An automatic identification method and system for bridge vibration monitoring of frequency and damping ratio

Abstract

An automatic identification method and system for frequency and damping ratio in bridge vibration monitoring includes: S1, performing Fourier transform on the actual monitoring data of the bridge to obtain an approximate first-order natural frequency of the bridge, determining the initial damping ratio, and constructing a free decaying vibration signal of a damped single-degree-of-freedom spring oscillator; S2, using a cross-correlation function to locate and filter out the top few signal segments in the actual monitoring data that have the highest correlation with the constructed free decaying vibration signal; S3, based on spectral analysis, dividing the top few signal segments into single-frequency free decaying vibration signals and multi-frequency free decaying vibration signals, and calculating the frequency and damping ratio for each of the single-frequency and multi-frequency free decaying vibration signals. This invention has the advantages of wide applicability, high identification accuracy, high working efficiency, and no need for prior information.

Description

Technical Field

[0001] This invention relates to the field of bridge health monitoring, and in particular to an automatic identification method and system for bridge vibration monitoring frequency and damping ratio. Background Technology

[0002] Frequency and damping ratio are important modal parameters of bridge structures, reflecting the overall safety level of the bridge and playing a crucial role in bridge health monitoring. Bridge frequencies are typically obtained through Fourier transform. However, due to the influence of passing vehicles, frequency measurements often introduce certain errors. Furthermore, accurately estimating the damping ratio based on monitoring data remains a challenge.

[0003] Common methods for calculating damping ratio include the half-power bandwidth method, the exponential decay method (EA), the stochastic subspace identification method (SSI), the eigensystem realization algorithm (ERA), autoregressive models with external inputs, frequency domain decomposition, numerical algorithms for subspace state space identification, and continuous wavelet transform. Among these methods, the EA method is generally considered a relatively reliable and accurate one. However, this method requires the structure's free vibration response, and therefore can only be used for vibration tests where controlled excitation can be applied, such as falling weights and jumping trucks.

[0004] In fact, during the daily operation of a bridge, the excitation it receives is usually from the traffic flow. This is a typical non-stationary random excitation. Bridges under random traffic flow typically do not produce free vibration. The excitation transmitted by the traffic flow around the bridge through the soil structure coupling can be approximated as an impulse excitation, meaning the time it acts on the bridge is negligible compared to the bridge's vibration response time. Under this excitation, the bridge will produce significant free-dampening vibration. If a similar free-dampening vibration signal cannot be found in the bridge's monitoring data, it is difficult to accurately extract the bridge's damping ratio and frequency. However, manually extracting such a response from a large amount of data is impractical.

[0005] Therefore, identifying the frequency and damping ratio of a bridge from its monitoring data remains a technical challenge. Summary of the Invention

[0006] The main objective of this invention is to overcome the aforementioned deficiencies in the prior art and to propose an automatic identification method and system for frequency and damping ratio in bridge vibration monitoring. This method and system have the advantages of wide applicability, high identification accuracy, high working efficiency, and no need for prior information.

[0007] The present invention adopts the following technical solution:

[0008] An automatic identification method for frequency and damping ratio in bridge vibration monitoring, characterized by comprising:

[0009] S1. Perform Fourier transform on the actual monitoring data of the bridge to obtain the approximate first-order natural frequency of the bridge, determine the initial damping ratio, and construct the free decay vibration signal of a damped single-degree-of-freedom spring oscillator.

[0010] S2, using the cross-correlation function to locate and filter out the first few segments of signals in the actual monitoring data that have the highest correlation with the constructed free decay vibration signal;

[0011] S3, based on spectrum analysis, the selected first few segments of signal are divided into single-frequency free decay vibration signal and multi-frequency free decay vibration signal, and the frequency and damping ratio are calculated for the single-frequency free decay vibration signal and the multi-frequency free decay vibration signal respectively;

[0012] S4. Plot the frequency and damping of the first few signal segments into a frequency-damping scatter plot, and take the average of the calculated frequency and damping ratio to obtain the final identification result.

