Bridge cable force automatic tracking method based on frequency domain energy optimization reorganization

Abstract

The application provides a bridge cable force automatic tracking method based on frequency domain energy optimization recombination. During bridge operation monitoring, aiming at the difficulty in automatic picking of peaks caused by the noise pseudo-peak of cable acceleration signal spectrum and the time-varying distribution difference of modal energy in the frequency domain, firstly, the normalized fast Fourier transform algorithm is used to convert the cable vibration time history into the frequency domain in sections; then the obtained multiple frequency spectra are subjected to mean smoothing pretreatment to obtain the smoothed spectrum with the pseudo-peak noise removed. Then, according to the logarithmic processing of the smoothed spectrum, the optimization recombination of the modal energy of each order in the frequency domain is realized to improve the robustness of the automatic picking of peaks; finally, according to the setting of the reasonable interval of the automatic picking of peaks in the frequency domain based on the theoretical fundamental frequency of the cable, and the limitation of the normalized frequency domain energy, the frequency domain sliding window peak searching algorithm and the vibration string theory formula are combined to realize the automatic stable tracking of the bridge cable force. The application can solve the technical problem that the cable force calculation of the traditional method is not accurate enough.

Description

Technical Field

[0001] This invention relates to the field of bridge structural health monitoring and parameter identification technology, specifically to an automatic bridge cable force tracking method based on frequency domain energy optimization and recombination. Background Technology

[0002] Cables are key components of long-span bridges such as suspension bridges, cable-stayed bridges, and through-arch bridges. Cables play a crucial role in supporting the main girder and transferring vehicle loads to the substructure. Therefore, changes in cable internal forces are an important indicator of the overall structural safety of a bridge. Under the combined effects of multiple factors such as temperature variations, wind loads, overloaded vehicles, and uneven structural settlement, the cable forces in service bridges exhibit time-varying characteristics. Frequent changes in cable force can easily lead to fatigue of the cable wires. It should be noted that harsh environmental corrosion and cable wire fatigue are significant contributing factors to cable breakage and even complete cable failure. Once a cable breaks, the forces in adjacent cables inevitably increase, causing stress concentration in the cable wires and creating significant safety hazards for the bridge. Therefore, cable force is an essential measurement during bridge operation.

[0003] In the prior art, the invention patent with publication number CN119128501A describes a method for real-time tracking of bridge cable force based on automated peak extraction. This method addresses the problem of tedious and difficult manual extraction of peak values ​​from real-time, batch power spectral density maps. First, it converts the acceleration signals collected by the sensor into frequency domain information through fast Fourier transform. Then, it performs data smoothing on the power spectral density map. Next, it preliminarily extracts the initial peak values ​​from the power spectral density map based on the data maximum search method. Then, it imposes restrictions on the minimum significance, minimum height, and minimum spacing of the initial peak values ​​based on the significance definition and minimum spacing calculation method to eliminate spurious peaks. Finally, based on the peak values ​​after eliminating spurious peaks, it calculates the cable force by combining modal analysis and vibration string theory.

[0004] However, existing cable force identification methods typically use cable fundamental frequency data as the representative value of natural frequency, and then substitute it into the vibration string theory formula to calculate cable force. Its accuracy is severely limited by the peak picking accuracy of single-order modes. The above technical solutions use the most conventional height and spacing as the discrimination index for peak selection, without comprehensively considering the influence of noise and insignificant components on peak selection. Therefore, the calculated cable force is not accurate enough. Summary of the Invention

[0005] To address the shortcomings of existing technologies, this invention proposes an automatic bridge cable force tracking method based on frequency domain energy optimization and recombination, in order to solve the technical problem that traditional methods in the prior art are not accurate enough in calculating cable force.

[0006] The technical solution adopted in this invention is as follows: Firstly, a method for automatic tracking of bridge cable force based on frequency domain energy optimization and reorganization is provided, comprising the following steps: acquiring the cable acceleration signal of a bridge health monitoring system within a unit time period; dividing the cable acceleration signal into multiple equal-length windows in the time domain according to the input time series to obtain multiple window time histories; performing frequency domain transformation on each window time history segment by segment, followed by multi-segment mean smoothing preprocessing to obtain a smoothed spectrum of the cable acceleration signal; performing logarithmic processing on the smoothed spectrum to obtain the logarithmic spectrum of the cable acceleration signal; determining a reasonable spacing for automatic peak picking in the frequency domain, and a lower limit threshold for frequency domain normalized energy; acquiring the modal frequencies of each order in the logarithmic spectrum of the cable acceleration signal according to the reasonable spacing and the lower limit threshold; calculating the frequency difference between adjacent orders according to each modal frequency, and using a minimization objective function to search for the representative value of the cable's natural frequency; and calculating the target cable force of the bridge cable according to the representative value of the cable's natural frequency.

