fourier transform; then performing data preprocessing on the power spectral density map to ensure the peak value extraction accuracy; peak values in the power spectral density map are preliminarily extracted based on a data maximum value searching method, then the minimum saliency, the minimum height and the minimum spacing of the peak values are limited to eliminate false peaks, and resonance peaks in the power spectral density map and corresponding frequencies and frequency intervals of the resonance peaks are recognized; on the basis of a modal analysis method and a vibration string theory, cable force tracking is finally realized and is used for guiding subsequent bridge structure evaluation work.

Description

Technical Field

[0001] The invention belongs to the field of bridge structure health monitoring and data mining, and in particular relates to a real-time tracking method for bridge cable forces based on automatic peak value extraction. Background Art

[0002] As a key component of a cable-stayed bridge, the cable plays a key role in supporting the main beam and transferring vehicle loads to the bridge tower. However, the bridge structure is inevitably affected by harsh environmental erosion or overweight vehicles. Such factors may cause damage to the overall structure of the bridge, which in turn causes abnormal changes in the internal force of the cable. Therefore, the change in the internal force of the cable is an important indicator for evaluating the safety of the overall structure of the bridge. Therefore, it is very important to monitor the condition of the bridge during the operation and maintenance stage. In recent years, with the development of bridge structure health monitoring systems, various sensors have been widely deployed at various locations on the bridge to measure the response of the bridge under actual working conditions and various environmental factors in real time. This provides the possibility of using bridge monitoring data to evaluate and track the tension of the cable in real time.

[0003] In actual bridge operation and maintenance, various methods including vibration frequency method, magnetic flux method, and oil pressure gauge have been developed to measure cable tension. The method based on oil pressure gauge is more accurate and intuitive, but it is usually used in the construction stage; the method based on magnetic flux is more expensive and significantly affected by the environment. Thanks to the advantages of the vibration frequency method, which is simple, fast, and easy to maintain, this method has been widely used in cable tension measurement. This type of method usually obtains the dynamic characteristics of the cable by analyzing the vibration data collected by the accelerometer deployed on the inclined cable. The operational modal analysis method based on the Bayesian framework can identify the most likely values ​​of the modal parameters and quantify the uncertainty of the identification results based on the only output vibration data caused by environmental excitation or wind, traffic loads, etc.

[0004] For vibration-based monitoring systems, extracting modal frequencies from the measured signal is a necessary step. The peak selection method based on the frequency domain has been widely used due to its simplicity. This step traditionally relies on manual selection by technicians. However, this method is susceptible to fatigue or misjudgment. In addition, when the bridge is operating normally, the natural frequency of the cable will change with the influence of the external environment. The vibration-based monitoring system requires real-time synchronous correction, which is time-consuming, labor-intensive and impractical for manual operation. Summary of the invention

[0005] Purpose of the invention: To achieve automatic extraction of modal frequencies, the present invention proposes a method for automatically identifying natural frequencies from power spectrum density diagrams based on actual monitoring data of bridges. This method can track natural frequencies in real time and convert the cable forces at the corresponding moment based on the frequency-cable force relationship, thereby achieving cable force tracking.

[0006] Technical solution: A real-time tracking method for bridge cable force based on peak value automatic extraction of the present invention comprises the following steps:

[0007] Step 1: Set the window length and window step size for the long-term monitoring data of the target cable-stayed bridge;

[0008] Step 2, collecting acceleration time history data, and inputting the acceleration time history data into the peak extraction model in the form of a moving window in time sequence;

[0009] Step 3: For each window of data, first perform fast Fourier transform and then perform data smoothing;

[0010] Step 4, performing preliminary peak extraction on the data obtained in step 3 to obtain a preliminary peak value;

[0011] Step 5: Calculate the most likely minimum significance, minimum height and minimum spacing of the preliminary peak in step 4 based on the significance definition and the minimum spacing calculation method, and remove pseudo peaks according to these three criteria to obtain the processed peaks;

[0012] Step 6: Based on the peak value and uncertainty principle processed in step 5, the natural frequency value and the corresponding frequency range of the cable are extracted;

[0013] Step 7: Based on the modal analysis method and vibrating string theory, other modal parameters and cable forces are calculated to achieve real-time tracking of the cable forces of the target cable-stayed bridge.

