A bridge curvature influence line extraction and damage positioning method based on continuous wavelet transform

Abstract

This invention relates to a method for extracting bridge curvature influence lines and locating damage based on continuous wavelet transform (CWT), belonging to the field of structural health monitoring in civil engineering. This invention aims to overcome the problems of low computational efficiency of Fourier transform, strong rigidity of low-pass filter thresholds, and easy loss of feature information in existing technologies. It proposes a method for extracting bridge curvature influence lines and locating damage based on CWT. This method can efficiently acquire frequency domain information and flexibly adjust thresholds while preserving key features of the curvature influence lines, thereby improving the extraction accuracy and computational efficiency of the curvature influence lines, and ultimately achieving accurate identification of bridge structural damage locations.

Description

Technical Field

[0001] This invention relates to a method for extracting the influence line of bridge curvature and locating damage based on continuous wavelet transform, belonging to the field of structural health monitoring in civil engineering. Background Technology

[0002] With the continuous growth of transportation demand, the safety and reliability of bridges, as key infrastructure in the transportation system, are receiving increasing attention. During long-term service, bridges are subjected to repeated vehicle loads and the coupled effects of various environmental factors such as temperature changes, wind and rain erosion, and corrosion, which can easily lead to problems such as material fatigue, component damage, and structural performance degradation, thereby affecting the safe operation and service life of bridges.

[0003] To achieve efficient assessment and timely maintenance of the structural health of in-service bridges, structural health monitoring (SHM) technology has become an important research direction and engineering tool. Its primary task is the identification and location of bridge damage. By deploying various types of sensors, such as accelerometers, strain gauges, and displacement gauges, on the bridge structure, the dynamic response signals of the structure under vehicle loads are collected in real time. Combined with signal processing, feature extraction, and pattern recognition technologies, long-term monitoring of the bridge's operational status and identification of potential damage can be achieved.

[0004] Because the influence line of a bridge is highly sensitive to structural stiffness, its shape will change abruptly when the bridge stiffness changes due to damage. Based on this physical characteristic, bridge damage identification methods based on the principle of dynamic-static transformation have been widely used. This method analyzes the dynamic response signal of the structure under moving loads, extracts the influence line (IL) and its changing characteristics, and constructs damage-sensitive indices accordingly, thereby achieving damage location in key parts of the bridge.

[0005] Among these methods, damage identification based on acceleration response has attracted widespread attention from researchers and engineers due to the low cost and ease of deployment of sensors, and its ability to be implemented under normal bridge operation conditions. This method utilizes Fourier transform combined with low-pass filtering to extract curvature influence lines from the bridge's acceleration signal, and uses changes in the average curvature influence line as a damage indicator to identify potential damage locations in the structure. The advantage of this method is that it does not require dense sensor deployment, exhibiting good engineering operability and application potential.

[0006] However, this method has the following shortcomings: (1) Limitations of Fourier transform. The basis functions of Fourier transform are fixed-frequency sine or cosine functions that extend infinitely in the time domain. In order to accurately extract the influence lines of bridge curvature (such as beam structures with a "triangle" shape), a large number of Fourier basis functions must be superimposed, resulting in low computational efficiency. (2) Rigid constraints of low-pass filtering. The curvature influence lines are mainly formed by the superposition of low-frequency quasi-static components of various modes of the structure. However, within a certain low-frequency range, it is necessary to retain a certain amount of high-frequency components to reconstruct its key morphological features (such as the triangle vertex shape of the curvature influence lines of beam structures and the local protrusions caused by damage). Existing methods use a low-pass filtering strategy with a fixed cutoff frequency to directly filter out all frequency components above the threshold. When the threshold is set unreasonably, it is easy to weaken or lose the key information of the influence lines, reducing the reliability of the results.

