A Long-Term Tracking and Identification Method for Bridge Dynamic Characteristics Based on a Combination of Bandpass Filtering and Random Decrease Method

Abstract

This invention discloses a long-term tracking and identification method for bridge dynamic characteristics based on a combination of bandpass filtering and random decrementing. It extracts long-term environmental random excitation acceleration monitoring data of the main girder from a bridge health monitoring system, preprocesses the acceleration data, and calculates the power spectrum of each segment by hour. The center frequencies of each mode are extracted using peak picking, and the energy concentration frequency intervals of the modes of interest are calculated, followed by bandpass filtering. The random excitation response acceleration signals of each mode are converted into free decay signals using random decrementing, and the damping of each mode is fitted using an exponential function model. Based on the multi-mode parameters of the bridge, frequency and modal damping time-history diagrams are plotted according to the time history, enabling long-term tracking and identification of bridge dynamic characteristics. The advantages of this invention are a significant improvement in the accuracy, automation, and computational efficiency of bridge modal parameter identification.

Description

Technical Field

[0001] This invention relates to the field of structural monitoring, and in particular to a long-term tracking and identification method for bridge dynamic characteristics based on a combination of bandpass filtering and random decrementing. Background Technology

[0002] The dynamic characteristics of a structure are crucial indicators for evaluating its vibration performance and operational status. Among these, the evolution of the structure's natural frequencies directly reflects its damage and long-term performance; changes in structural damping are a key factor leading to abnormal vibrations, such as vortex-induced resonance in long-span suspension bridges. To better understand the operational status and performance evolution of long-span suspension bridges during their service life, and to detect and promptly intervene in controlling various abnormal vibration behaviors, it is essential to conduct follow-up research and analyze the characteristic patterns of the long-term dynamic characteristics of long-span bridge systems, including natural frequencies and modal damping.

[0003] With the development of structural health monitoring technology, many large bridges have now deployed health monitoring systems to achieve real-time monitoring of structural response and environmental data. The massive monitoring database provides a foundation for conducting bridge operational modal analysis and studying the long-term dynamic characteristics of bridges. However, there are currently three main difficulties in conducting long-term tracking research on the dynamic characteristics of bridges based on health monitoring systems:

[0004] 1) Algorithm accuracy:

[0005] Accurately identifying each mode from monitoring data is fundamental to long-term dynamic characteristic tracking. For the dense-frequency characteristics of long-span bridges, existing bridge operational modal analysis methods often suffer from problems such as identifying spurious modes, order misalignment, and mode omission. Furthermore, these methods generally have low accuracy and high dispersion in identifying damping results for long-span bridges. For engineering structures such as bridges with multimodal dense-frequency characteristics, simply processing the monitoring signal using the random subtraction method cannot obtain multimodal damping values.

[0006] 2) Degree of algorithm automation:

[0007] The quality of modal parameter estimation, including damping, is highly dependent on the user's parameter selection. The key parameter in identification is the modal order, and incorrect estimation of the modal order can introduce significant bias into the damping estimation. In addition, the identification process often requires manual estimation of the modal order. While such manual intervention is acceptable for a few identification tasks, it is not suitable for large-scale, long-term, and continuous modal parameter identification and tracking scenarios.

[0008] 3) Algorithm computation efficiency:

[0009] Traditional modal decomposition methods such as EMD and VMD require repeated screening or iterative steps; the FFD method requires matrix factorization (SVD), resulting in poor computational stability and efficiency. With the development of methods such as stochastic subspace algorithms, modal analysis can be automated. These methods eliminate the need to predetermine the system order, but at the cost of significantly increased computational costs. They struggle with long-term tracking studies of bridge dynamic characteristics in massive databases, and require data with very long time series to ensure identification quality. This leads to excessively long time intervals for modal parameter tracking, resulting in sparse tracking that easily misses anomalous changes, thus diminishing the significance of the tracking.