[0007] Furthermore, based on the fundamental frequency of the Lasso theory, the reasonable spacing for automatic peak picking in the frequency domain is calculated.

[0008] Furthermore, the reasonable spacing is set to 0.9 times the theoretical fundamental frequency of the cable.

[0009] Furthermore, the lower limit threshold of the frequency domain normalized energy is determined by the frequency domain determination criterion for significant vibration of slender structures.

[0010] Furthermore, the frequency domain criteria for determining significant vibrations of the slender structure include: vibrations in the Fourier spectrum below 1 / ... All information is considered noise and insignificant components; the lower limit threshold of the frequency domain normalized energy is set to 1 / 3 of the energy corresponding to the peak frequency. .

[0011] Furthermore, based on the reasonable spacing and lower threshold, the sliding window peak-finding method is used to search for the modal frequencies of each order in the logarithmic spectrum of the cable acceleration signal.

[0012] Furthermore, the minimization objective function is constructed based on the combination of modal frequencies obtained by sliding window peak finding, and the frequency difference vector of adjacent order frequencies in the frequency combination.

[0013] Furthermore, based on the representative value of the natural frequency of the cable, the target cable force of the bridge is calculated using the vibrating string theory.

[0014] In a second aspect, an electronic device is provided, comprising: one or more processors; a storage device for storing one or more programs; wherein when the one or more programs are executed by the one or more processors, the one or more processors implement the automatic bridge cable force tracking method based on frequency domain energy optimization reorganization as described in the first aspect.

[0015] Thirdly, a computer program product is provided, including a computer program / instruction that, when executed by a processor, implements the steps of the automatic bridge cable force tracking method based on frequency domain energy optimization and reorganization as described in the first aspect.

[0016] As can be seen from the above technical solution, the beneficial technical effects of the present invention are as follows: By performing frequency domain energy optimization and recombination through logarithmic processing and automatically picking up peak values ​​in the frequency domain based on the cable's own dynamic characteristics, high-precision automatic calculation and tracking identification of cable force is achieved. By quickly solving the minimization objective function, the optimal value of the fundamental frequency and the difference between adjacent order frequencies is adaptively extracted as the representative value of the natural frequency, which can effectively avoid cable force calculation errors caused by local noise in the frequency domain and misidentification of the fundamental frequency. Attached Figure Description

[0017] To more clearly illustrate the specific embodiments of the present invention or the technical solutions in the prior art, the accompanying drawings used in the description of the specific embodiments or the prior art will be briefly introduced below. In all the drawings, similar elements or parts are generally identified by similar reference numerals. In the drawings, the elements or parts are not necessarily drawn to scale.

[0018] Figure 1 This is a flowchart of the automatic tracking process for cable force calculation according to the present invention; Figure 2 This is the 10-minute acceleration signal time history of a 78.3m suspension cable of a suspension bridge used for analysis in this embodiment of the invention; Figure 3 This is a comparison chart of the acceleration spectrum of a 78.3m suspension cable of a suspension bridge before and after improvement over a 10-minute period, as shown in this embodiment of the invention. Figure 4 This is a comparison chart of the frequency domain peak values ​​of the acceleration of a 78.3m suspension cable of a suspension bridge over a certain period of 10 minutes, as shown in this embodiment of the invention. Figure 5 This is the result of one continuous cycle tracking of the natural frequency of the 78.3m suspension cable of the suspension bridge in this embodiment of the invention; Figure 6 This is the result of one continuous cycle tracking of the natural frequency of the 49.0m suspension cable of the suspension bridge in this embodiment of the invention; Figure 7 This is a continuous one-week tracking result of the cable force of suspension bridges of different lengths in an embodiment of the present invention; Figure 8 This is the 10-minute acceleration signal time history of a 110.1m cable-stayed bridge used for analysis in the comparative example of this invention; Figure 9 This is the normalized Fourier spectrum of the acceleration of a 110.1m cable-stayed bridge cable in the comparative example of this invention over a 10-minute period; Figure 10This is the normalized smoothed logarithmic spectrum of the acceleration of a 110.1m cable-stayed bridge cable in the comparative example of this invention over a 10-minute period. Detailed Implementation

[0019] The embodiments of the technical solution of the present invention will now be described in detail with reference to the accompanying drawings. These embodiments are merely illustrative of the technical solution of the present invention and are therefore intended to limit the scope of protection of the present invention.

