Bridge displacement influence line identification method based on acceleration signal

Abstract

The invention discloses a bridge displacement influence line identification method based on an acceleration signal, and relates to the technical field of bridge monitoring, and the method comprises the steps: carrying out the zero mean processing and quadratic integration of a vertical original acceleration signal of a bridge, and obtaining an approximate dynamic displacement response; according to the span number, the bridge length of each span and the approximate dynamic displacement response, a piecewise linear function is constructed to correct the approximate dynamic displacement response, and an accurate dynamic displacement response is obtained; and filtering the accurate dynamic displacement response by using a self-adaptive polynomial weighted smoothing filter, extracting quasi-static displacement response, and dividing the quasi-static displacement response by the weight of the vehicle to obtain a displacement influence line. Acceleration signals are optimized through a signal processing technology, and in combination with an error correction algorithm, the accuracy of bridge displacement measurement can be remarkably improved. Meanwhile, the adaptive polynomial weighted smoothing filter can adaptively adjust the window size and the polynomial order according to the local change of the signal, so that the over-fitting or under-fitting phenomenon is avoided.

Description

Technical Field

[0001] The present invention relates to the technical field of bridge monitoring, and in particular to a method for identifying bridge displacement influence lines based on acceleration signals. Background Art

[0002] During daily bridge operations, external forces such as vehicle loads, wind, and earthquakes can cause complex deformation and vibration in bridge structures, leading to various defects such as cracks. The occurrence and accumulation of these defects seriously threaten the safety and durability of bridges. Therefore, monitoring bridges, particularly assessing their residual bearing capacity by measuring their displacement influence lines, is crucial to ensuring structural safety and extending their service life.

[0003] Measuring the displacement influence line requires accurate acquisition of the bridge's displacement response. While traditional displacement sensors can directly measure displacement, they have significant limitations in practical engineering applications: strict installation requirements, high maintenance costs, and susceptibility to temperature, humidity, and environmental interference signals, which reduces the stability and reliability of measurement results.

[0004] In contrast, accelerometers are more widely used in bridge monitoring due to their low cost and easy installation. In theory, displacement information can be obtained by integrating the acceleration signal twice. However, in practice, noise interference, signal drift, and accumulated errors during the numerical integration process often make the displacement results obtained by this integration inaccurate, especially in the low-frequency range. Therefore, how to overcome these technical difficulties, accurately and reliably integrate the bridge's displacement response from the acceleration signal, and then successfully identify the displacement influence line, has become a key issue that needs to be addressed. Summary of the Invention

[0005] The purpose of the present invention is to provide a bridge displacement influence line identification method based on acceleration signals, which aims to overcome the above-mentioned problems existing in the prior art.

[0006] To achieve the purpose, the present invention provides the following technical solutions: A bridge displacement influence line identification method based on acceleration signals includes the following steps: Step S1, performing zero-mean processing and quadratic integration on the original vertical acceleration signal of the bridge measured by the acceleration sensor to obtain an approximate dynamic displacement response of the bridge in the vertical direction; Step S2: constructing a piecewise linear function to correct the approximate dynamic displacement response based on the number of spans of the bridge to be tested, the length of each span, and the approximate dynamic displacement response obtained in step S1, and obtaining the accurate vertical dynamic displacement response of the bridge by removing the trend term piecewise. In step S3, the accurate dynamic displacement response obtained in step S2 is filtered using an adaptive polynomial weighted smoothing filter to extract the vertical quasi-static displacement response of the bridge; the quasi-static displacement response is then divided by the vehicle weight to obtain the vertical displacement influence line of the bridge.

[0007] Furthermore, the step S1 specifically includes: Step S101: Detect the vehicle passing the bridge to be tested at a constant speed along a straight line, and measure and record the original acceleration signal of the acceleration sensor. , sampling frequency , and vehicle speed , vehicle weight , total number of bridge spans Length of each span ; , ; Step S102: the original acceleration signal Perform zero mean processing to obtain an acceleration signal with a mean of zero :

[0008] in, are discrete sampling time points, ; Step S103: zero acceleration signal Perform a numerical integration to obtain the velocity signal :

[0009] in, ; Step S104: Speed ​​signal Perform a numerical integration to obtain the approximate vertical displacement signal of the bridge :

[0010] .