[0010] In order to achieve accurate and automatic identification of operating modal parameters with minimal computational consumption, there is an urgent need for a method for tracking and identifying the dynamic characteristics of long-term bridge monitoring signals. Summary of the Invention

[0011] The technical problem to be solved by this invention is to provide a long-term tracking and identification method for bridge dynamic characteristics based on a combination of bandpass filtering and random subtraction. The single-component signal extraction based on bandpass filtering has higher computational stability and efficiency, while the random subtraction method has a denoising effect in the signal processing process, thereby improving the damping fitting accuracy.

[0012] To address the aforementioned technical problems, this invention provides a long-term tracking and identification method for bridge dynamic characteristics based on a combination of bandpass filtering and random decrementing. The method extracts long-term environmental random excitation acceleration monitoring data of the main girder from a bridge health monitoring system, preprocesses the acceleration data, calculates the power spectrum of each segment by hour, extracts the center frequencies of each mode using peak picking, calculates the frequency ranges of energy concentration for the modes of interest, and performs bandpass filtering. The filtered environmental random excitation response acceleration signals are then converted into free decay signals using random decrementing, and the damping of each mode is fitted using an exponential function model. Based on the multi-mode parameters of the bridge, frequency and modal damping time-history diagrams are plotted according to the time history, achieving long-term tracking and identification of bridge dynamic characteristics. The method includes the following steps:

[0013] Step S1: Extract the long-term environmental random excitation acceleration monitoring data of the main beam obtained by the bridge health monitoring system, preprocess the acceleration data, and use the preprocessed acceleration data acc for structural dynamic characteristic identification;

[0014] Preprocessing includes removing outlier data, filling in missing data, regressing local outliers, and time-domain signal denoising to improve the reliability of acceleration data;

[0015] Step S2: Extract the modal frequencies of each order, including the following steps:

[0016] S21: Divide the original acceleration signal acc into hourly segments to construct the calculation frame acc. i ,

[0017] Where: i is the hour number of the acceleration signal, i.e. the i-th acceleration calculation frame;

[0018] S22: Calculate acc i The power spectral density;

[0019] S23: Extract the peak values ​​of the power spectral density using a peak-picking method, and read the corresponding x-coordinates of the peak points to obtain the center frequency f of each mode. n Where n = 1, 2, 3..., is the modal order of interest;

[0020] Step S3: Based on bandpass filtering, obtain the single-mode acceleration components of each order, including the following steps:

[0021] S31: Calculate the energy of the narrowband frequency signal, defining the ratio of the filtered narrowband signal energy to the complete single-mode signal energy as α:

[0022]

[0023] Where: E represents the energy symbol, and Δf represents the center frequency f. n The nearby narrowband frequency range, ξ n For the nth modal damping;

[0024] S32: Calculate the bandpass filter frequency range;

[0025] To avoid energy loss during the filtering stage, it is desirable that the single-mode signals obtained after filtering retain more than 90% of the original energy of each mode, i.e., α > 90%. For long-span bridges, the damping of each mode is on the order of approximately 0.5%, and a preliminary estimate is made based on this value.

[0026] Preliminary estimates suggest that the single-sided bandwidth of each modal filter is 4%-5% of the modal center frequency, i.e., Δf / f n =4% - 5%; Total filter bandwidth f low -f up It is 8%-10% of the center frequency;

[0027] Where: f low f is the lower limit of the filter frequency. low =0.95~0.96f n ;f up f is the upper limit of the filtering frequency. up =1.04~1.05f n ;

[0028] S33: Pass through an IIR bandpass filter, according to the preset filter passband flow -f up Calculate frame acceleration acc i Bandpass filtering was performed to obtain the single-mode acceleration components of each order. Where n = 1, 2, 3... represents the modal order of interest;

[0029] Step S4: Calculate modal damping, including the following steps:

[0030] S41: The filtered single-mode signal is processed using a random decrement method. Converted into a free decay signal x n (t);

[0031] S42: Construct the exponential function x(t) as follows, and fit the modal damping:

[0032]

[0033] Where: x(t) is the constructed single-mode exponential function signal, n is the mode order, A0 is the initial amplitude of the nth-order signal, and ω n ξ n , φ n These represent the angular frequency, damping, and initial phase of the nth mode, respectively.