[0014] Furthermore, in step 1, the window refers to a segment of acceleration signal, the window length is the duration of the segment of signal, and the window step length is the length of the window translation on the time axis.

[0015] Further, in step 3, the fast Fourier transform adopts a unilateral power spectrum density, assuming is the acceleration time history response of the structure in n measurement degrees of freedom, N is the number of sample points in each data channel, and its one-sided scaled fast Fourier transform is defined as:

[0016]

[0017] Where Δt is the sampling time interval, i 2 = -1, for each k = 1, ..., N q -1, F k The corresponding frequency position is f k =k / NΔt, where N q =int(N / 2)+1 is the Nyquist frequency, where int(·) is the rounding function.

[0018] Furthermore, in step 3, the data smoothing process uses a Savitzky-Golay filter or a moving average method.

[0019] Further, step 4 is specifically as follows: preliminary peak extraction is performed through a function maximum point search algorithm, for the power spectrum density-frequency mapping relationship p(f k ), the peak value is where the first-order derivative function changes from positive to negative. Define the function q(f k ) is p(f k ) is the symbolic function of the derivative function, that is:

[0020]

[0021] Where signump.] is a sign function, which returns 1 for positive numbers and 0 for non-positive numbers. Then, we further apply the function q(f k ) Find the difference. If there is a position z such that q(f z+1 )-q(f z )<0, then the position z is the function p(f k ), which is the initial peak extraction position.

[0022] Furthermore, in step 5, the significance is defined as the minimum height difference required for a peak to reach any higher peak. For a given peak, the significance is calculated in the following manner: for each path connecting the peak and any higher peak, the lowest point on each path is found, and the reference height is defined as the highest point among these points; the significance is the difference between the peak height and the reference height.

[0023] Furthermore, in step 5, the minimum significance is set to 0.1p max , where p max is the maximum value of the power spectrum density in the current window; the minimum height is set to the average value of the power spectrum density in the current window; the minimum spacing is calculated by the following method:

[0024] For the preprocessed data p=[p1,p2,…,p N ], the maximum value matrix is ​​calculated by the following formula:

[0025]

[0026] Where L = ceil(N / 2)-1, ceil(x) is the upward rounding function; for each k, the maximum matrix element m when i∈[1,k]∪[N-k+1,N] is taken k,i The average value is 0;

[0027] Then calculate the density s of each column of the maximum matrix i , that is, the proportion of non-zero elements in this column, for si ≤0.85, replace all the elements in the column with 0 and record s i >0.85 will form a new array s p , search so that s p Take the isosceles triangle area on both sides of the maximum value, if there exists a z±j column satisfying:

[0028]

[0029] Then all elements of the column are replaced by 0, where the nnz(x) function returns the number of non-zero elements in x;

[0030] The search area range is given as follows:

[0031] When z≤L+1

[0032]

[0033] When z>L+1

[0034]

[0035] This cycle continues until s is traversed. p All elements in the matrix, thus obtaining the updated maximum value matrix, in which the positions of the columns with non-zero elements form a new set Then the error matrix r = [r1, r2, ..., r n ] is calculated by the following formula:

[0036]

[0037] abs(x) is the absolute value function, round(x) returns the integer closest to x, and d l (n) = l n+1 -l n is the difference value of l. Find the position that makes the sum of r columns the smallest and record it as λ, then the minimum peak spacing is 0.95d l (λ).

[0038] Furthermore, in step 6, the frequency interval is f(1±2ζ), wherein f is the peak value after processing obtained in step 5, and ζ is the damping ratio of the structure, which defaults to 1%.

[0039] Furthermore, in step 7, the modal analysis method is a modal identification method based on frequency domain data analysis, using a Bayesian operational modal analysis method.

[0040] Further, in step 7, the vibrating string theory is a cable force-frequency conversion relationship, and the cable force is calculated according to the following formula:

[0041]

[0042] Where T is the cable force, f n is the nth natural frequency, L represents the distance between the fixed ends of the cable, and m represents the mass of the cable per unit length.