[0013] Step S1 specifically includes:

[0014] Preprocess the actual monitoring data;

[0015] The acceleration signal of the preprocessed actual monitoring data is defined as X(t), and the acceleration signal X(t) is a signal with a sampling frequency of f. s Sampling time is T X The time series has a signal length of L. X L X =f s T X ;

[0016] Perform a Fourier transform on X(t):

[0017]

[0018] Where e is the natural logarithm, i is the imaginary unit, and ω is the angular frequency;

[0019] By identifying the position of the highest peak in the spectrum through peak picking, an approximate first-order natural frequency of the bridge can be obtained.

[0020] Determine the initial damping ratio And construct the signal Y(t) of the free decaying vibration of a damped single-degree-of-freedom spring oscillator:

[0021]

[0022] The signal Y(t) is a signal with the same sampling frequency f. s Sampling time is T YThe time series has a signal length of L. Y L Y =f s T Y .

[0023] The preprocessing includes:

[0024] First, the actual monitoring data is processed to remove trend terms in order to remove the offset in the original signal;

[0025] Secondly, the actual monitoring data is low-pass filtered to reduce measurement noise interference.

[0026] Step S2 specifically includes:

[0027] Calculate the cross-correlation function between the acceleration signal X(t) and the free decay vibration signal Y(t):

[0028]

[0029] This yields the correlation vector between signals X(t) and Y(t). And simultaneously obtain the lagged index vector of the correlation.

[0030] Take the k values ​​with the largest absolute values ​​in the correlation vector R, and find their corresponding position indices in the hysteresis index vector L. Then, select the k segments of signals with the highest correlation between the actual monitoring data and the constructed free decay vibration signal, X1(t), X2(t), ..., X... k (t).

[0031] Step S3 specifically includes:

[0032] For the first few signal segments X1(t), X2(t), ..., X k (t) Perform Fourier transform:

[0033]

[0034] Where e is the natural logarithm, i is the imaginary unit, ω is the angular frequency, and k ranges from 10 to 30.

[0035] Peaks in each spectrum are obtained by peak picking, and those peaks greater than the initially set threshold are recorded as valid peaks; a signal with 1 valid peak is the single-frequency free decay vibration signal, and a signal with more than 1 valid peak is the multi-frequency free decay vibration signal.

[0036] In step S3, the frequency and damping ratio of the single-frequency free decay vibration signal are directly calculated using the exponential decay method, and the peak value A in the signal is obtained through peak picking.m and the corresponding time t m Given the index m, the logarithm of the peak value and its corresponding index are linearly fitted using the least squares method to obtain:

[0037] lnA=a·n+b

[0038] Where lnA is the logarithmic value of the crest, and n is the wave number.

[0039]

[0040]

[0041] Where M is the total wavenumber of the single-frequency free decay vibration signal;

[0042] Calculate the damping ratio:

[0043]

[0044] Calculation frequency:

[0045]

[0046] In step S3, the multi-frequency free decay vibration signal is decomposed into multiple single-frequency free decay vibration signals by variational nonlinear component decomposition method, and the frequency and damping ratio of each single-frequency free decay vibration signal are calculated by exponential decay method.

[0047] An automatic frequency and damping ratio identification system for bridge vibration monitoring, characterized in that it comprises:

[0048] An accelerometer, installed below the main beam of a bridge, is used to convert the bridge's vibration acceleration into a voltage signal, thereby measuring the bridge's vibration acceleration.

[0049] The signal acquisition module receives the voltage signal from the accelerometer, converts it from an analog signal to a digital signal, and then records the signal.

[0050] The correlation analysis module receives the time history signal recorded by the signal acquisition module and uses the cross-correlation function to filter out the free decay vibration signal in the signal.