[0007] In summary, the acceleration response method combining Fourier transform and low-pass filtering suffers from low computational efficiency, insufficient feature fidelity, and inflexible threshold selection when extracting curvature influence lines, thus limiting its engineering application in bridge damage localization. Therefore, a new method is urgently needed that combines time-frequency localization characteristics, allows for flexible adjustment of the frequency threshold, and efficiently extracts curvature influence lines to achieve rapid and accurate bridge damage localization based on acceleration response. Summary of the Invention

[0008] The purpose of this invention is to provide a method for extracting bridge curvature influence lines and locating damage based on continuous wavelet transform, so as to solve the technical problems mentioned in the background art.

[0009] This invention provides a method for extracting bridge curvature influence lines and locating damage based on continuous wavelet transform, comprising: Accelerometers pre-placed on the monitoring sections of the bridge under test are used to collect the acceleration response signals of the bridge when a vehicle load passes over it. The time interval for crossing the bridge is determined based on the time of entry and exit of the vehicles crossing the bridge; a standard signal is extracted from the acceleration response signal based on the time interval for crossing the bridge; the standard signal is preprocessed to obtain the analysis signal; Perform continuous wavelet transform on the analyzed signal to obtain the distribution map of wavelet coefficients on the time-scale plane; The effective time range is determined based on the time of entry and exit of vehicles crossing the bridge. Based on the effective time range and the predetermined effective scale range, the corresponding effective area is selected from the distribution map and subjected to inverse continuous wavelet transform to reconstruct the bridge curvature influence line that characterizes the relationship between the vehicle load application location and the curvature response of the monitoring section. Using an accelerometer at the same monitoring section, the acceleration response signals of the same vehicle crossing the bridge at different bridge surface roughnesses were collected, and the bridge curvature influence lines were extracted respectively. The average curvature influence line was obtained by taking the mean value. Damage indices are calculated by comparing the average curvature influence lines of the benchmark bridge and the bridge under test, and the damage location of the bridge under test is determined based on the peak position of the damage indices.

[0010] In a preferred embodiment, the time when a vehicle enters or exits the bridge is determined based on the laser rangefinder.

[0011] In a preferred embodiment, preprocessing the standard signal to obtain the analysis signal includes: A copy of the standard signal is made, the sign is reversed, and time-mirrored extension is performed. This copy is then spliced ​​with the original standard signal to form an extended signal. The extended signal has zero values ​​at both ends. The extended signal is further copied three times to obtain the analysis signal.

[0012] As a preferred embodiment, the expression for performing continuous wavelet transform on the analyzed signal is: In the formula, ψ * ( t ) is the wavelet mother function ψ ( t The complex conjugate of ); b It is a translation factor over time; s The scaling factor is represented by the center frequency of the wavelet mother function. Inversely proportional; It involves analyzing signals; These are the calculated wavelet coefficients, used for time-frequency analysis of the signal; It is a unit step function, where Indicates angular frequency; It is the normalization constant, where It is the time-bandwidth product. The parameter is used to characterize the symmetry of the generalized Morse wavelet function.

[0013] As a preferred embodiment, the expression for selecting the corresponding effective region from the distribution map and performing inverse continuous wavelet transform is: In the formula, and These represent the lower and upper limits of the valid time range, respectively. and These correspond to the minimum and maximum scales within the effective scale range, respectively. The minimum scale is the scale corresponding to the first-order frequency of the bridge, and the maximum scale is the scale corresponding to a pre-set minimum allowable frequency. Indicates the monitoring section.

[0014] As a preferred embodiment, the expression for determining the effective time range based on the bridge entry and exit times of vehicles crossing the bridge is as follows: In the formula, and These represent the times when vehicles enter and exit the bridge, respectively.

[0015] As a preferred embodiment, the expression for the mean curvature influence line is: In the formula, This indicates the total number of times vehicles crossed the bridge; Indicates the first Secondary use The influence line of bridge curvature is extracted from the acceleration response signal collected by the acceleration sensor at the monitoring section.

[0016] In a preferred embodiment, the expression for the damage index is: in, and These represent the average curvature influence line and the reference curvature influence line obtained from the current test of the bridge under test, respectively.

[0017] As a preferred embodiment, the reference bridge adopts any of the following: Undamaged bridges before they are opened to traffic after completion; The bridge under test in the previous test, and the preset time interval between the previous test and this test.