[0020] It should be noted that, unless otherwise stated, the technical or scientific terms used in this application should have the ordinary meaning as understood by one of ordinary skill in the art to which this invention pertains.

[0021] This application provides an automatic bridge cable force tracking method based on frequency domain energy optimization and reorganization, comprising the following steps: Step 1: Acquire the cable acceleration signal of the bridge health monitoring system within a unit time period, and divide the cable acceleration signal into multiple equal-length windows in the time domain according to the input time series. In specific implementations, the selection of window length is not limited and can be set according to project needs.

[0022] Step 2: After performing frequency domain transformation on each window of time history segment by segment, perform multi-segment mean smoothing preprocessing to obtain the smoothed spectrum of the cable acceleration signal. In step 2, the segment-by-segment frequency domain conversion employs a normalized Fourier transform, let {x} j ∈R: j=0,…, N−1} is the time history of the cable acceleration signal measured by the bridge health monitoring system, where N is the total number of sample points in the time series. The mean smoothed spectrum obtained by applying mean smoothing to the normalized Fourier spectrum of n segments with a window length of W is defined as P(k): Where W = T / Δt, T is the single-segment smoothing time interval, and Δt is the sampling time interval; e represents the natural constant, i 2 = -1, for each k = 1,…,N q -1, X(k) and P(k) both correspond to frequencies f. k = k / W△t, where N q =int(W / 2)+1 is the Nyquist frequency, where int(∙) is the floor function.

[0023] Step 3: Logarithmically process the smoothed spectrum obtained in Step 2 to obtain the logarithmic spectrum of the cable acceleration signal. In step 3, the logarithmic spectrum D(k) is obtained by transforming the smooth spectrum P(k): Where ln(∙) is the natural logarithm operator.

[0024] In this step, by performing logarithmic processing on the smoothed spectrum, the frequency domain energy can be optimized and recombined.

[0025] Step 4: Determine the reasonable spacing for automatic peak picking in the frequency domain, and the lower threshold of the frequency domain normalized energy. Step 4 In a specific implementation, based on the phenomenon that the fundamental frequency and cable force of the bridge only increase and do not decrease during its service life, the reasonable spacing f0 for automatic peak picking in the frequency domain is determined according to the theoretical fundamental frequency of the cable; according to the frequency domain judgment criteria for significant vibration behavior of slender structures, the lower limit h0 of the frequency domain normalized energy can be determined.

[0026] Step 5: Based on the reasonable spacing and lower threshold determined in Step 4, use the sliding window peak-finding method to search for the modal frequencies of each order in the logarithmic spectrum of the cable signal. In step 5, in a specific implementation, a reasonable interval f0 is used as the sliding window spacing of the horizontal axis of the logarithmic spectrum, and [h0,+∞) is used as the search range of the vertical axis of the logarithmic spectrum. The frequency of each mode of the cable is calculated by the frequency domain sliding window peak finding method.

[0027] Step 6: Calculate the frequency difference between adjacent orders based on the modal frequencies obtained in Step 5, and search for the representative value of the cable's natural frequency according to the minimization objective function. In step 6, the objective function is established based on the combination f of each modal frequency obtained by sliding window peak finding, and the frequency difference vector c of adjacent order frequencies in the frequency combination f. Thus, the identification of the cable's natural frequency can be transformed into a problem of minimizing the objective function, i.e.: in, The objective function is to minimize the residuals, round(∙) is the rounding operator, and H is the order of the cable modes obtained by peak picking through a sliding window in the frequency domain. The frequencies of each mode, from smallest to largest, are { f}. h ∈R: h =1,…, H}, thus obtaining the frequency difference between two adjacent orders { c g ∈R: g=1,…, H} satisfies (c1 is the fundamental frequency); F is the representative value of the cable's natural frequency, which is the frequency difference that minimizes the objective function op, equivalent to the optimal value of the fundamental frequency and the frequency difference between adjacent orders.

[0028] Step 7: Calculate the target cable force of the bridge based on the representative value of the cable's natural frequency. In step 7, the frequency-force conversion relationship in the vibrating string theory is as follows: Where T is the cable force, F represents the natural frequency, L represents the distance between the two anchor ends of the cable, and m represents the mass of the cable per unit length.

[0029] The cable force calculated in this step can be used to automatically track the cable force of the target cable on the bridge.

[0030] Example The following uses long-term monitoring data of cable acceleration from a health monitoring system of a long-span suspension bridge. The automatic cable force tracking method based on frequency domain energy optimization and recombination provided in this application is used to automatically track and calculate the cable force, thereby verifying the implementation effect of the technical solution of this application. The verification process is as follows: According to industry standards, the analysis scale for each input program is set to 10 minutes. The 10-minute sling acceleration time history for a single input program is as follows: Figure 2 As shown.