[0011] Furthermore, the step S2 specifically includes: Step S201, calculate the time it takes for the detection vehicle to pass through each bridge pier; set the time it takes for the detection vehicle to pass through the first The time for each pier is , calculate the detection vehicle passing Time for each pier:

[0012] in, For the span length; Step S202: divide the vertical approximate displacement signal of the bridge into Each segment corresponds to the time interval when a vehicle passes through two consecutive bridge piers, that is, from arrive ; Then use the linear function to correct each segment of the approximate displacement signal to remove the trend term caused by numerical integration:

[0013] Step S203: The corrected displacement signals of the segments are connected in sequence to reconstruct the accurate vertical displacement response signal of the complete bridge. ,Right now The union of the segment-corrected displacement signals:

[0014] in, For the The displacement signal after correction, .

[0015] Furthermore, the step S3 specifically includes: Step S301, define the adaptive polynomial weighted smoothing filter parameters, including the maximum window size , minimum window size , maximum polynomial order , minimum polynomial order , threshold factor and window overlap ratio ; Step S302: Based on the window overlap ratio , calculate the window step size :

[0016] Step S303: dynamically calculate the window size based on the local characteristics of the accurate dynamic displacement signal and polynomial order :

[0017]

[0018] in, For accurate displacement response signal, is the variance of the local area of ​​the accurate displacement response signal; Step S304: performing local polynomial fitting on the accurate displacement response signal of each window, and filtering the fitting result through a weighted smoothing filter to obtain a vertical quasi-static displacement signal of the bridge; Step S305: Divide the quasi-static displacement response by the vehicle weight to obtain the vertical displacement influence line of the bridge.

[0019] Furthermore, in step S304, local polynomial fitting is performed:

[0020] in, is the time vector, The accurate displacement response signal for each window; The fitting results are filtered by a weighted smoothing filter to obtain the vertical quasi-static displacement signal of the bridge :

[0021] in, is the initial smoothing value:

[0022] is the weighting factor:

[0023] is the local variance; In step S305, the vertical displacement influence line of the bridge is calculated. : .

[0024] A bridge displacement influence line identification device based on acceleration signals, the system is used to implement any of the above methods, including an acceleration sensor, an integral calculation module, a linear correction module and a signal separation module; The acceleration sensor is installed below the main beam of the bridge and is used to measure the original vertical acceleration signal of the bridge; The integral calculation module is used to perform a second integration on the original acceleration signal to obtain an approximate vertical dynamic displacement response of the bridge; The linear correction module is used to receive the approximate dynamic displacement response output by the integral calculation module and obtain the accurate vertical displacement response of the bridge using linear correction; The signal separation module is used to receive the accurate displacement response output by the linear correction module, and use an adaptive polynomial weighted smoothing filter to separate the accurate displacement response into a quasi-static displacement response and a dynamic displacement response, thereby calculating the vertical displacement influence line of the bridge.

[0025] Compared with the prior art, the present invention has the following beneficial effects: First, the present invention optimizes the acceleration signal through signal processing technology and combines it with an error correction algorithm, especially for the noise drift and cumulative error that occur during the two integration processes of the acceleration signal. This can effectively avoid the integration error in traditional technologies and significantly improve the accuracy of bridge displacement measurement.

[0026] Secondly, through local weighting and post-processing steps, the present invention effectively reduces noise in the signal while preserving key signal trends, ultimately obtaining an accurate bridge displacement influence line. Specifically, an adaptive polynomial weighted smoothing filter is used to filter the bridge's accurate dynamic displacement response. The window size and polynomial order are adaptively adjusted based on local variations in the signal, thus avoiding overfitting or underfitting.

[0027] Third, accelerometers are relatively inexpensive and easy to install, allowing them to be installed in locations where displacement sensors are inaccessible. They are already widely used in various structural health monitoring systems. Without the need for additional displacement sensors, accurate bridge displacement responses can be obtained simply by utilizing existing accelerometers and applying advanced signal processing and correction algorithms. This reduces the overall cost of the monitoring system, broadens its application scenarios, and offers significant economic benefits. BRIEF DESCRIPTION OF THE DRAWINGS

[0028] Figure 1 This is a flow chart of the bridge displacement influence line identification method based on acceleration signals in the present invention.

[0029] Figure 2 This is the acceleration time-history response curve of the second span of a three-span continuous beam bridge.

[0030] Figure 3 For Figure 2 The acceleration time-history response curve shown is the displacement signal obtained by quadratic integration.

[0031] Figure 4 For Figure 2 The acceleration time-history response curve shown is the corrected displacement signal.

[0032] Figure 5 For Figure 2 The acceleration time-history response curve and the filtered displacement signal are shown, including the original displacement signal (a), the filtered quasi-static displacement signal (b), and the filtered vibration signal (c).

[0033] Figure 6 For Figure 2 The acceleration time history response curve is shown, and the influence line is identified.