[0034] The free decay signal x obtained by random decrementing method is expressed in this exponential function form. n (t) is fitted to obtain the nth-order modal damping ξ. n ;

[0035] Step S5: Repeat steps S2 and S4 to obtain the frequency and modal damping values ​​of the bridge for each hour. Taking the massive health monitoring data of the actual bridge over many years as an example, the hourly monitoring data is used as the calculation frame to obtain the multi-mode parameters of the bridge for that hour. Then, the calculation results are plotted into frequency and modal damping time history diagrams according to the time history to achieve long-term tracking and identification of the bridge's dynamic characteristics, study the evolution law of bridge frequency and damping with respect to time and wind speed, and summarize the evolution characteristics of the working condition and operation characteristics of long-span suspension bridges from long-term tracking, and study the law of vortex-induced vibration of long-span suspension bridges due to damping evolution.

[0036] The superior effects of this invention are as follows:

[0037] 1) This invention proposes a modal identification and tracking calculation scheme based on bandpass filtering (BPF) and random decrementing method (RDT): First, the single-mode component signal of the structure under random excitation is obtained using bandpass filtering (BPF), and then the free decay signal is extracted from the single-mode component using RDT for damping fitting. Compared with modal decomposition methods such as EMD and VMD, the single-component signal extraction based on bandpass filtering does not require repeated screening or iteration steps. Compared with the FFD method, matrix factorization (SVD) is not required, thus having higher computational stability and efficiency. The method of this invention determines the filtering bandwidth based on the energy ratio, and naturally determines the corresponding modal order, avoiding the model pricing problem in analysis methods such as SSI. The single-component modal extraction is placed before RDT instead of the other way around, avoiding the weakening or even elimination of some modes during the RDT process. In addition, RDT has a denoising effect in the signal processing, improving the damping fitting accuracy.

[0038] 2) This invention identifies the modal frequencies and damping of bridges from monitored acceleration signals. Compared with the prior art, the method of this invention has greatly improved the accuracy of bridge modal parameter identification, the degree of automation, and the computational efficiency.

[0039] 3) Through analysis of numerical examples, this invention demonstrates that the method proposed in this invention can effectively identify structural frequencies and damping, has high computational efficiency, and can operate stably and continuously.

[0040] 4) The long-term dynamic characteristics of bridges are tracked and identified using the method of this invention, the evolution of bridge frequency and damping with respect to time and wind speed is studied, and the evolution of working conditions and operational characteristics of long-span suspension bridges is summarized from long-term tracking. The law of vortex-induced vibration of long-span suspension bridges due to damping evolution is also studied. Attached Figure Description

[0041] The accompanying drawings, which form part of this application, are used to provide a further understanding of the invention. The illustrative embodiments of the invention and their descriptions are used to explain the invention and do not constitute an undue limitation of the invention. In the drawings:

[0042] Figure 1 This is a flowchart of a specific embodiment of the present invention;

[0043] Figure 2 The acceleration and power spectral density used for the example are calculated.

[0044] Figure 3 Set the bandpass filter width;

[0045] Figure 4 Modal damping is used to fit the exponential function of the signal after random decrementing. Detailed Implementation

[0046] The embodiments of the present invention will be described in detail below with reference to the accompanying drawings.