[0051] The time-frequency analysis module receives the free decay vibration signal output by the correlation analysis module, uses Fourier transform to divide the free decay vibration signal into single-frequency free decay vibration signal and multi-frequency free decay vibration signal, and then uses variational nonlinear component decomposition to decompose the multi-frequency free decay vibration signal into multiple single-frequency free decay vibration signals.

[0052] The linear fitting module receives the single-frequency free decay vibration signal output by the time-frequency analysis module and uses linear fitting to calculate the frequency and damping of the bridge.

[0053] As can be seen from the above description of the present invention, compared with the prior art, the present invention has the following beneficial effects:

[0054] 1. This invention can realize the automatic identification of the entire process from free attenuation signal extraction to damping ratio identification in measured signals. It can achieve automatic identification without the need for manual screening of signal segments and database establishment. It can be well applied to real-time and continuous signal processing and has broad application prospects in bridge health detection.

[0055] 2. Compared with traditional damping identification methods, the present invention constructs a damped single-free decay signal based on the structural natural frequency obtained by Fourier transform of the actual signal. It is not sensitive to the vibration mode of the free decay signal in the measured signal, has strong robustness, and is more suitable for operation in the operating environment. Attached Figure Description

[0056] Figure 1 This is a flowchart of the method of the present invention;

[0057] Figure 2 The acceleration time history response curve of a certain distributed measuring point on a bridge;

[0058] Figure 3 The signal of the free decaying vibration of a damped single-degree-of-freedom spring oscillator;

[0059] Figure 4 The correlation coefficient between the actual monitoring data of the 03B0105 distribution measurement point and the constructed attenuation signal;

[0060] Figure 5 A schematic diagram showing the actual monitoring data and identified attenuation sections of the 03B0105 distribution measurement point;

[0061] Figure 6 The process of calculating the damping ratio;

[0062] Figure 7 A schematic diagram of the scatter plot distribution and average value of the frequency-damping ratio of the measurement points for 03B0105.

[0063] Figure 8 The correlation coefficient between the measured signal and the constructed attenuated signal at the 03B0114 distribution measurement point;

[0064] Figure 9 A schematic diagram showing the measured signal and the identified attenuation section at the 03B0114 distribution measurement point;

[0065] Figure 10 This is a schematic diagram of signal decomposition.

[0066] Figure 11 The process of calculating the damping ratio;

[0067] Figure 12 This is a schematic diagram showing the scatter distribution and average value of the first-order frequency-damping ratio and the second-order frequency-damping ratio.

[0068] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. Detailed Implementation

[0069] The present invention will be further described below through specific embodiments.

[0070] The invention will now be described in more depth and detail with reference to the accompanying illustrations and specific implementation examples. These figures and examples will provide readers with a more intuitive understanding, enabling a clearer presentation and comprehension of the invention's structure, working principle, and application scenarios.

[0071] See Figure 1 An automatic identification method for frequency and damping ratio in bridge vibration monitoring, comprising:

[0072] S1. Perform Fourier transform on the actual monitoring data of the bridge to obtain the approximate first-order natural frequency of the bridge, determine the initial damping ratio, and construct the free decay vibration signal of a damped single-degree-of-freedom spring oscillator.

[0073] This step specifically includes:

[0074] The actual monitoring data is first preprocessed. The preprocessing includes: first, removing the trend term from the actual monitoring data to remove the offset in the original signal; second, applying low-pass filtering to the actual monitoring data to reduce measurement noise interference.

[0075] The acceleration signal of the preprocessed actual monitoring data is defined as X(t), where the signal X(t) is a signal with a sampling frequency of f. s Sampling time is T X The time series has a signal length of L. X L X =f s T X ;

[0076] Perform a Fourier transform on X(t):

[0077]

[0078] Where e is the natural logarithm, i is the imaginary unit, and ω is the angular frequency.

