A method for identifying bridge structural damage using a test vehicle based on synchronization theory

Abstract

This invention belongs to the field of bridge structure damage identification technology, specifically involving a method for identifying bridge structure damage using a test vehicle based on synchronization theory. The method includes the following steps: Step 1: Install two sensors on the middle of the two axles of a test vehicle. This test vehicle can be any existing type of traffic vehicle or a self-designed vehicle. Step 2: The test vehicle passes over the bridge under test at a constant speed, simultaneously collecting the acceleration response signals of the front and rear axles until the test vehicle completely leaves the bridge. Step 3: Filter the obtained signals to obtain the nth-order mode shape response signal. Step 4: Cluster the front and rear axle acceleration signals of the test vehicle according to the measurement point values ​​required by synchronization theory using a clustering method. Step 5: Calculate the required mode shape using the clustered measurement point values ​​according to synchronization theory. Step 6: Perform stiffness inversion on the obtained nth-order frequency and mode of the bridge using an improved direct stiffness method to identify the cross-sectional bending stiffness of each unit node.

Description

Technical Field

[0001] This invention belongs to the field of bridge structure damage identification technology, specifically relating to a method for identifying bridge structure damage using a test vehicle based on synchronization theory. Background Technology

[0002] my country has a long history of bridge construction, with its building materials, construction methods, and application scenarios maturing and improving alongside the progress of Chinese civilization. While enjoying the convenience and economic growth brought about by the large-scale expansion of bridge construction, it is equally important to pay attention to the structural safety hazards posed by the increasing number of aging bridges in service. The integration of rapid bridge health detection, damage assessment, and subsequent reinforcement scheme design has become a research hotspot for scholars and experts. Bridge health detection and assessment systems possess considerable potential for theoretical research and technological development. Based on the ability to identify vibration signals in bridge dynamic effect analysis, excitation sources can be divided into environmental excitation sources and artificial excitation sources. The key to time-frequency domain modal identification methods under environmental excitation lies in the identification and collection of output signals. Previous bridge health monitoring methods required the deployment of numerous sensors on the bridge structure to obtain response data from operational bridge structures; this method is known as the direct measurement method. This method boasts advantages such as simplicity, directness, and high measurement accuracy. Furthermore, after years of research, numerous modal identification methods have emerged, including frequency domain decomposition, random subspace methods, Hilbert-Huang transform methods, time series methods, modal identification methods based on blind source separation theory, and modal analysis methods based on Bayesian theory, among others. Using modal identification methods to infer the safety state of a structure does not require interrupting its normal use, making it possible to conduct condition assessments of civil engineering structures during normal service, which has significant research and engineering value.

[0003] However, direct measurement methods still have many shortcomings: such as long testing cycles, high economic and labor costs, and traffic disruption. Meanwhile, existing traditional modal identification methods also have the following drawbacks: frequency domain decomposition methods lack theoretical refinement, and damping identification requires inverse Fourier transform, implemented in the time domain through exponential decay, which is affected by truncation errors, resulting in low accuracy; random subspace methods have slow computation speeds, are time-consuming, have high hardware requirements, and lack concise explicit expressions; the Hilbert-Huang transform method requires complex recursions, and its computation time is actually longer than the short-time Fourier transform, making it unsuitable for the Fast Fourier Transform (FFT). The Hilbert-Huang transform is faster only in special cases (combining relatively simple data), and it also lacks concise explicit expressions. Time series methods and blind source separation also suffer from long computation times and lack concise explicit expressions.

[0004] In summary, most existing structural modal identification methods suffer from serious problems such as low efficiency, limited applicability, and lack of a concise explicit expression related to the modality. These problems severely hinder the efficiency and accuracy of bridge structural damage identification. Summary of the Invention

[0005] To address the aforementioned shortcomings in existing technologies, this invention proposes a method for identifying bridge structural damage using a test vehicle based on synchronization theory. This method can significantly reduce the number of signal sampling points and requires only a small number of sensors to obtain bridge modes. Furthermore, the use of a test vehicle to collect bridge modes improves the efficiency of bridge mode identification, thereby significantly enhancing the efficiency and accuracy of bridge structural damage identification.