[0018] Compared with the prior art, the present invention has the following beneficial effects: This invention aims to overcome the problems of low computational efficiency of Fourier transform, strong rigidity of low-pass filter threshold, and easy loss of feature information in existing technologies. It proposes a method for extracting bridge curvature influence lines and locating damage based on continuous wavelet transform (CWT). This method can efficiently acquire frequency domain information and flexibly adjust the threshold while preserving key features of the curvature influence lines, thereby improving the extraction accuracy and computational efficiency of the curvature influence lines, and ultimately achieving accurate identification of bridge structural damage locations. Attached Figure Description

[0019] Figure 1 This is an analytical framework diagram of a bridge damage localization method based on continuous wavelet transform and acceleration response.

[0020] Figure 2 This is a representation of the generalized Morse wavelet function, where: (a) is the time domain representation; (b) is the frequency domain representation.

[0021] Figure 3 This is a schematic diagram of the bridge verification model used in this invention.

[0022] Figure 4 It is the acceleration data collected by sensor SM in the verification model.

[0023] Figure 5 The analysis signal is obtained after data preprocessing. .

[0024] Figure 6 It is to analyze signals Distribution of wavelet coefficients on the time-scale plane after continuous wavelet transform (white box area is the effective area).

[0025] Figure 7 It is the curvature influence line obtained by reconstructing the wavelet coefficients of the effective region through inverse continuous wavelet transform, and the comparison result with the theoretical curvature influence line.

[0026] Figure 8 The result diagram is the influence line of the average curvature of the bridge, where: (a) is the reference bridge; (b) is the bridge to be tested.

[0027] Figure 9 This is a diagram showing the damage index results calculated based on the curvature influence line. Detailed Implementation

[0028] The present invention will be further described below with reference to the accompanying drawings. The following embodiments are only used to more clearly illustrate the technical solution of the present invention, and should not be used to limit the scope of protection of the present invention.

[0029] Combination Figure 1 This embodiment provides a method for extracting bridge curvature influence lines and locating damage based on continuous wavelet transform, which includes: Step S1: Using acceleration sensors pre-installed on the monitoring sections of the bridge under test, collect the acceleration response signals of the bridge when a vehicle load passes over it. ;in Indicates the first The monitoring section can be any cross-sectional location of the bridge under test.

[0030] Step S2: Based on the time when vehicles cross the bridge. and the moment of getting off the bridge Determine the bridge crossing time interval [ , Based on the bridge crossing time interval, from the acceleration response signal Extracting standard signals ; for the standard signal Preprocessing is performed to obtain the analysis signal ; This embodiment accurately identifies the effective time interval for vehicles entering and leaving the bridge using a laser ranging device. This embodiment uses the standard signal... Preprocessing is performed to obtain the analysis signal The specific process includes, After making a copy and reversing the symbol, perform time mirroring extension to match the original standard signal. splicing to form an extended signal Extended signal Zero values ​​are taken at both ends to satisfy the boundary conditions of the curvature influence line of a simply supported beam. To avoid the boundary effects of continuous wavelet transform, the following is used: Make three more copies to obtain the analysis signal. .

[0031] Step S3: Perform continuous wavelet transform on the analyzed signal to obtain the distribution map of wavelet coefficients on the time-scale plane; This embodiment analyzes the signal. By performing continuous wavelet transform and utilizing the wavelet mother function with time-frequency localization characteristics, the signal can be decomposed into multiple scales, thereby obtaining the time-frequency distribution characteristics of the analyzed signal.

[0032] The definition of continuous wavelet transform is as follows: (1) In the formula, ψ * ( t ) is the wavelet mother function ψ ( t The complex conjugate of ); b It is a translation factor over time; s The scaling factor is represented by the center frequency of the wavelet mother function. Inversely proportional; These are the calculated wavelet coefficients, used for time-frequency analysis of the signal.