[0034] Figure 7 This is a structural block diagram of the bridge displacement influence line identification device based on acceleration signals in the present invention. DETAILED DESCRIPTION

[0035] The specific embodiments of the present invention are described below with reference to the accompanying drawings. In order to fully understand the present invention, many details are described below, but for those skilled in the art, the present invention can be implemented without these details.

[0036] like Figure 1 and Figure 7 As shown, a bridge displacement influence line identification method based on acceleration signals includes the following steps: Step S1: performing zero-mean processing and quadratic integration on the original vertical acceleration signal of the bridge measured by the acceleration sensor to obtain an approximate dynamic displacement response of the bridge in the vertical direction.

[0037] In a specific embodiment, the above step S1 specifically includes: Step S101: Detect the vehicle passing the bridge to be tested at a constant speed along a straight line, and measure and record the original acceleration signal of the acceleration sensor. , sampling frequency , and vehicle speed , vehicle weight , total number of bridge spans Length of each span ; , .

[0038] Step S102: the original acceleration signal Perform zero mean processing to obtain an acceleration signal with a mean of zero :

[0039] in, are discrete sampling time points, .

[0040] Step S103: zero acceleration signal Perform a numerical integration to obtain the velocity signal :

[0041] in, .

[0042] Step S104: Speed ​​signal Perform a numerical integration to obtain the approximate vertical displacement signal of the bridge :

[0043] .

[0044] In the above step S1, the zero-mean processing can eliminate the noise drift that may exist in the acceleration signal. This is the basis for the subsequent quadratic integration, preventing the quadratic integration result from producing false linear or quadratic trends. It can effectively avoid the integration error in traditional technology and significantly improve the accuracy of bridge displacement measurement.

[0045] In step S2, a piecewise linear function is constructed to correct the approximate dynamic displacement response based on the number of spans of the bridge to be tested, the length of each span, and the approximate dynamic displacement response obtained in step S1. The accurate vertical dynamic displacement response of the bridge is obtained by removing the trend term piecewise.

[0046] In a specific embodiment, step S2 specifically includes: Step S201, calculate the time it takes for the detection vehicle to pass through each bridge pier; set the time it takes for the detection vehicle to pass through the first The time for each pier is , calculate the detection vehicle passing Time for each pier:

[0047] in, For the The span is long.

[0048] Step S202: divide the vertical approximate displacement signal of the bridge into Each segment corresponds to the time interval when a vehicle passes through two consecutive bridge piers, that is, from arrive ; Then use the linear function to correct each segment of the approximate displacement signal to remove the trend term caused by numerical integration:

[0049] in, are discrete sampling time points, .

[0050] Step S203: The corrected displacement signals of the segments are connected in sequence to reconstruct the accurate vertical displacement response signal of the complete bridge. ,Right now The union of the segment-corrected displacement signals:

[0051] in, For the The displacement signal after correction, .

[0052] In step S2 of the present invention, a piecewise linear model is constructed based on the bridge's actual physical structural information (number of spans, length of each span) and the approximate dynamic displacement response obtained in step S1. This model is designed to describe and capture the low-frequency trend term errors accumulated during the integration process (primarily due to the integration constant, sensor low-frequency noise, and baseline drift, manifested as slowly varying displacement baselines). The constructed piecewise linear function is then used to correct the approximate dynamic displacement response obtained in step S1. By combining piecewise linear fitting with the bridge's structural information, it better conforms to the actual physical boundary conditions of the displacement constraints at the bridge supports. It can effectively remove low-frequency trend term errors introduced by integration that do not conform to the bridge's actual physical constraints, significantly improve the low-frequency baseline, and obtain an accurate dynamic displacement response that is closer to reality.

[0053] In step S3, the accurate dynamic displacement response obtained in step S2 is filtered using an adaptive polynomial weighted smoothing filter to extract the vertical quasi-static displacement response of the bridge; the quasi-static displacement response is then divided by the vehicle weight to obtain the vertical displacement influence line of the bridge.

[0054] In a specific embodiment, the above step S3 specifically includes: Step S301, define the adaptive polynomial weighted smoothing filter parameters, including the maximum window size , minimum window size , maximum polynomial order , minimum polynomial order , threshold factor and window overlap ratio .

[0055] Step S302: Based on the window overlap ratio , calculate the window step size : .

[0056] Step S303: dynamically calculate the window size based on the local characteristics of the accurate dynamic displacement signal and polynomial order :

[0057]

[0058] in, For accurate displacement response signal, is the variance of the accurate displacement response signal in the local area.