[0079] By identifying the position of the highest peak in the spectrum through peak picking, an approximate first-order natural frequency of the bridge can be obtained.

[0080] Determine the initial damping ratio And construct the signal Y(t) of the free decaying vibration of a damped single-degree-of-freedom spring oscillator:

[0081]

[0082] The signal Y(t) is a signal with the same sampling frequency f. s Sampling time is T Y (The recommended duration is 10 to 20 times the approximate first-order period of the bridge) time series with a signal length of L. Y L Y =f s T Y .

[0083] S2, using the cross-correlation function, identifies and filters out the top few signal segments from the actual monitoring data that have the highest correlation with the constructed free decay vibration signal. Specifically, these include:

[0084] Calculate the cross-correlation function between the acceleration signal X(t) and the signal Y(t) of free decaying vibration:

[0085]

[0086] This yields the correlation vector between signals X(t) and Y(t). And simultaneously obtain the lagged index vector of the correlation.

[0087] Take the k values ​​with the largest absolute values ​​in the correlation vector R, and find their corresponding position indices in the hysteresis index vector L. Then, select the k segments of signals with the highest correlation between the actual monitoring data and the constructed free decay vibration signal, X1(t), X2(t), ..., X... k (t).

[0088] S3, based on the spectrum analysis, the first few segments of the selected signals are divided into single-frequency free decay vibration signals and multi-frequency free decay vibration signals. The frequency and damping ratio are calculated for single-frequency free decay vibration signals and multi-frequency free decay vibration signals respectively.

[0089] Specifically, it includes:

[0090] For the first few signal segments X1(t), X2(t), ..., X k (t) Perform Fourier transform:

[0091]

[0092] Where e is the natural logarithm, i is the imaginary unit, and ω is the angular frequency. The value of k ranges from 10 to 30.

[0093] Peaks in each spectrum are obtained by peak picking. Peaks greater than the initially set threshold are recorded as valid peaks. A signal with 1 valid peak is a single-frequency free decay vibration signal, and a signal with more than 1 valid peak is a multi-frequency free decay vibration signal.

[0094] For a single-frequency freely decaying vibration signal, the frequency and damping ratio are directly calculated using the exponential decay method, and the peak value A in the signal is obtained through peak picking. m and the corresponding time t m Given the index m, the logarithm of the peak value and its corresponding index are linearly fitted using the least squares method to obtain:

[0095] lnA=a·n+b

[0096] Where lnA is the logarithmic value of the crest, and n is the wave number.

[0097]

[0098]

[0099] Where M is the total wavenumber of a single-frequency free decaying vibration signal;

[0100] Calculate the damping ratio:

[0101]

[0102] Calculation frequency:

[0103]

[0104] For a multi-frequency free decay vibration signal, the signal is decomposed into multiple single-frequency free decay vibration signals by variational nonlinear component decomposition method, and then the frequency and damping ratio of each single-frequency free decay vibration signal are calculated by exponential decay method.

[0105] S4. Plot the frequency and damping of the first few signal segments into a frequency-damping scatter plot, and take the average of the calculated frequency and damping ratio to obtain the final recognition result.

[0106] Based on this, the present invention also proposes an automatic identification system for frequency and damping ratio in bridge vibration monitoring, comprising:

[0107] An accelerometer, installed below the main beam of a bridge, is used to convert the bridge's vibration acceleration into a voltage signal, thereby measuring the bridge's vibration acceleration.

[0108] The signal acquisition module receives the voltage signal from the accelerometer, converts it from an analog signal to a digital signal, and then records the signal.

[0109] The correlation analysis module receives the time history signal recorded by the signal acquisition module and uses the cross-correlation function to filter out the free decay vibration signal in the signal.

[0110] The time-frequency analysis module receives the free decay vibration signal output by the correlation analysis module, uses Fourier transform to divide the free decay vibration signal into single-frequency free decay vibration signal and multi-frequency free decay vibration signal, and then uses variational nonlinear component decomposition to decompose the multi-frequency free decay vibration signal into multiple single-frequency free decay vibration signals.