[0006] To solve the above-mentioned technical problems, the present invention adopts the following technical solution:

[0007] A method for identifying bridge structural damage using a test vehicle based on synchronization theory includes the following steps:

[0008] Step 1: Install two sensors on the middle of the two axles of a test vehicle. This test vehicle can be any existing type of transportation vehicle or a self-designed vehicle.

[0009] Step 2: The test vehicle passes over the bridge under test at a constant speed, and the acceleration response signal is collected simultaneously until the test vehicle has completely left the bridge.

[0010] Step 3: Filter the obtained signal to obtain the mode response signal of a certain nth order.

[0011] Step 4: Cluster the acceleration signals of the front and rear wheels of the test vehicle according to the measurement point values ​​required by the synchronization theory.

[0012] Step 5: Calculate the required vibration modes using the measurement point values ​​obtained from clustering according to the synchronization theory.

[0013] Step 6: For the obtained nth-order frequency and mode of the bridge, the improved direct stiffness method is used to perform stiffness inversion in order to identify the cross-sectional bending stiffness of each element node.

[0014] Furthermore, in steps one and two, the test vehicle passes through the bridge under test at a constant speed, and the equations of motion for the bridge structure and the test vehicle can be expressed as follows:

[0015]

[0016]

[0017] In the formula: These represent the vertical acceleration and displacement of the test vehicle, respectively; u(x,t) represents the vertical displacement of the bridge. for To obtain the partial derivative with respect to time; u″″(x,t) is To obtain the partial derivative with respect to displacement; δ, x, and t are the Diclave function, horizontal displacement, and time of action, respectively; Assuming the bridge has uniform mass, F(t) represents the load application function, which in this case indicates two discrete moving loads acting on the beam. H(.) represents the unit step function, and the remaining parameters are defined as follows:

[0018]

[0019] Here, t represents the travel time, L is the bridge length, v represents the vehicle speed, and m is the speed of the vehicle. v Let g be the mass of the vehicle body, g be the acceleration due to gravity, t' be the time it takes for a single axle to travel across the entire bridge, t' be the position of the kth axle to the center of gravity of the vehicle, as shown in the figure; and t' be the time it takes for the kth wheel to enter the bridge.

[0020] Furthermore, in steps three and four, the obtained bridge signals are solved using the modal superposition method, and the vertical displacement of the bridge can be expressed as:

[0021]

[0022] Where, φ n Y represents the nth vibration mode of the bridge. n (t) represents the generalized coordinates corresponding to the nth vibration mode. For a simply supported beam, its vibration mode is sin(nπx / L). Therefore, by filtering the signal to the kth frequency, only the kth frequency signal is obtained. The n signals collected from the front and rear axles at a certain vehicle distance (2m in this example) and a certain vehicle speed (2m / s in this example), after being filtered to a certain frequency, can be expressed by formula (4):

[0023]

[0024]

[0025] Where, φ kn The mode shape value at the nth point of the kth order mode, Y k(t1) The generalized coordinates corresponding to the vibration mode at time t1 of order k.

[0026] Analysis of the test vehicle's movement reveals, as shown in the diagram below, that both the front and rear wheels of the test vehicle successively pass through the same point, t in the diagram. a This indicates a specific moment after the revolver enters the bridge. △ t represents the ratio of the vehicle's length to its speed, which is the time required for the test vehicle to travel the same distance as the vehicle's length.

[0027] From formulas (5) and (6), it can be seen that the ratio of the two wheel axle signals at the same moment is And this time is separated by a car distance. △ t (taking 100s as an example) also has By analogy, the time required to travel one car length along the bridge can be obtained. △ mode ratio of t Observations show that, based on the existence of mode shape components at the same time for two adjacent components, a certain mode shape value can be assumed, and these points can be obtained and normalized to obtain the desired bridge mode shape. The above method is called the synchronous theory for acquiring bridge modal information through bridge motion. At the same time, in order to obtain a more accurate bridge mode shape, when comparing the ratio of two wheel axle signals at the same time, various clustering methods (such as statistical moment clustering and least squares clustering) are used to cluster the signals at the same time.