[0043] Beneficial effects: Compared with the prior art, the present invention has the following significant advantages:

[0044] (1) Most existing peak extraction methods rely on manual selection; the bridge intelligent cable force tracking method based on cable vibration data in this application uses the physical characteristics of cable vibration acceleration for adaptive identification, which significantly improves the extraction efficiency.

[0045] (2) This method uses the theory of vibrating strings, i.e. the theoretical characteristics of the data, and is rigorously derived and statistically significant, ensuring that the differences between the selected modal peaks are approximately equal. The real-time changes in the cable force can be obtained according to the cable frequencies of each order, making the frequency-based cable force identification process more intuitive.

[0046] (3) The present invention has a fast computing speed and a small memory requirement, and is suitable for a long-term real-time health monitoring system for bridge structures. All analysis processes are implemented through programming, and are accurate and efficient. The results provide a basis for health detection and safety assessment of cable-stayed bridge structures.

[0047] (4) The present invention solves the problem of automatically extracting and tracking the cable frequency (that is, the peak value) of the cable after Fourier transforming the cable vibration acceleration data, and can realize automatic extraction of multiple cable frequencies in the spectrum and tracking. BRIEF DESCRIPTION OF THE DRAWINGS

[0048] Figure 1 For data used for analysis;

[0049] Figure 2 For comparison with before and after treatment;

[0050] Figure 3 This is a comparison chart before and after peak removal;

[0051] Figure 4 is the extracted frequency value and the corresponding frequency interval;

[0052] Figure 5 is a flow chart of the present invention;

[0053] Figure 6 is the frequency tracking result;

[0054] Figure 7 To track the results. DETAILED DESCRIPTION

[0055] The technical solution of the present invention is further described below in conjunction with the accompanying drawings.

[0056] Step 1: To analyze the long-term monitoring data of a cable-stayed bridge, the window length and window step are set to 1 hour. Take one of the windows as an example for analysis. The data used for analysis is as follows: Figure 1 shown.

[0057] Step 2: Input the acceleration time history data into the peak extraction program in the form of a moving window in time sequence.

[0058] Step 3: Perform fast Fourier transform and data smoothing on each window data. The pre-processed data is as follows: Figure 2 shown.

[0059] Step 4: Perform preliminary peak extraction on the preprocessed data. The preliminary peak extraction method is a function maximum point search algorithm. For the power spectrum density-frequency mapping relationship p(f k ), define the function q(f k ) is p(f k ) is the sign function of the derivative function, that is

[0060]

[0061] where signum[.] is the sign function, which returns 1 for positive numbers and 0 for non-positive numbers. k ) Find the difference. If there is a position z such that q(f z+1 )-q(f z )<0, then the position z is the function p(f k ), which is the initial peak extraction position.

[0062] Step 5: Calculate the most likely minimum significance, minimum height and minimum spacing of the peak, and remove the pseudo peaks based on these three criteria. Figure 3 As shown in the figure, it can be seen that the pseudo peaks generated by noise can be effectively filtered, and the retained peaks are all resonant peaks that reflect the natural frequency of the structure.

[0063] The minimum significance is set to 0.1p max , where p max is the maximum value of the power spectral density in the current window.

[0064] The minimum height is set to the average value of the power spectrum density in the current window.

[0065] The minimum spacing is calculated by the following method:

[0066] For the preprocessed data p=[p1,p2,…,p N], the maximum value matrix is ​​calculated by the following formula:

[0067]

[0068] Where L = ceil(N / 2)-1, ceil(x) is the upward rounding function; for each k, the maximum matrix element m when i∈[1,k]∪[N-k+1,N] is taken k,i The average value is 0.

[0069] Then calculate the density s of each column of the maximum matrix i , that is, the proportion of non-zero elements in this column. i ≤0.85, replace all the elements in the column with 0. And record s i >0.85 will form a new array s p . Search makes s p Take the isosceles triangle area on both sides of the maximum value, if there exists a z±j column satisfying

[0070]

[0071] Then all elements of the column are replaced by 0. The nnz(x) function returns the number of non-zero elements in x.