[0033] Combination Figure 2 In this embodiment, based on the shape of the curvature influence line, the generalized Morse wavelet function (GMW) is selected as the mother wavelet function, and its time-domain and frequency-domain representations are shown in the appendix. Figure 2As shown, the mathematical form of this function is: (2) In the formula, It is a unit step function, where Indicates angular frequency; It is the normalization constant, where It is the time-bandwidth product, parameter Characterizing the symmetry of the generalized Morse wavelet function. In this embodiment, the following is selected: , This allows for the acquisition of a mother wavelet function with good symmetry and reasonable frequency band coverage. Unlike the traditional Fourier transform, the basis functions of the continuous wavelet transform have tight support in the time domain, taking values ​​only within a finite interval, which can effectively capture the local structure of the signal. By selecting a mother wavelet function with a shape similar to the curvature influence line, the curvature influence line and its damage features can be efficiently extracted using fewer basis functions.

[0034] Step S4: Determine the effective time range based on the time when the vehicle enters and exits the bridge. Based on the effective time range and the predetermined effective scale range, select the corresponding effective region from the distribution map and perform inverse continuous wavelet transform to reconstruct the bridge curvature influence line that characterizes the relationship between the vehicle load application location and the curvature response of the monitoring section. This embodiment selects an effective region (corresponding to a time range) from the distribution map based on the amplitude and phase information of the wavelet coefficients. , and scale range , The data was reconstructed using the Inverse Continuous Wavelet Transform (iCWT) to obtain the influence line of bridge curvature. ,in This indicates the monitoring section of the accelerometer.

[0035] The definition of inverse continuous wavelet transform is as follows: (3) In the formula, and This indicates the lower and upper time limits of the corresponding standard signal in the analyzed signal; and These respectively represent the lower and upper limits of the effective scale range; and The minimum and maximum scales are the main low-frequency components of the signal, typically taken as the scales corresponding to the first-order frequency of the bridge and the minimum permissible frequency of the signal. Unlike the rigid cutoff frequency of traditional low-pass filters, this invention sets the center frequency of the wavelet mother function. This allows for flexible control over the frequency domain. The wavelet mother function has a wide coverage range in the frequency domain, capable of simultaneously including low-frequency principal components and some high-frequency information required to construct the curvature influence line, thereby avoiding the loss of feature information and ensuring the integrity of the curvature influence line shape.

[0036] Step S5: Using the same accelerometer at the same monitoring section, collect the acceleration response signals of the same vehicle when crossing the bridge at different bridge surface roughnesses, and extract the bridge curvature influence lines respectively. Take the average value to obtain the average curvature influence line. To enhance stability, single-sample data may contain noise interference. The average curvature influence line obtained by averaging the values ​​under various bridge surface roughnesses can effectively eliminate noise interference. Curvature influence lines are extracted from the acceleration signals of multiple vehicle bridge crossing tests, and the average curvature influence line is obtained by averaging their values. : (4) In the formula, This indicates the total number of times vehicles crossed the bridge; Indicates the first Secondary use The influence line of bridge curvature is extracted from the acceleration response signal of the accelerometer at the monitoring section.

[0037] Step S6: Calculate the damage index by comparing the average curvature influence lines of the reference bridge and the bridge under test, and determine the damage location of the bridge under test based on the peak position of the damage index.

[0038] This embodiment compares the average curvature influence lines of the reference bridge and the bridge under test (which are respectively...). and This involves calculating damage indices based on the curvature influence line to accurately identify the location of bridge damage. The definition is as follows: (5) Damage indicators The peak position corresponds to the longitudinal damage location of the bridge, thus enabling accurate location of bridge damage.

[0039] The reference bridge may be any of the following: Undamaged bridges before they are opened to traffic after completion; The bridge under test in the previous test, and the preset time interval between the previous test and this test.

[0040] The following description uses a specific example, as shown in the attached figure. Figure 3 As shown, taking a highway bridge as the research object, the damage localization effect of the method proposed in this invention is verified by numerical model.