[0028] By synchronously moving the test vehicle until the information of the entire bridge is obtained, the nth order mode of the bridge structure is finally obtained. Using the obtained nth order bridge mode, the stiffness of the bridge unit nodes is obtained by the improved direct stiffness method. The basic principle is to use the central difference method to obtain the modal curvature of the test mode, and at the same time, the mode is understood as the displacement vector generated by the modal inertial force. Then, the modal bending moment and modal curvature at the corresponding test mode and the corresponding frequency are obtained. The stiffness of the bridge nodes is then obtained by Equation (5) to achieve the purpose of stiffness identification.

[0029]

[0030] Where EI represents the flexural stiffness of the cross section. Let M represent the nth mode of the bridge, M be the section bending moment, and v” be the modal curvature.

[0031] Furthermore, the number of sensors is at least two.

[0032] Furthermore, the method described in step three requires filtering the collected acceleration response to include only the nth-order vertical acceleration mode response of the structure.

[0033] Furthermore, the above method requires comparing the structural signals at different positions of the vehicle inspection location and at the same time at a fixed position.

[0034] Furthermore, the method requires comparing the structural signals at different measuring point locations and at the same fixed measuring point location at the same time.

[0035] Furthermore, the clustering method is least squares or statistical moments.

[0036] Compared with the prior art, the present invention has at least the following advantages:

[0037] 1. This invention improves the problem of the time-consuming and laborious process of obtaining structural health status using a large number of sensors. It can obtain the modal information of each order required by the structure with only two sensors, which greatly reduces the number of sensors required.

[0038] 2. After filtering the nth order frequency, the ratio of the nth order mode components of the front and rear wheels of the test vehicle at a certain moment is the ratio of the standard modes of the two positions of the bridge at that order mode. Furthermore, the ratio of the mode component signals of the two axles at a time Δt, which is one vehicle distance apart along the bridge, both have the same mode shape at the same time.

[0039] 3. This invention has a concise explicit relationship, making the logic clearer and more understandable, thus improving the serious problem that other methods do not have a concise explicit expression related to the modality;

[0040] 4. The present invention uses a test vehicle to collect signals, which is convenient and fast, and can greatly improve the efficiency of bridge damage identification. Attached Figure Description

[0041] Figure 1 This is a schematic diagram of the Liziwan Bridge in an embodiment of a method for identifying bridge structural damage using a test vehicle based on synchronization theory according to the present invention;

[0042] Figure 2 This is a flowchart illustrating the first-order vibration mode identification process of a bridge structure based on synchronization theory using a test vehicle, according to an embodiment of the present invention.

[0043] Figure 3 This is a numerical simulation unit partitioning diagram of an embodiment of the method for identifying bridge structural damage using a test vehicle based on synchronization theory according to the present invention;

[0044] Figure 4 Comparison of bridge damage identified by different methods (4 elements, damage level 30%, ζ) n =0.00);

[0045] Figure 5 Comparison of bridge damage identified by different methods (4 elements, damage level 30%, ζ) n =0.01);

[0046] Figure 6 Comparison of bridge damage identified by different methods (4 elements, damage level 30%, ζ) n =0.02);

[0047] Figure 7 Comparison of bridge damage identified by different methods (4 elements, damage level 30%, ζ) n =0.03);

[0048] Figure 8 Comparison of bridge damage identified by different methods (4 elements, damage level 30%, S) NR =10dB);

[0049] Figure 9 Comparison of bridge damage identified by different methods (4 elements, damage level 30%, S) NR =20dB);

[0050] Figure 10 Comparison of bridge damage identified by different methods (4 elements, damage level 30%, S) NR =30dB);

[0051] Figure 11 Comparison of bridge damage identified by different methods (4 elements, damage level 30%, S) NR =40dB);

[0052] Figure 12 This is a schematic diagram of the coupling effect between a two-axle asymmetric vehicle and a bridge in an embodiment of a method for identifying bridge structural damage using a test vehicle based on synchronization theory according to the present invention.