[0072] The search area range is given as follows:

[0073] When z≤L+1

[0074]

[0075] When z>L+1

[0076]

[0077] This cycle continues until s is traversed. p All elements in the matrix, thus obtaining the updated maximum value matrix, in which the positions of the columns with non-zero elements form a new set Then the error matrix r = [r1, r2, ..., r n ] is calculated by the following formula:

[0078]

[0079] abs(x) is the absolute value function, round(x) returns the integer closest to x, and d l (n) = l n+1 -l n is the difference value of l. Find the position that makes the sum of r columns the smallest and record it as λ, then the minimum peak spacing is 0.95d l (λ).

[0080] Step 6: According to the peak value and uncertainty principle obtained in step 5, the natural frequency value and the corresponding frequency range of the cable are extracted. The frequency range is set to f(1±2ζ), where f is the peak value obtained in step 5, and ζ is the damping ratio of the structure, which is 1% by default. The extracted frequency value and the corresponding frequency range are as follows: Figure 4 This shows that this method can effectively track multi-order modes in real time in actual engineering, and provide accurate structural natural frequencies and corresponding frequency ranges for frequency domain-based analysis methods.

[0081] Step 7: Based on the modal analysis method and vibrating string theory, other modal parameters and cable forces are calculated, and the calculation results of each window are output in time sequence to achieve cable force tracking.

[0082] The data flow of the above-mentioned peak extraction-based cable force tracking method is as follows: Figure 5 According to the above process, the six-month measured data of a cable-stayed bridge are analyzed and calculated, and the frequency and cable force tracking results are shown as follows. Figure 6 and Figure 7 As shown. It can be seen that the frequencies of the cables remain basically stable during the normal operation stage, the natural frequency remains stable, the acceleration sensor on the cable works normally, and the noise is within the normal range, which is consistent with the actual operation status. The results show that the cable force tracking method based on peak extraction proposed in the present invention can overcome the influence of multiple false modes and interference peaks (secondary peaks) under the normal operation of the cable-stayed bridge, more accurately identify the cable frequencies of the cable vibration, and realize real-time tracking of the cable frequencies of the cable-stayed bridge cables.

[0083] The above embodiments are only preferred implementation modes of the present invention. It should be pointed out that ordinary technicians in this technical field can make several improvements and equivalent substitutions without departing from the principles of the present invention. These technical solutions after improvements and equivalent substitutions to the claims of the present invention all fall within the protection scope of the present invention.

Claims

1. A real-time tracking method for bridge cable force based on peak value automatic extraction, characterized in that: The steps include: Step 1: Set the window length and window step size for the long-term monitoring data of the target cable-stayed bridge; Step 2, collecting acceleration time history data, and inputting the acceleration time history data into the peak extraction model in the form of a moving window in time sequence; Step 3: For each window of data, first perform fast Fourier transform and then perform data smoothing; Step 4, performing preliminary peak extraction on the data obtained in step 3 to obtain a preliminary peak value; Step 5: Calculate the most likely minimum significance, minimum height and minimum spacing of the preliminary peak in step 4 based on the significance definition and the minimum spacing calculation method, and remove pseudo peaks according to the above three criteria to obtain the processed peaks; Step 6: Based on the peak value and uncertainty principle processed in step 5, the natural frequency value and the corresponding frequency range of the cable are extracted; Step 7: Based on the modal analysis method and vibrating string theory, other modal parameters and cable forces are calculated to achieve real-time tracking of the cable forces of the target cable-stayed bridge.

2. A real-time tracking method for bridge cable force based on peak value automatic extraction according to claim 1, characterized in that: In step 1, the window refers to a segment of acceleration signal, the window length is the duration of the segment of signal, and the window step is the length of the window translation on the time axis.