[0041] The selected bridge is a simple supported concrete beam bridge, 40 m long, with an elastic modulus of 3 × 10⁻⁶ m. 10 N / m 2 The moment of inertia of the cross section is 3532 m. 4 The bridge has a mass of 10,000 kg / m per meter, and the damping ratio of each vibration mode is assumed to be 5%. One-dimensional beam elements are used for modeling, with each element having a spatial length of 0.25 m. The bridge surface roughness is classified according to ISO 8608 standard Class C. An accelerometer SM is installed in the middle of the bridge, with a sampling frequency of 200 Hz.

[0042] The vehicle parameters are set as follows: speed 5m / s, mass 1750 kg, suspension spring stiffness 1.8×10⁻⁶. 7 N / m, damping coefficient is 1.44×10 5 N·s / m.

[0043] The bridge acceleration response acquired by sensor SM is shown in the attached figure. Figure 4 As shown. Based on the time of vehicle entry and exit from the bridge, it is determined that the vehicle entered the bridge at 3.6 seconds. ), 11.6 s away from the bridge ( The signal within the corresponding time interval is used as the standard signal. .

[0044] After extracting the standard signal, it is mirrored by reversing the sign and sampling order of the signal, and then concatenated with the original signal to form an extended signal. The extended signal is copied three times, and the final result is shown in the attached image. Figure 5 The analysis signal shown The data within the red box represents the original standard signal. This processing method effectively eliminates the boundary effects of continuous wavelet transform.

[0045] Perform continuous wavelet transform on the analyzed signal, calculate the wavelet coefficients, and plot their time-scale distribution, as shown in the attached figure. Figure 6 As shown in the figure, the effective region with a time range of [16 s, 24 s] and a scale range of [53.8, 3224.4] is selected. An inverse continuous wavelet transform is performed on the selected wavelet coefficients to obtain the curvature influence line in the time domain, as shown in the attached figure. Figure 7 As shown in the figure. The results show that the extracted curvature influence lines exhibit a typical triangular distribution, with their peak positions coinciding with the placement of the accelerometer and closely matching the theoretical curvature influence lines, thus verifying the accuracy of the extracted results.

[0046] Furthermore, by varying the bridge surface roughness, the same vehicle was used to pass over the bridge under 100 different roughness conditions, resulting in 100 curvature influence lines. The average curvature influence line of these lines was then taken as the average curvature influence line for the bridge. To verify the damage localization effect, an undamaged bridge was assumed to be the baseline bridge, and the bridge under test was assumed to be damaged with a 20% reduction in elastic modulus within one unit length at position D1. The average curvature influence lines for the baseline bridge and the bridge under test were calculated separately, and the results are attached. Figure 8 As shown in (a) and (b).

[0047] The damage index of the curvature influence line was calculated according to equation (5), and the results are shown in the appendix. Figure 9 As shown in the figure, the damage index exhibits a significant peak at approximately 30 m longitudinally along the bridge, corresponding to damage location D1, while the index values ​​at other locations are lower, indicating that the damage index proposed in this invention can accurately locate the bridge damage location.

[0048] In summary, the bridge damage localization method proposed in this invention, which extracts curvature influence lines from acceleration response based on continuous wavelet transform, can achieve efficient extraction of frequency domain information and flexible adjustment of threshold while maintaining the integrity of curvature influence line features. This significantly improves the accuracy and computational efficiency of damage identification and has good prospects for engineering applications.

[0049] The above embodiments are only used to illustrate the technical principles and implementation methods of the present invention, and are not intended to limit the present invention. Adjustments and optimizations made to different bridge types, sensor deployment methods, damage locations, vehicle load conditions, or signal processing parameters without departing from the essential content of the technical solution of the present invention are all equivalent technical solutions of the present invention and should be protected by the present invention.