[0059] Step S304 : performing local polynomial fitting on the accurate displacement response signal of each window, and filtering the fitting result by a weighted smoothing filter to obtain a quasi-static vertical displacement signal of the bridge.

[0060] The above local polynomial fit:

[0061] in, is the time vector, The accurate displacement response signal for each window; The fitting results are filtered by a weighted smoothing filter to obtain the vertical quasi-static displacement signal of the bridge :

[0062] in, is the initial smoothing value:

[0063] is the weighting factor:

[0064] is the local variance.

[0065] Step S305: Divide the quasi-static displacement response by the vehicle weight to calculate the vertical displacement influence line of the bridge: : .

[0066] In step S3 of the present invention, a filter is used to separate the high-frequency dynamic vibration component (the vibration of the bridge under the influence of the vehicle) from the low-frequency static / quasi-static displacement component (the slowly changing displacement caused primarily by the vehicle's gravity) in the signal. This effectively separates the low-frequency static / quasi-static displacement caused by the vehicle (the essence of the influence line) from the displacement response containing strong vibrations. Dividing the signal by the vehicle's weight yields the inherent characteristics of the bridge (i.e., the displacement influence line), which can be used for subsequent bridge assessment and load identification. The adaptive polynomial weighted smoothing filter automatically adjusts filtering parameters (such as window size and polynomial order) based on the local characteristics of the displacement signal (such as curvature changes and vibration intensity), ensuring optimal smoothing of vibration noise at varying vehicle speeds and bridge characteristics. This filter also maximizes the preservation of the static displacement morphology (peak value and shape), avoiding distortion of the displacement influence line caused by excessive smoothing.

[0067] Practice Test like Figure 2-Figure 6As shown in the figure, a finite element model of a bridge is created in Abaqus software. It is a 120-meter simply supported beam bridge designed as a three-span structure with a single span length of 40 meters. , moment of inertia , mass per unit length , elastic modulus , and constructed the Class A road roughness. In addition, an acceleration sensor was set only in the span of the second span of the bridge, and the acceleration sensor collected the vertical acceleration of the bridge at a sampling rate of 100 Hz.

[0068] The data from Abaqus software was converted to MATLAB format to obtain the acceleration curve at the bridge midspan measurement point. This acceleration curve was then quadratically integrated and linearly corrected, effectively avoiding the integration errors associated with traditional techniques and significantly improving the accuracy of static displacement measurements. This method provides a valuable data processing tool for static bridge inspections. Accurate static displacement data can be obtained using existing modules, significantly reducing the overall cost of bridge monitoring systems and offering high practicality and economic benefits.

[0069] First, convert the raw data format detected by the acceleration sensor into mat, and retrieve the time and its corresponding acceleration. The raw acceleration signal is as follows Figure 2 shown.

[0070] According to the above step S1, after the acceleration signal is processed by zero mean, the approximate displacement signal is obtained by quadratic integration, such as Figure 3 shown.

[0071] According to the above step S2, the displacement data obtained by the quadratic integration is corrected by a piecewise linear function. Figure 4 shown.

[0072] Next, according to the above step S3, the modified displacement signal is filtered into a quasi-static signal and a vibration signal using an adaptive polynomial weighted smoothing filter. The result is as follows: Figure 5 shown.

[0073] Finally, the displacement influence line is identified from the quasi-static displacement signal using formula (714). The identification result is as follows: Figure 6 shown.

[0074] In the actual data test of a bridge, it was proved that the influence line identification method proposed in this invention has strong robustness and is expected to be applied to real-time health monitoring of bridges.

[0075] like Figure 1-Figure 7As shown, the present invention also discloses and protects a bridge displacement influence line identification device based on acceleration signals. The system is used to implement the above method, including an acceleration sensor, an integral calculation module, a linear correction module and a signal separation module connected to each other; The acceleration sensor is installed below the main beam of the bridge and is used to measure the original vertical acceleration signal of the bridge; The integral calculation module is used to perform a second integration on the original acceleration signal to obtain an approximate vertical dynamic displacement response of the bridge; The linear correction module is used to receive the approximate dynamic displacement response output by the integral calculation module and obtain the accurate vertical displacement response of the bridge using linear correction; The signal separation module is used to receive the accurate displacement response output by the linear correction module, and use an adaptive polynomial weighted smoothing filter to separate the accurate displacement response into a quasi-static displacement response and a dynamic displacement response, thereby calculating the vertical displacement influence line of the bridge.

[0076] The above is only a specific implementation of the present invention, but the design concept of the present invention is not limited to this. Any non-substantial changes to the present invention using this concept shall be deemed as an infringement of the protection scope of the present invention.