[0031] The input time series is divided into multiple equal-length windows based on the signal sampling frequency, and frequency domain transformation is performed window by window using normalized Fourier transform. The resulting multi-segment spectra are then preprocessed with mean smoothing to obtain the smoothed spectrum corresponding to the current 10-minute cable acceleration input. The smoothed spectrum is then logarithmically processed to achieve frequency domain energy optimization and reconstruction of the cable acceleration signal. The improved cable frequency domain signal is shown below. Figure 3 As shown.

[0032] The reasonable spacing for automatic peak picking in the frequency domain is calculated based on the fundamental frequency of the cable theory, and the lower limit of the normalized energy in the frequency domain is determined by the criteria for judging significant vibrations of slender structures. The fundamental frequency of the cable theory is calculated by trial and error using the cable force, cable length, and cable linear density of the completed bridge. The reasonable spacing for automatic peak picking in the frequency domain is set to 0.9 times the fundamental frequency of the cable theory. The criterion for judging significant vibrations of slender structures is that the energy level below the maximum peak value in the Fourier spectrum is 1 / All information is considered noise and insignificant components; the lower limit threshold for frequency domain normalized energy is set to 1 / 3 of the energy corresponding to the peak frequency. .

[0033] Using a reasonable spacing as the window length, frequency domain sliding window peak finding is performed to automatically pick up the peak values ​​of the frequency characteristics of each mode of the cable. Valid peak values ​​exceeding the lower energy threshold are as follows: Figure 4 As shown.

[0034] To compare with other cable force calculation methods, the automatic cable force tracking method of this application was used to track and identify the vibration signals of two suspension cables of different lengths within one revolution of a suspension bridge. The calculated natural frequencies of the two cables are as follows: Figure 5 and Figure 6As shown. The results of tracking and identifying 1008 sets of natural frequencies over a week show that, compared with the "coarse method of directly taking the peak frequency" and the "traditional method without frequency domain energy reconstruction", the "tracking method based on frequency domain energy optimization and reconstruction" mentioned in this application does not exhibit the problem of "step-skipping" misidentification of the natural frequency of the cable. Therefore, the proposed method can achieve 100% robust identification of the representative value F of the natural frequency of cables of different lengths.

[0035] like Figure 7 As shown, after frequency domain energy optimization and recombination, substituting the natural frequency tracking results of the two cables of different lengths into the vibration string theory formula reveals that the relative changes in cable force for each cable do not exceed 10% of its median cable force (i.e., the dead load cable force), fully meeting the calculation accuracy requirements stipulated by industry standards. Therefore, the automatic bridge cable force tracking method based on frequency domain energy optimization and recombination proposed in this invention can effectively overcome the adverse effects of spurious peaks in spectral noise and differences in time-varying frequency domain energy distribution, and can achieve high-precision, continuous, and stable automatic tracking of the cable force T of bridge cables.

[0036] Comparative Example To compare the implementation effect of the cable force calculation method in this application and the prior art, acceleration data was collected from a 110.1m cable-stayed bridge used in a field test of a long-span cable-stayed bridge. The time series length was 10 minutes. Figure 8 As shown. The weight per meter of the cable is 101.83 kg / m, its theoretical natural frequency is 1.34 Hz, and its theoretical cable force is 8867 kN.

[0037] For existing methods of calculating cable tension, such as Figure 9 As shown, the acceleration signal is converted to the frequency domain using the traditional method without frequency domain energy reconstruction. Then, the peak values ​​of the spectrum are automatically picked up using the sliding window peak-finding method. Ultimately, only the second-order mode frequency (2.67Hz) and the fourth-order mode frequency (5.35Hz) of the cable can be effectively extracted. After frequency difference calculation and objective function optimization, the natural frequency of the cable is found to be 2.67Hz. Substituting this into the vibration string theory formula, the cable force is found to be 35204kN.

[0038] Regarding the technical solution of this application, such as Figure 10 As shown, the proposed method, which involves frequency domain energy optimization and recombination, converts the acceleration signal to the frequency domain. Then, the peak values ​​of the spectrum are automatically picked using the sliding window peak-finding method, effectively extracting the 3rd to 7th mode frequencies (2.68, 3.96, 5.32, 6.64, 8.01, and 9.33 Hz) of the stay cable. After frequency difference calculation and objective function optimization, the natural frequency of the stay cable is found to be 1.33 Hz. Substituting this into the vibration string theory formula yields a cable force of 8735 kN, which is completely different from the 35204 kN calculated using existing techniques.