Claims

1. A method for extracting bridge curvature influence lines and locating damage based on continuous wavelet transform, characterized in that, include: Accelerometers pre-placed on the monitoring sections of the bridge under test are used to collect the acceleration response signals of the bridge when a vehicle load passes over it. The time interval for crossing the bridge is determined based on the time when vehicles enter and exit the bridge. A standard signal is extracted from the acceleration response signal based on the bridge crossing time interval; The standard signal is preprocessed to obtain the analysis signal; Perform continuous wavelet transform on the analyzed signal to obtain the distribution map of wavelet coefficients on the time-scale plane; The effective time range is determined based on the time of entry and exit of vehicles crossing the bridge. Based on the effective time range and the predetermined effective scale range, the corresponding effective area is selected from the distribution map and subjected to inverse continuous wavelet transform to reconstruct the bridge curvature influence line that characterizes the relationship between the vehicle load application location and the curvature response of the monitoring section. Using an accelerometer at the same monitoring section, the acceleration response signals of the same vehicle crossing the bridge at different bridge surface roughnesses were collected, and the bridge curvature influence lines were extracted respectively. The average curvature influence line was obtained by taking the mean value. Damage indices are calculated by comparing the average curvature influence lines of the benchmark bridge and the bridge under test, and the damage location of the bridge under test is determined based on the peak position of the damage indices.

2. The method for extracting bridge curvature influence lines and locating damage based on continuous wavelet transform according to claim 1, characterized in that, The times when vehicles cross the bridge are on and off the bridge are determined by the laser rangefinder.

3. The method for extracting bridge curvature influence lines and locating damage based on continuous wavelet transform according to claim 1, characterized in that, The preprocessing of the standard signal to obtain the analysis signal includes: A copy of the standard signal is made, the sign is reversed, and time-mirrored extension is performed. This copy is then spliced ​​with the original standard signal to form an extended signal. The extended signal has zero values ​​at both ends. The extended signal is further copied three times to obtain the analysis signal.

4. The method for extracting bridge curvature influence lines and locating damage based on continuous wavelet transform according to claim 1, characterized in that, The expression for performing continuous wavelet transform on the analyzed signal is as follows: In the formula, ψ * ( t ) is the wavelet mother function ψ ( t The complex conjugate of ); b It is a translation factor over time; s The scaling factor is represented by the center frequency of the wavelet mother function. Inversely proportional; It involves analyzing signals; These are the calculated wavelet coefficients, used for time-frequency analysis of the signal; It is a unit step function, where Indicates angular frequency; It is the normalization constant, where It is the time-bandwidth product. The parameter is used to characterize the symmetry of the generalized Morse wavelet function.

5. The method for extracting bridge curvature influence lines and locating damage based on continuous wavelet transform according to claim 4, characterized in that, The expression for selecting the corresponding effective region from the distribution map and performing inverse continuous wavelet transform is: In the formula, and These represent the lower and upper limits of the valid time range, respectively. and These correspond to the minimum and maximum scales within the effective scale range, respectively. The minimum scale is the scale corresponding to the first-order frequency of the bridge, and the maximum scale is the scale corresponding to the preset minimum allowable frequency. Indicates the monitoring section.

6. The method for extracting bridge curvature influence lines and locating damage based on continuous wavelet transform according to claim 5, characterized in that, The expression for determining the effective time range based on the entry and exit times of vehicles crossing the bridge is as follows: In the formula, and These represent the times when vehicles enter and exit the bridge, respectively.

7. The method for extracting bridge curvature influence lines and locating damage based on continuous wavelet transform according to claim 5, characterized in that, The expression for the mean curvature influence line is: In the formula, This indicates the total number of times vehicles crossed the bridge; Indicates the first Secondary use The influence line of bridge curvature is extracted from the acceleration response signal collected by the acceleration sensor at the monitoring section.

8. The method for extracting bridge curvature influence lines and locating damage based on continuous wavelet transform according to claim 7, characterized in that, The expression for the damage index is: in, and These represent the average curvature influence line and the reference curvature influence line obtained from the current test of the bridge under test, respectively.

9. The method for extracting bridge curvature influence lines and locating damage based on continuous wavelet transform according to claim 8, characterized in that, The reference bridge shall be any of the following: Undamaged bridges before they are opened to traffic after completion; The bridge under test in the previous test, and the preset time interval between the previous test and this test.

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