[0111] The linear fitting module receives the single-frequency free decay vibration signal output by the time-frequency analysis module and uses linear fitting to calculate the frequency and damping of the bridge.

[0112] The system of the present invention adopts the above-mentioned automatic identification method for frequency and damping ratio in bridge vibration monitoring. It plots the frequency and damping of the first few signal segments into a frequency-damping scatter plot, and takes the average of the calculated frequency and damping ratio to obtain the final identification result.

[0113] This invention can automatically extract the low-order frequencies and damping ratios of bridges from structural vibration monitoring signals. It has the advantages of wide applicability, high recognition accuracy, high working efficiency and no need for prior information, and has broad application prospects in bridge health detection.

[0114] Application Examples

[0115] Taking the Z24 bridge as an example, it is a classic post-tensioned prestressed concrete double-unit box girder bridge with a main span of 30 meters and side spans of 14 meters. The bridge was monitored continuously for nearly a year, with artificially controlled damage gradually applied in the later stages of monitoring. Using the Z24 bridge as the engineering background of a civil engineering system, researchers defined the research topic SIMCES, established the benchmark problem for the Z24 bridge, and studied a series of issues in the field of health monitoring, including natural frequencies, mode shapes, damping ratio under bridge damage, and structural modal parameter changes caused by environmental factors. The Z24 bridge has become the benchmark bridge for many scholars studying bridge health monitoring. Therefore, choosing this bridge as the research object for the experiment has strong practical significance.

[0116] The monitoring of a certain Z24 bridge was divided into 9 distributions, each with 33 channels. 28 channels were located on the bridge deck, and 5 channels served as reference points (3 of which were located on the bridge deck, and 2 were located on the bridge piers). The sensors on the Z24 bridge collected 65,536 samples at a sampling rate of 100Hz. After converting the bin format data provided by the SVS website to mat format in MATLAB, the acceleration time-history response curves for a certain distribution point on the Z24 bridge could be obtained, as shown below. Figure 2 As shown, under environmental excitation, vibration signals exhibit many typical free decay signals. It is worth noting that the measured data used for identification does not require multiple measurement points; monitoring data collected by a single accelerometer can be used for identification using this method. Therefore, the automatic identification technology using this method can avoid the drawbacks of installing multiple sensors.

[0117] First, Fourier transform is performed on the actual monitoring data to obtain the approximate first-order natural frequency of the bridge. The initial damping ratio is determined, and a signal of free decay vibration of a damped single-degree-of-freedom spring oscillator is constructed. Figure 3 The constructed damped free decay time history curve is shown.

[0118] Next, the correlation coefficient between the measured signal and the constructed free decaying vibration signal is determined using the cross-correlation function, such as... Figure 4 As shown, the correlation between the two signals is used to locate and filter the top few signal segments with the largest values. The results are as follows: Figure 5 As shown.

[0119] Finally, further screening was conducted, and the top few signal segments were divided into single-frequency free decay vibration signals and multi-frequency free decay vibration signals based on spectral analysis. Peak values ​​in each spectrum were obtained through peak picking, with peak values ​​exceeding an initially set threshold being designated as valid peaks. Signals with one valid peak value were classified as single-frequency free decay vibration signals, while signals with more than one valid peak value were classified as multi-frequency free decay vibration signals.

[0120] For a single-frequency signal, the damping ratio and frequency are obtained directly using Fourier transform and exponential decay method. The logarithm of the peak value and its corresponding index are then linearly fitted using the least squares method, such as... Figure 6 As shown, (a) represents a certain extraction attenuation segment, and (b) represents the linear fit between the peak logarithm and wavenumber. Further, the damping ratio and frequency are calculated, and the results are as follows: Figure 7The distribution of frequency-damping ratio at the measured points and its average value are shown (★). In this example, the original data only contains a first-order free decaying vibration signal; therefore, the Fourier transform of the decay segment extracted from the measured data only yields the first-order frequency. The automatic identification results proposed in this invention are compared with the natural frequencies and damping ratios identified based on reference-based combined deterministic-random subspace and DBSCAN, as shown in Table 1.

