A real-time tracking method for bridge cable forces based on automatic peak extraction

Abstract

The present invention discloses a real-time tracking method for bridge cable forces based on automatic peak extraction. To address the problem of tedious and difficult manual extraction of peak values ​​in real-time and batch power spectrum density graphs, the method first converts the acceleration signal collected by the sensor into frequency domain information through fast Fourier transform; then, the power spectrum density graph is preprocessed to ensure the accuracy of peak extraction; based on the data maximum search method, the peak values ​​in the power spectrum density graph are preliminarily extracted; then, restrictions are imposed on the minimum significance, minimum height and minimum spacing of the peak values ​​to eliminate pseudo-peaks, thereby realizing the identification of resonant peaks and their corresponding frequencies and frequency intervals in the power spectrum density graph; finally, based on the modal analysis method and vibrating string theory, cable force tracking is realized and used to guide subsequent bridge structure assessment work.

Description

Technical Field

[0001] The present 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, stay cables play a crucial role in supporting the main beams and transmitting vehicle loads to the bridge towers. However, bridge structures are inevitably affected by harsh environments or overweight vehicles. Such factors may damage the overall bridge structure and cause abnormal changes in the internal forces of the stay cables. Therefore, changes in the internal forces of the stay cables are an important indicator for assessing the safety of the overall bridge structure. Therefore, monitoring the condition of the bridge during the operation and maintenance phase is crucial. In recent years, with the development of bridge structural health monitoring systems, various sensors have been widely deployed at various locations on bridges to measure the bridge's response to actual working conditions and various environmental factors in real time. This makes it possible to use bridge monitoring data to evaluate and track the tension of the stay cables in real time.

[0003] In actual bridge operation and maintenance, various methods have been developed to measure cable tension, including the vibration frequency method, magnetic flux method, and oil pressure gauge. The oil pressure gauge-based method is more accurate and intuitive, but is usually used in the construction phase; the magnetic flux-based method is 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 acceleration sensor 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. Frequency-domain peak selection methods are widely used due to their simplicity. This step has traditionally relied on manual selection by technicians. However, this method is susceptible to fatigue or misjudgment. Furthermore, during normal operation of a bridge, the natural frequency of the cables will change due to environmental influences. Vibration-based monitoring systems require real-time synchronous corrections, which is time-consuming, labor-intensive, and impractical for manual operation. Summary of the Invention

[0005] Purpose of the Invention: To automatically extract modal frequencies, this paper proposes a method for automatically identifying natural frequencies from power spectrum density plots based on actual bridge monitoring data. This method can track natural frequencies in real time and calculate the corresponding cable forces based on the frequency-cable force relationship, thereby achieving cable force tracking.

[0006] Technical solution: The present invention provides a real-time bridge cable force tracking method based on automatic peak value extraction, comprising 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: Collect acceleration time history data and input 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: Perform preliminary peak extraction on the data obtained in step 3 to obtain a preliminary peak value;

[0011] Step 5: Calculate the minimum significance, minimum height, and minimum spacing of the preliminary peaks in step 4 based on the significance definition and the minimum spacing calculation method, and remove pseudo peaks based on the minimum significance, minimum height, and minimum spacing to obtain processed peaks.

[0012] Step 6: Based on the peak value and uncertainty principle processed in step 5, the natural frequency value and 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 acceleration signal, and the window step is the length of the window translation on the time axis.

[0015] Furthermore, 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] Furthermore, 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 position is where the first-order derivative function turns from positive to negative, and the function q(f k ) is p(f k )The symbolic function of the derivative function, that is:

[0020]

[0021] Where signum[.] is the 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 way: for each path connecting the peak 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 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 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 For columns with values ​​less than or equal to 0.85, replace all elements in the column with 0 and record s i The positions >0.85 are grouped into 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 that satisfies:

[0028]

[0029] Then replace all elements of the column with 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 , thus obtaining the updated maximum 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] Where abs(x) is the absolute value function, round(x) returns the nearest integer to x, and d l (n) = l n+1 -l n The difference value of l is found. The position where the sum of the r columns is the smallest is recorded as λ, and the minimum peak spacing is 0.95d l (λ).

[0038] Furthermore, in step 6, the frequency interval is f(1±2ζ), where f is the peak value obtained after processing 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, and adopts a Bayesian operational modal analysis method.