[0053] Figure 13 This is a diagram of the motion trajectory of a test vehicle in an embodiment of a method for identifying bridge structural damage using a test vehicle based on synchronization theory according to the present invention. Detailed Implementation

[0054] To enable those skilled in the art to better understand the present invention, the technical solution of the present invention will be further described below in conjunction with the accompanying drawings and embodiments.

[0055] A method for identifying bridge structural damage using a test vehicle based on synchronization theory, characterized by the following steps:

[0056] Step 1: Install two sensors on the middle of the two axles of a test vehicle. This test vehicle can be any existing type of transportation vehicle or a self-designed vehicle.

[0057] Step 2: The test vehicle passes over the bridge under test at a constant speed, and the acceleration response signals of the front and rear axles are collected simultaneously until the test vehicle has completely left the bridge.

[0058] Step 3: Filter the obtained signal to obtain the mode response signal of the nth order.

[0059] Step 4: Cluster the acceleration signals of the front and rear wheels of the test vehicle according to the measurement point values ​​required by the synchronization theory;

[0060] Step 5: Calculate the required nth mode shape using the clustered measurement point values ​​according to synchronization theory;

[0061] Step 6: For the obtained nth-order frequency and mode of the bridge, the improved direct stiffness method is used to perform stiffness inversion in order to identify the cross-sectional bending stiffness of each element node.

[0062] In steps one and two, the test vehicle passes through the bridge under test at a constant speed. The equations of motion for the bridge structure and the test vehicle can be expressed as follows:

[0063]

[0064]

[0065] In the formula: These represent the vertical acceleration and displacement of the test vehicle, respectively; u(x,t) represents the vertical displacement of the bridge. for To obtain the partial derivative with respect to time; u″″(x,t) is To obtain the partial derivative with respect to displacement; δ, x, and t are the Diclave function, horizontal displacement, and time of action, respectively; Assuming the bridge has uniform mass, F(t) represents the load application function, which in this case represents two discrete moving loads acting on the beam. H(.) represents the unit step function, and the remaining parameters are defined as follows:

[0066]

[0067] Here, t represents the travel time, L is the bridge length, v represents the vehicle speed, and m is the speed of the vehicle. v Let g be the mass of the vehicle body, g be the acceleration due to gravity, t' be the time it takes for a single axle to travel across the entire bridge, and p be the acceleration due to gravity. k This represents the position of the k-th axle relative to the vehicle's center of gravity; t k This indicates the time when the k-th wheel enters the bridge.

[0068] In steps three and four, the obtained bridge signals are solved using the modal superposition method, and the vertical displacement of the bridge can be expressed as:

[0069]

[0070] Where, φ n Y represents the nth vibration mode of the bridge. n (t) is the generalized coordinate corresponding to the nth vibration mode. Since the vibration mode of a simply supported beam is sin(nπx / L), after filtering the signal to the kth frequency, only the kth signal is obtained. The n signals collected from the front and rear axles of the test vehicle at a certain distance and speed can be expressed by formula (4) after filtering to a certain frequency:

[0071]

[0072]

[0073] Where, φ kn The mode shape value at the nth point of the k-th mode shape. The generalized coordinates corresponding to the vibration mode at time t1 of order k.

[0074] Analysis of the test vehicle's movement reveals that both the front and rear wheels will successively pass through the same point, as shown in the diagram t. a This indicates a specific moment after the revolver enters the bridge. △ t represents the ratio of the vehicle's length to its speed, that is, the time required for the test vehicle to travel the same distance as its body length.