[0039] By comparing traditional methods with the method proposed in this application, it was found that the cable force identified by traditional methods for this typical 10-minute cable vibration signal is completely wrong and has no practical value. However, the improved cable force calculation method based on frequency domain energy optimization and reconstruction adopted in this application can accurately and effectively obtain the cable force.

[0040] By adopting the technical solution of this application, frequency domain energy optimization and recombination are performed based on logarithmic processing, and peak values ​​in the frequency domain are automatically picked up based on the dynamic characteristics of the cable itself, thus realizing high-precision automatic calculation and tracking identification of cable force. By quickly solving the minimization objective function, the optimal value of the fundamental frequency and the frequency difference between adjacent orders is adaptively extracted as the representative value of the natural frequency, which can effectively avoid cable force calculation errors caused by local noise in the frequency domain and misidentification of the fundamental frequency.

[0041] The technical solution proposed in this application has a fast computing speed and low memory requirements, which meets the automation and timeliness requirements of bridge health monitoring systems.

[0042] In some embodiments of this application, an electronic device is also provided, comprising: one or more processors; a storage device for storing one or more programs; and when the one or more programs are executed by the one or more processors, the one or more processors implement the aforementioned automatic bridge cable force tracking method based on frequency domain energy optimization and reorganization.

[0043] In some embodiments of this application, a computer program product is also provided, including a computer program / instruction that, when executed by a processor, implements the steps of the aforementioned automatic bridge cable force tracking method based on frequency domain energy optimization and reorganization.

[0044] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention, and they should all be covered within the scope of the claims and specification of the present invention.

Claims

1. A method for automatic tracking of bridge cable forces based on frequency domain energy optimization and recombination, characterized in that, Includes the following steps: Acquire the cable acceleration signal of the bridge health monitoring system within a unit time period, and divide the cable acceleration signal into multiple equal-length windows in the time domain according to the input time series to obtain multiple window time histories; After performing frequency domain transformation on each window time history segment, and then performing multi-segment mean smoothing preprocessing, the smooth spectrum of the cable acceleration signal is obtained. Logarithmic processing is performed on the smoothed spectrum to obtain the logarithmic spectrum of the cable acceleration signal; Determine the reasonable spacing for automatic peak picking in the frequency domain, as well as the lower limit threshold for the frequency domain normalized energy; Based on the reasonable spacing and lower threshold, the sliding window peak-finding method is used to search for the modal frequencies of each order in the logarithmic spectrum of the cable acceleration signal. The frequency difference between adjacent orders is calculated based on the frequency of each modality, and the representative value of the cable's natural frequency is searched by minimizing the objective function. The objective function is constructed based on the combination of modal frequencies obtained by sliding window peak finding, and the frequency difference vector between adjacent orders in the combination of modal frequencies. The target cable force of the bridge is calculated based on the representative value of the cable's natural frequency.

2. The automatic bridge cable force tracking method based on frequency domain energy optimization and reorganization according to claim 1, characterized in that, The reasonable spacing for automatic peak picking in the frequency domain is calculated based on the fundamental frequency of the Lasso theory.

3. The automatic bridge cable force tracking method based on frequency domain energy optimization and recombination according to claim 2, characterized in that, The reasonable spacing is set to 0.9 times the theoretical fundamental frequency of the cable.

4. The automatic bridge cable force tracking method based on frequency domain energy optimization and recombination according to claim 1, characterized in that, The lower limit threshold of the frequency domain normalized energy is determined by the frequency domain judgment criterion for significant vibration of slender structures.

5. The automatic bridge cable force tracking method based on frequency domain energy optimization and recombination according to claim 4, characterized in that, The frequency domain criteria for determining significant vibrations of the slender structure include: vibrations in the Fourier spectrum below 1 / ... All information is considered noise and insignificant components; the lower limit threshold for frequency domain normalized energy is set to 1 / 3 of the energy corresponding to the peak frequency. .

6. The automatic bridge cable force tracking method based on frequency domain energy optimization and recombination according to claim 1, characterized in that, Based on the representative value of the natural frequency of the cable, the cable force of the target cable of the bridge is calculated using the vibrating string theory.

7. An electronic device, characterized in that, include: One or more processors; Storage device for storing one or more programs; When the one or more programs are executed by the one or more processors, the one or more processors implement the automatic bridge cable force tracking method based on frequency domain energy optimization and reorganization as described in any one of claims 1-6.

8. A computer program product comprising a computer program / instructions, characterized in that, When the computer program / instruction is executed by the processor, it implements the steps of the automatic bridge cable force tracking method based on frequency domain energy optimization and reorganization as described in any one of claims 1-6.

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