3. The real-time tracking method of bridge cable force based on peak value automatic extraction according to claim 1 is characterized in that: In step 3, the fast Fourier transform adopts a single-sided power spectrum density, assuming is the acceleration time history response of the structure in n measurement degrees of freedom, N is the number of sample points in each data channel, and its one-sided scaled fast Fourier transform is defined as: Where Δt is the sampling time interval, i 2 = -1, for each k = 1, ..., N q -1, F k The corresponding frequency position is f k =k / NΔt, where N q =int(N / 2)+1 is the Nyquist frequency, where int(·) is the rounding function.

4. The method for real-time tracking of bridge cable forces based on peak value automatic extraction according to claim 1 is characterized in that: In step 3, the data smoothing process uses a Savitzky-Golay filter or a moving average method.

5. The method for real-time tracking of bridge cable forces based on peak value automatic extraction according to claim 1 is characterized in that: Step 4 is as follows: preliminary peak extraction is performed through a function maximum point search algorithm, for the power spectrum density-frequency mapping relationship p(f k ), the peak value is where the first-order derivative function changes from positive to negative. Define the function q(f k ) is p(f k ) is the symbolic function of the derivative function, that is: Where signum[.] is a sign function that returns 1 for positive numbers and 0 for non-positive numbers. Then, we further apply the function q(f k ) Find the difference. If there is a position z such that q(f z+1 )-q(f z )<0, then the position z is the function p(f k ), which is the initial peak extraction position.

6. The method for real-time tracking of bridge cable forces based on peak value automatic extraction according to claim 1 is characterized in that: In step 5, the significance is defined as the minimum height difference required for a peak to reach any higher peak. For a given peak, the significance is calculated in the following way: for each path connecting the peak top and any higher peak, find the lowest point on each path, and the reference height is defined as the highest point among these points; the significance is the difference between the peak top height and the reference height.

7. The method for real-time tracking of bridge cable forces based on peak value automatic extraction according to claim 1 is characterized in that: In step 5, the minimum significance is set to 0.1p max , where p max is the maximum value of the power spectrum density in the current window; the minimum height is set to the average value of the power spectrum density in the current window; the minimum spacing is calculated by the following method: For the preprocessed data p=[p1,p2,…,p N ], the maximum value matrix is ​​calculated by the following formula: Where L = ceil(N / 2)-1, ceil(x) is the upward rounding function; for each k, the maximum matrix element m when i∈[1,k]∪[N-k+1,N] is taken k,i The average value is 0; Then calculate the density s of each column of the maximum matrix i , that is, the proportion of non-zero elements in this column, for s i ≤0.85, replace all the elements in the column with 0 and record s i >0.85 will form a new array s p , search so that s p Take the isosceles triangle area on both sides of the maximum value, if there exists a z±j column satisfying: Then all elements of the column are replaced by 0, where the nnz(x) function returns the number of non-zero elements in x; The search area range is given as follows: When z≤L+1 When z>L+1 This cycle continues until s is traversed. p All elements in the matrix, thus obtaining the updated maximum value matrix, in which the positions of the columns with non-zero elements form a new set Then the error matrix r = [r1, r2, ..., r n ] is calculated by the following formula: abs(x) is the absolute value function, round(x) returns the integer closest to x, and d l (n) = l n+1 -l n The difference value of l is found, and the position where the sum of the r columns is the smallest is recorded as λ, then the minimum peak spacing is 0.95d l (λ).

8. The method for real-time tracking of bridge cable forces based on peak value automatic extraction according to claim 1 is characterized in that: In step 6, the frequency interval is f(1±2ζ), where f is the processed peak value obtained in step 5, and ζ is the damping ratio of the structure, which defaults to 1%.

9. The method for real-time tracking of bridge cable forces based on peak value automatic extraction according to claim 1 is characterized in that: In step 7, the modal analysis method is a modal identification method based on frequency domain data analysis, and adopts a Bayesian operational modal analysis method.

10. The method for real-time tracking of bridge cable forces based on peak value automatic extraction according to claim 1 is characterized in that: In step 7, the vibrating string theory is a cable force-frequency conversion relationship, and the cable force is calculated according to the following formula: Where T is the cable force, f n is the nth natural frequency, L represents the distance between the fixed ends of the cable, and m represents the mass of the cable per unit length.

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