[0047] like Figure 1 As shown, this invention provides a long-term tracking and identification method for bridge dynamic characteristics based on a combination of bandpass filtering and random decrementing. It extracts long-term environmental random excitation acceleration monitoring data of the main beam obtained from a bridge health monitoring system, preprocesses the acceleration data, calculates the power spectrum of each segment by hour, extracts the center frequencies of each mode using peak picking, calculates the frequency range of energy concentration for the modes of interest, and performs bandpass filtering. The filtered environmental random excitation response acceleration signals are converted into free decay signals using random decrementing, and the damping of each mode is fitted using an exponential function model. Based on the multi-mode parameters of the bridge, frequency and modal damping time history diagrams are plotted according to the time history to achieve long-term tracking and identification of bridge dynamic characteristics. The method includes the following steps: Step S1: Extract long-term environmental random excitation acceleration monitoring data of the main beam obtained from a bridge health monitoring system. The acceleration data is preprocessed, and the preprocessed acceleration data (acc) is used for structural dynamic characteristic identification.

[0048] By removing abnormal data, filling in missing data, regressing local outliers, and performing time-domain signal denoising, the abnormal peaks and local missing data in the original data were significantly reduced, as well as the environmental noise in the original data was reduced, thus minimizing the impact of monitoring anomalies on the error of power spectrum peak picking.

[0049] Step S2: Extract the modal frequencies of each order, including the following steps:

[0050] S21: Divide the original acceleration signal acc into hourly segments to construct the calculation frame acc. i ,

[0051] Where i is the hour number of the acceleration signal, that is, the i-th acceleration calculation frame;

[0052] S22: Calculate acc i The power spectral density, such as Figure 2 As shown;

[0053] S23: Extract the peak values ​​of the power spectral density using a peak-picking method, and read the corresponding x-coordinates of the peak points to obtain the center frequency f of each mode. n , where n = 1, 2, 3..., represents the modal order of interest.

[0054] Step S3: Based on bandpass filtering, obtain the single-mode acceleration components of each order. In this embodiment, the main calculation is of the first 6 modal parameters of the bridge, such as... Figure 3 As shown, it includes the following steps:

[0055] S31: Calculate the energy of the narrowband frequency signal, defining the ratio of the filtered narrowband signal energy to the complete single-mode signal energy as α:

[0056]

[0057] Where E represents the energy symbol, and Δf represents the center frequency f. n The nearby narrowband frequency range, ξ n For the nth modal damping;

[0058] S32: Calculate the bandpass filter frequency range;

[0059] To avoid energy loss during the filtering stage, it is desirable that the single-mode signals obtained after filtering retain more than 90% of the original energy of each mode, i.e., α > 90%. For long-span bridges, the damping of each mode is on the order of approximately 0.5%, and a preliminary estimate is made based on this value.

[0060] Preliminary estimates suggest that the single-sided bandwidth of each modal filter is 4%-5% of the modal center frequency, i.e., Δf / f n =4% - 5%; Total filter bandwidth f low -f up It is 8%-10% of the center frequency;

[0061] Among them, f low f is the lower limit of the filter frequency. low =0.95~0.96f n ;f up f is the upper limit of the filtering frequency. up =1.04~1.05f n ;

[0062] S33: Pass through an IIR bandpass filter, according to the preset filter passband f low -f up Calculate frame acceleration acc i Bandpass filtering was performed to obtain the single-mode acceleration components of each order. Where n = 1, 2, 3... represents the modal order of interest.

[0063] Step S4: Calculate modal damping, including the following steps:

[0064] S41: The filtered single-mode signal is processed using a random decrement method. Converted into a free decay signal x n (t);

[0065] S42: Construct the exponential function x(t) as follows, and fit the modal damping:

[0066]

[0067] Where x(t) is the constructed single-mode exponential function signal, n is the mode order, A0 is the initial amplitude of the nth-order signal, and ω n ξ n , φ n These represent the angular frequency, damping, and initial phase of the nth mode, respectively.

[0068] The free decay signal x obtained by random decrementing method is expressed in this exponential function form. n (t) is fitted to obtain the first 6 modal damping ξ of the bridge. n ,like Figure 4 As shown.