[0075] From formulas (5) and (6), it can be seen that the ratio of the two wheel axle signals at the same moment is And this time is separated by a car distance. △ t also has By analogy, the time required to travel one car length along the bridge can be obtained. △ mode ratio of t Observations show that, based on the existence of mode shape components at the same time for two adjacent components, a certain mode shape value can be assumed. By obtaining these points and normalizing them, the desired bridge mode shape can be obtained. This method is called the synchronous theory for acquiring bridge modal information through bridge motion. Furthermore, to obtain more accurate bridge mode shapes, various clustering methods are used to cluster the signals at the same time when comparing the ratio of two wheel axle signals at the same moment.

[0076] By synchronously moving the test vehicle until the information of the entire bridge is obtained, the nth-order mode of the bridge structure is finally obtained. Using the obtained nth-order bridge mode, the stiffness of the bridge unit nodes is obtained through the improved direct stiffness method. The basic principle is to use the central difference method to obtain the modal curvature of the test mode, and at the same time, the mode is understood as the displacement vector generated by the modal inertial force. Then, the modal bending moment and modal curvature at the corresponding test mode and the corresponding frequency are obtained. The stiffness of the bridge nodes is then obtained through equation (7) to achieve the purpose of stiffness identification.

[0077]

[0078] Where EI represents the flexural stiffness of the cross section. Let M represent the nth mode of the bridge, M be the section bending moment, and v” be the modal curvature.

[0079] The number of sensors is at least two.

[0080] Step three requires filtering the collected acceleration response to include only the first-order vertical acceleration mode component of the structure. The clustering method used is least squares and statistical moments.

[0081] 1. Theoretical Foundation

[0082] 1.1 Theoretical Derivation

[0083] A test vehicle equipped with sensors on its front and rear axles passes over the bridge under test at a constant speed. The equations of motion for the bridge structure and the test vehicle can be expressed as follows:

[0084]

[0085]

[0086] In the formula: These represent the vertical acceleration and displacement of the test vehicle, respectively; u(x,t) represents the vertical displacement of the bridge. for To obtain the partial derivative with respect to time; u″″(x,t) is To obtain the partial derivative with respect to displacement; δ, x, and t are the Diclave function, horizontal displacement, and time of action, respectively; Assuming the bridge has uniform mass, F(t) represents the load application function, which in this case indicates two discrete moving loads acting on the beam. H(.) represents the unit step function, and the remaining parameters are defined as follows:

[0087]

[0088] Here, t represents the travel time, L is the bridge length, v represents the vehicle speed, and m is the speed of the vehicle. v Let g be the mass of the vehicle body, t' be the acceleration due to gravity, t' be the time it takes for a single axle to cross the entire bridge, and t' represent the position of the k-th axle relative to the vehicle's center of gravity. Figure 12 As shown; this indicates the time when the k-th wheel enters the bridge.

[0089] The vertical displacement of the bridge can be expressed as follows: The obtained bridge signal is solved using the modal superposition method.

[0090]

[0091] Where, φ n Y represents the nth vibration mode of the bridge. n (t) represents the generalized coordinates corresponding to the nth vibration mode. For a simply supported beam, the vibration mode is sin(nπx / L). Therefore, by filtering the signal to the kth frequency, only the kth frequency signal is obtained. The n signals collected from the front and rear axles of the test vehicle at a certain distance (2m in this example) and a certain speed (2m / s in this example), after being filtered to a certain frequency, can be expressed by formula (4):

[0092]

[0093]

[0094] Where, φ kn The mode shape value at the nth point of the k-th mode shape. The generalized coordinates corresponding to the vibration mode at time t1 of order k.

[0095] Analysis of the test vehicle's movement process reveals that, for example Figure 13 As shown, the front and rear wheels of the test vehicle will successively pass through the same point, t in the figure. a This indicates a specific moment after the revolver enters the bridge. △ t represents the ratio of the vehicle's length to its speed, which is the time required for the test vehicle to travel the same distance as the vehicle's length.