Claims

1. A bridge displacement influence line identification method based on acceleration signals, characterized by: The following steps are involved: Step S1, performing zero-mean processing and quadratic integration on the original vertical acceleration signal of the bridge measured by the acceleration sensor to obtain an approximate dynamic displacement response of the bridge in the vertical direction; Step S2: constructing a piecewise linear function to correct the approximate dynamic displacement response based on the number of spans of the bridge to be tested, the length of each span, and the approximate dynamic displacement response obtained in step S1, and obtaining the accurate vertical dynamic displacement response of the bridge by removing the trend term piecewise. In step S3, the accurate dynamic displacement response obtained in step S2 is filtered using an adaptive polynomial weighted smoothing filter to extract the vertical quasi-static displacement response of the bridge; the quasi-static displacement response is then divided by the vehicle weight to obtain the vertical displacement influence line of the bridge.

2. The bridge displacement influence line identification method based on acceleration signals according to claim 1 is characterized in that: The step S1 specifically includes: Step S101: Detect the vehicle passing the bridge to be tested at a constant speed along a straight line, and measure and record the original acceleration signal of the acceleration sensor. , sampling frequency , and vehicle speed , vehicle weight , total number of bridge spans Length of each span ; , ; Step S102: the original acceleration signal Perform zero mean processing to obtain an acceleration signal with a mean of zero : in, are discrete sampling time points, ; Step S103: zero acceleration signal Perform a numerical integration to obtain the velocity signal : in, ; Step S104: Speed ​​signal Perform a numerical integration to obtain the approximate vertical displacement signal of the bridge : 。 3. The bridge displacement influence line identification method based on acceleration signals according to claim 1 is characterized in that: The step S2 specifically includes: Step S201, calculate the time it takes for the detection vehicle to pass through each bridge pier; set the time it takes for the detection vehicle to pass through the first The time for each pier is , calculate the detection vehicle passing Time for each pier: in, For the span length; Step S202: divide the vertical approximate displacement signal of the bridge into Each segment corresponds to the time interval when a vehicle passes through two consecutive bridge piers, that is, from arrive ; Then use the linear function to correct each segment of the approximate displacement signal to remove the trend term caused by numerical integration: Step S203: The corrected displacement signals of the segments are connected in sequence to reconstruct the accurate vertical displacement response signal of the complete bridge. ,Right now The union of the segment-corrected displacement signals: in, For the The displacement signal after correction, .

4. The bridge displacement influence line identification method based on acceleration signals according to claim 1 is characterized in that: The step S3 specifically includes: Step S301, define the adaptive polynomial weighted smoothing filter parameters, including the maximum window size , minimum window size , maximum polynomial order , minimum polynomial order , threshold factor and window overlap ratio ; Step S302: Based on the window overlap ratio , calculate the window step size : Step S303: dynamically calculate the window size based on the local characteristics of the accurate dynamic displacement signal and polynomial order : in, For accurate displacement response signal, is the variance of the local area of ​​the accurate displacement response signal; Step S304: performing local polynomial fitting on the accurate displacement response signal of each window, and filtering the fitting result through a weighted smoothing filter to obtain a vertical quasi-static displacement signal of the bridge; Step S305: Divide the quasi-static displacement response by the vehicle weight to obtain the vertical displacement influence line of the bridge.

5. The bridge displacement influence line identification method based on acceleration signals according to claim 4 is characterized in that: In step S304, local polynomial fitting is performed: in, is the time vector, The accurate displacement response signal for each window; The fitting results are filtered by a weighted smoothing filter to obtain the vertical quasi-static displacement signal of the bridge : in, is the initial smoothing value: is the weighting factor: is the local variance; In step S305, the vertical displacement influence line of the bridge is calculated. : 。 6. A bridge displacement influence line identification device based on acceleration signals, characterized by: The system is used to implement the method according to any one of claims 1 to 5, comprising an acceleration sensor, an integral calculation module, a linear correction module and a signal separation module; The acceleration sensor is installed below the main beam of the bridge and is used to measure the original vertical acceleration signal of the bridge; The integral calculation module is used to perform a second integration on the original acceleration signal to obtain an approximate vertical dynamic displacement response of the bridge; The linear correction module is used to receive the approximate dynamic displacement response output by the integral calculation module and obtain the accurate vertical displacement response of the bridge using linear correction; The signal separation module is used to receive the accurate displacement response output by the linear correction module, and use an adaptive polynomial weighted smoothing filter to separate the accurate displacement response into a quasi-static displacement response and a dynamic displacement response, thereby calculating the vertical displacement influence line of the bridge.

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