[0121] Table 1

[0122]

[0123] To further test this method, it can also be applied to the identification of damping ratios in multi-frequency free decay vibration signals. Acceleration data (03B0114) from channel 5 of the Z24 bridge at a specific moment is selected, and the method is still used as described above. Figure 3 The constructed damped single-degree-of-freedom free decay vibration signal is used to locate and filter the free decay signal in the measured signal.

[0124] Next, the correlation coefficient between the measured signal and the constructed free decaying vibration signal is determined using the cross-correlation function, such as... Figure 8 As shown, the correlation between the two signals is used to locate and filter the top few signal segments with the largest values. The results are as follows: Figure 9 As shown.

[0125] For multi-frequency signals, the variational nonlinear component decomposition method is first used to decompose them into multiple single-frequency signals, such as... Figure 10 As shown, (a) is the original signal; (b) is the decomposed first-order single-frequency signal; and (c) is the decomposed second-order single-frequency signal. Figure 11 This demonstrates the process of calculating the damping ratio of a decomposed single-frequency signal using the exponential decay method. (a) shows a single-frequency signal from the decomposition; (b) shows the linear fit between the peak logarithm and wavenumber. Then, the frequency is obtained by performing a Fourier transform on each single-frequency signal, and the arithmetic mean is taken. The frequency-damping scatter plot of the freely decaying vibration signal is shown below. Figure 12 A schematic diagram of the scatter distribution and average value of the first-order frequency-damping ratio and second-order frequency-damping ratio (★) is shown. The automatic identification results proposed in this invention are compared with the natural frequencies and damping ratios identified based on reference-based combined deterministic-random subspace and DBSCAN, as shown in Table 2. The proposed automatic damping ratio identification method based on structural vibration monitoring data achieves automatic identification of frequency and damping ratio, and can be well applied to real-time, continuous signal processing.

[0126] Table 2

[0127]

[0128] To further clarify, the vibration characteristics of the free decay signals selected from the measured signals are not very similar to those of the constructed damped single-degree-of-freedom free decay vibration signals, but both can ultimately be identified and extracted. As long as the decay response curve in the measured data approximately matches the shape of the constructed damped free decay curve, the decay segment in the data can be identified. In this Z24 bridge measured data test, the automatic modal identification method proposed in this invention was demonstrated to have strong robustness and holds promise for application in real-time health monitoring.

[0129] It should be emphasized that the foregoing examples are merely for illustrating the technical content of this invention and do not represent its sole definition. Although we have described this invention in detail through preferred examples, those skilled in the art should understand that they can make appropriate adjustments or equivalent substitutions to these technical contents. These changes should still adhere to the core concept of this invention and not exceed its defined scope, and should all be included within the scope of the invention's benefits.