[0096] From formulas (5) and (6), it can be seen that the ratio of the two wheel axle signals at the same moment is And this time is separated by a car distance. △ t (taking 100s as an example) also has By analogy, the time required to travel one car length along the bridge can be obtained. △ mode ratio of t Observations show that, based on the existence of mode shape components at the same time for two adjacent components, a certain mode shape value can be assumed, and these points can be obtained and normalized to obtain the desired bridge mode shape. The above method is called the synchronous theory for acquiring bridge modal information through bridge motion. At the same time, in order to obtain a more accurate bridge mode shape, when comparing the ratio of two wheel axle signals at the same time, various clustering methods (such as statistical moment clustering and least squares clustering) are used to cluster the signals at the same time.

[0097] By synchronously moving the test vehicle until the information of the entire bridge is obtained, the nth order mode of the bridge structure is finally obtained. Using the obtained nth order bridge mode, the stiffness of the bridge unit nodes is obtained by the improved direct stiffness method. The basic principle is to use the central difference method to obtain the modal curvature of the test mode, and at the same time, the mode is understood as the displacement vector generated by the modal inertial force. Then, the modal bending moment and modal curvature at the corresponding test mode and the corresponding frequency are obtained. The stiffness of the bridge nodes is then obtained by Equation (5) to achieve the purpose of stiffness identification.

[0098]

[0099] Where EI represents the flexural stiffness of the cross section. Let M represent the nth mode of the bridge, M be the section bending moment, and v” be the modal curvature.

[0100] 1.2 Bridge Structural Damage Identification Process

[0101] Considering that the identification of the first-order vibration mode is the easiest and relatively accurate method for testing civil engineering structures, the process for identifying the first-order vibration mode of a bridge using the method of this invention is as follows: Figure 2 As shown, the clustering method used in this paper is least squares clustering.

[0102] 2 Numerical Simulation

[0103] Model of Liziwan Bridge on the Chongqing Fuling-Xiamen-Chengdu Railway. A schematic diagram of the bridge is shown below. Figure 1 As shown, the bridge has a span of 30m, uses C50 concrete with an elastic modulus of E = 32.5 GPa, and a moment of inertia of 0.79m. 4 .

[0104] The numerical simulation used a 3m spacing between different measuring points. The bridge was divided into 10 equally spaced units, as shown in the schematic diagram of the unit division. Figure 3 As shown, each rectangular block represents a different unit of the bridge and is represented by a circled number. For example, the third unit is represented by "③". The numbers 0 to 10 are the unit node numbers, which are the bridge measurement point numbers. In this example, all 4 units under all working conditions are set with 30% damage.

[0105] The test vehicle was driven across the full bridge at a constant speed, according to... Figure 2 The flowchart shown calculates the bending stiffness of the bridge.

[0106] In the damage identification process, the influence of factors such as bridge damping ratio and environmental noise cannot be ignored. The numerical simulation section will use the method of this invention, the random subspace method, and the Hilbert-Huang transform method for mode shape identification, and then use the improved direct stiffness method to identify the bridge stiffness. The influence of the above factors on the identification of bridge mode shape and stiffness will be discussed. Finally, by comparing the errors of the three methods, the characteristics of the method of this invention will be analyzed.

[0107] The Modal Guarantee Criterion (MAC) is used to compare and analyze the differences in the first-order vibration modes proposed by the method in this invention, the random subspace method, and the Hilbert-Huang transform method. The MAC is defined as follows:

[0108]

[0109] 2.1 Study on Bridge Damping Ratio

[0110] For four damping ratio conditions (0.00, no damping, 0.01, 0.02, and 0.03), the bridge vibration mode curves were identified using the method of this invention, the Hilbert-Huang transform method, and the random subspace method. The flexural stiffness of the bridge was then identified using the improved direct stiffness method. The results are compared as follows: Figure 6 , Figure 7 , Figure 8 , Figure 9 As shown in Table 1.