[0040] Furthermore, 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 is the distance between the fixed ends of the cable, and m is 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; this application proposes a bridge intelligent cable force tracking method based on cable vibration data. This method uses the physical characteristics of cable vibration acceleration for adaptive identification, significantly improving the extraction efficiency.

[0045] (2) This method utilizes vibrating string theory, a theoretical property 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 variation of the cable force can be obtained based on the cable frequency 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, which is accurate and efficient, and its 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 the cable frequency (that is, the peak value) of the cable after Fourier transforming the cable vibration acceleration data and tracking it, and can realize the automatic extraction of multiple cable frequencies in the spectrum and tracking them. BRIEF DESCRIPTION OF THE DRAWINGS

[0048] Figure 1 For the 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 This is the frequency tracking result;

[0054] Figure 7 For the force tracking results. DETAILED DESCRIPTION

[0055] The technical solution of the present invention will be further described below with reference to 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 pre-processed 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 out, and the retained peaks are all resonant peaks reflecting the natural frequency of the structure.

[0063] Among them, the minimum significance is set to 0.1p max , where p max is the maximum 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 For columns with values ​​less than or equal to 0.85, replace all elements in the column with 0. And record s i The positions >0.85 are grouped into 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 , thus obtaining the updated maximum 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] Where abs(x) is the absolute value function, round(x) returns the nearest integer to x, and d l (n) = l n+1 -l n The difference value of l is found. The position where the sum of the r columns is the smallest is recorded as λ, and the minimum peak spacing is 0.95d l (λ).

[0080] Step 6: Based on the peak value obtained in step 5 and the uncertainty principle, 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 defaults to 1%. The extracted frequency value and the corresponding frequency range are as follows: Figure 4 This shows that this method can effectively track multiple 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. 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 in the figure, it can be seen that the various frequencies of the analyzed cables remain basically stable during normal operation, the natural frequency remains stable, the accelerometers on the cables operate normally, and the noise is within the normal range, consistent with the actual operating conditions. The results show that the cable force tracking method based on peak extraction proposed in this invention can overcome the influence of multiple false modes and interference peaks (secondary peaks) under the normal operation of cable-stayed bridges, more accurately identify the various frequencies of cable vibration of the cable, and realize real-time tracking of the various frequencies of the cable-stayed bridge cables.

[0083] The above embodiments are only preferred implementations of the present invention. It should be pointed out that for ordinary technicians in this technical field, several improvements and equivalent substitutions can be made 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 scope of protection of the present invention.

Claims

1. A real-time tracking method for bridge cable forces based on automatic peak value 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: Collect acceleration time history data and input 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: Perform preliminary peak extraction on the data obtained in step 3 to obtain a preliminary peak value; Step 5: Calculate the minimum significance, minimum height, and minimum spacing of the preliminary peaks in step 4 based on the significance definition and the minimum spacing calculation method, and remove pseudo peaks based on the minimum significance, minimum height, and minimum spacing to obtain processed peaks. Step 6: Based on the peak value and uncertainty principle processed in step 5, the natural frequency value and 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 forces 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 acceleration signal, and the window step is the length of the window translation on the time axis.

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

5. The method for real-time tracking of bridge cable forces based on automatic peak value extraction according to claim 1 is characterized in that: Step 4 is as follows: preliminary peak extraction is performed through the function maximum point search algorithm, for the power spectrum density-frequency mapping relationship p(f k ), the peak position is where the first-order derivative function turns from positive to negative, and the function q(f k ) is p(f k )The symbolic function of the derivative function, that is: Where signum[.] is the 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.

6. The method for real-time tracking of bridge cable forces based on automatic peak value 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 as follows: 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 automatic peak value 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 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 For columns with values ​​less than or equal to 0.85, replace all elements in the column with 0 and record s i The positions >0.85 are grouped into 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 that satisfies: Then replace all elements of the column with 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 , thus obtaining the updated maximum 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: Where abs(x) is the absolute value function, round(x) returns the nearest integer 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 automatic peak value extraction according to claim 1 is characterized in that: In step 6, the frequency interval is f(1±2ζ), where f is the peak value obtained after processing 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 automatic peak value 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 automatic peak value 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 is the distance between the fixed ends of the cable, and m is the mass of the cable per unit length.

Images