[0069] Step S5: Repeat steps S2 and S4 to obtain the frequency and modal damping values ​​of the bridge every hour. Through the processing of massive health monitoring data, the dynamic characteristics of the bridge are tracked and identified over a long period of time. The evolution of the bridge frequency and damping with respect to time and wind speed is studied. The evolution of the working condition and operation characteristics of long-span suspension bridges is summarized from the long-term tracking. The law of vortex-induced vibration of long-span suspension bridges due to damping evolution is studied.

[0070] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A long-term tracking and identification method for bridge dynamic characteristics based on a combination of bandpass filtering and random decrementing, characterized in that: Long-term environmental random excitation acceleration monitoring data of the main beam obtained from the bridge health monitoring system were extracted. The acceleration data were preprocessed and the signal power spectrum of each segment was calculated by hour. The center frequency of each mode was extracted by peak picking method. The energy concentration frequency range of the number of modes of interest was calculated and bandpass filtering was performed. The filtered environmental random excitation response acceleration signals of each order are converted into free decay signals using the random decrement method, and the modal damping of each order is fitted by an exponential function model. Based on the multi-order modal parameters of the bridge, frequency and modal damping time history diagrams are plotted according to the time history to realize long-term tracking and identification of the bridge's dynamic characteristics. Includes the following steps: Step S1: Extract the long-term environmental random excitation acceleration monitoring data of the main girder obtained from the bridge health monitoring system, preprocess the acceleration data, and then process the preprocessed acceleration data. Used for structural dynamic characteristic identification; Step S2: Extract the modal frequencies of each order, including the following steps: S21: For the original acceleration signal Divide the data into hourly segments to construct computation frames. , in: The hour number of the acceleration signal, i.e., the hour number. One acceleration calculation frame; S22: Calculation The power spectral density; S23: Extract the peak values ​​of the power spectral density using a peak-picking method, and read the corresponding x-coordinates of the peak points to obtain the center frequencies of each mode. ,in, , where represents the modal order of interest; Step S3: Based on bandpass filtering, obtain the single-mode acceleration components of each order, including the following steps: S31: Calculate the energy of the narrowband frequency signal, defining the ratio of the filtered narrowband signal energy to the complete single-mode signal energy as follows: : ； in: It is an energy symbol. Center frequency The nearby narrowband frequency range, For the first First-order modal damping; S32: Calculate the bandpass filter frequency range; After filtering, the single-mode signals of each order are obtained while preserving the original energy of each mode. The above describes the order of magnitude of the modal damping of long-span bridges. A preliminary estimate is made based on this value; Preliminary estimates suggest that the bandwidth of each modal filter on one side is equal to the modal center frequency. , Total filter bandwidth For the center frequency ; in: This is the lower limit of the filter frequency. ; This is the upper limit of the filter frequency. ; S33: Pass through an IIR bandpass filter, according to the preset filter passband. Calculate frame acceleration Bandpass filtering was performed to obtain the single-mode acceleration components of each order. ;in, , where represents the modal order of interest; Step S4: Calculate modal damping, including the following steps: S41: The filtered single-mode signal is processed using a random decrement method. Converted into a free decay signal ; S42: Constructing an exponential function The following is the fitted modal damping: ； in: For the constructed single-mode exponential function signal, The modal order is... for Initial amplitude of the first-order signal, They are respectively The angular frequency, damping, and initial phase of the first mode; The free decay signal obtained by random decrementing method is processed using this exponential function form. By fitting the data, we obtain the first... First-order modal damping ; Step S5: Repeat steps S2 and S4 to obtain the frequency and modal damping values ​​of the bridge every hour. Use the hourly monitoring data as a calculation frame to obtain the multi-mode parameters of the bridge for that hour. Plot the calculation results into a frequency and modal damping time history diagram according to the time history to realize the long-term tracking and identification of the bridge's dynamic characteristics.

2. The long-term tracking and identification method for bridge dynamic characteristics based on a combination of bandpass filtering and random decrementing method according to claim 1, characterized in that: In step S1, the preprocessing includes removing abnormal data, filling in missing data, regressing local outliers, and time-domain signal noise reduction.

Images