Claims

1. A method for automatically identifying frequency and damping ratio in bridge vibration monitoring, characterized in that, include: S1, Perform Fourier transform on the actual monitoring data of the bridge to obtain the approximate first-order natural frequency of the bridge, determine the initial damping ratio, and construct the free decay vibration signal of a damped single-degree-of-freedom spring oscillator; specifically including: The actual monitoring data is preprocessed; the preprocessing includes: First, the actual monitoring data is processed to remove trend terms in order to remove the offset in the original signal; Secondly, the actual monitoring data is low-pass filtered to reduce measurement noise interference; The acceleration signal of the preprocessed actual monitoring data is defined as... , acceleration signal The sampling frequency is Sampling time is The time series has a signal length of . , ; right Perform Fourier transform: ； in, It is the natural logarithm. It is the imaginary unit. It is the angular frequency; By identifying the position of the highest peak in the spectrum through peak picking, an approximate first-order natural frequency of the bridge can be obtained. ; Determine the initial damping ratio And a signal of free decaying vibration of a damped single-degree-of-freedom spring oscillator is constructed. : ； Signal The sampling frequency is the same. Sampling time is The time series has a signal length of . , ; S2, using a cross-correlation function, identify and filter out the top few signal segments in the actual monitoring data that have the highest correlation with the constructed free decay vibration signal; specifically including: Calculate the acceleration signal With the signal of the free decaying vibration Cross-correlation function: ; thus obtaining the signal and Correlation vector between And simultaneously obtain the relevance lag index vector. ; Take the correlation vector The largest absolute value in the middle values, and in the lag index vector Find its corresponding location index, and filter out the data with the highest correlation between the actual monitoring data and the constructed free decay vibration signal. segment signal, , , ..., ; S3. Based on the spectrum analysis, the selected first few segments of signal are divided into single-frequency free decay vibration signals and multi-frequency free decay vibration signals. The frequency and damping ratio of the single-frequency free decay vibration signal and the multi-frequency free decay vibration signal are calculated respectively. For the multi-frequency free decay vibration signal, the signal is decomposed into multiple single-frequency free decay vibration signals by the variational nonlinear component decomposition method. The frequency and damping ratio of each single-frequency free decay vibration signal are calculated by the exponential decay method. S4. Plot the frequency and damping of the first few signal segments into a frequency-damping scatter plot, and take the average of the calculated frequency and damping ratio to obtain the final identification result.

2. The automatic identification method for frequency and damping ratio in bridge vibration monitoring as described in claim 1, characterized in that, Step S3 specifically includes: For the first few segments of signal , , ..., Perform Fourier transform: ； middle, It is the natural logarithm. It is the imaginary unit. It is the angular frequency. The value range is 10-30; Peaks in each spectrum are obtained by peak picking, and those peaks greater than the initially set threshold are recorded as valid peaks; a signal with 1 valid peak is the single-frequency free decay vibration signal, and a signal with more than 1 valid peak is the multi-frequency free decay vibration signal.

3. The automatic identification method for frequency and damping ratio in bridge vibration monitoring according to claim 1, characterized in that: In step S3, the frequency and damping ratio of the single-frequency free decay vibration signal are directly calculated using the exponential decay method, and the peak value of the signal is obtained through peak picking. and the corresponding time and serial number By linearly fitting the logarithm of the peak value to its corresponding index using the least squares method, we obtain: ； in, The value is the logarithm of the peak. For wave number, ； ； in, The total wavenumber of the single-frequency free decay vibration signal; Calculate the damping ratio: ； Calculation frequency:

4. An automatic frequency and damping ratio identification system for bridge vibration monitoring, characterized in that, The automatic identification method for frequency and damping ratio in bridge vibration monitoring according to any one of claims 1 to 3 includes: An accelerometer, installed below the main beam of a bridge, is used to convert the bridge's vibration acceleration into a voltage signal, thereby measuring the bridge's vibration acceleration. The signal acquisition module receives the voltage signal from the accelerometer, converts it from an analog signal to a digital signal, and then records the signal. The correlation analysis module receives the time history signal recorded by the signal acquisition module and uses the cross-correlation function to filter out the free decay vibration signal in the signal. The time-frequency analysis module receives the free decay vibration signal output by the correlation analysis module, uses Fourier transform to divide the free decay vibration signal into single-frequency free decay vibration signal and multi-frequency free decay vibration signal, and then uses variational nonlinear component decomposition to decompose the multi-frequency free decay vibration signal into multiple single-frequency free decay vibration signals. The linear fitting module receives the single-frequency free decay vibration signal output by the time-frequency analysis module and uses linear fitting to calculate the frequency and damping of the bridge.

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