[0111] Table 1. MAC values ​​for mode identification under different methods

[0112]

[0113] As shown in the charts, the mode shapes with MAC values ​​extracted by the method of this invention and the random subspace method are both above 99.9990%, while the mode shape MAC value extracted by the Hilbert-Huang transform method is the lowest at 99.9950%. This indicates that both the method of this invention and the random subspace method can better identify the first-order mode shapes of the bridge structure under the influence of the bridge damping ratio. Furthermore, the diagrams of bridge bending stiffness identification by various methods under different damping ratios when all four elements are set with 30% damage show that the damping ratio has a relatively small impact on the bridge stiffness identification by various methods. Moreover, at the same damping ratio, the method of this invention and the other two methods can all identify damage well.

[0114] 2.2 Impact of Environmental Noise

[0115] In actual data acquisition environments, the impact of environmental noise on signals is unavoidable.

[0116] This section simulates contaminated signals by adding white noise to the signals collected by the test vehicle. The signal-to-noise ratio (SNR) is used as an indicator to judge the intensity of the added noise. The SNR is defined as:

[0117]

[0118] Where N j y represents the total number of data points collected by the test vehicle at the j-th node. ij δ represents the data corresponding to the i-th sampling interval collected by the test vehicle at the j-th node. ij This represents the noisy data corresponding to the i-th sampling interval collected by the test vehicle at the j-th node. From formula (8), it is known that the greater the noise intensity, the higher the signal-to-noise ratio S. NR The smaller it is.

[0119] Bridge damping ratio is taken as ζ n =0.03, set S respectively NR =10, 20, 30, 40 dB, four groups of noise-involved damage conditions, the three methods described in Section 2.1 are still used to identify bridge vibration modes, and the comparison results of vibration mode curves and bridge bending stiffness are as follows. Figure 10 , Figure 11 , Figure 12 , Figure 13 As shown in Table 2.

[0120] Table 2. MAC values ​​for mode identification under different methods

[0121]

[0122] As shown in the figures, environmental noise affects the accuracy of mode shape identification. The Hilbert-Huang transform method has relatively poor accuracy, especially under 10dB noise, where the MAC is only 99.8643%. The proposed method and the random subspace method achieve better results, both exceeding 99.9786%. Furthermore, the method presented in this paper demonstrates superior noise immunity compared to the other two methods when all four elements are at 30% damage, based on various noise conditions. It is worth noting that the random subspace-based mode shape identification method is more complex and computationally inefficient, while the proposed method based on time-series synchronization theory is simpler and more computationally efficient. Table 3 shows the computational time efficiency of the proposed method and the random subspace method for mode shape extraction under different influences.

[0123] Table 3. Mode identification efficiency under the influence of different factors.

[0124]

[0125] 3. Conclusion

[0126] Further analysis of the feasibility of the method of the present invention through numerical simulation yielded the following conclusions:

[0127] (1) Through theoretical derivation and numerical simulation research and analysis, it has been fully demonstrated that the method proposed in this invention can better identify bridge vibration modes and further identify bridge damage;

[0128] (2) The present invention considers the influence of bridge damping ratio and environmental noise in the numerical simulation part. The research results show that compared with Hilbert Huang method and random subspace method, the method proposed in this invention can adapt well to the change of bridge damping ratio and has strong anti-noise ability.

[0129] (3) The method of the present invention can be used for rapid detection, monitoring and evaluation of bridges. Compared with traditional mode shape and damage analysis methods, the mode shape extracted by the method of the present invention has great advantages in terms of accuracy, efficiency, convenience and economy, and provides a new method for rapid identification of various structural damages.

[0130] (4) Furthermore, this method improves upon the time-consuming and laborious problem of requiring numerous sensors to obtain structural health status. It only requires two sensors to obtain the necessary modal information for each order of the structure, significantly reducing the number of sensors needed. This theory posits that after filtering the nth order frequency, the ratio of the nth order mode shape components of the front and rear wheels of the test vehicle at a given moment is the ratio of the standard modes of that mode shape at two locations on the bridge. Moreover, the ratio of the mode shape component signals of the two axles separated by a vehicle distance Δt along the bridge both exhibit the same mode shape at the same time. This method possesses a concise explicit relationship, making the logic clearer and more understandable, thus overcoming the serious problem of other methods lacking a concise explicit expression related to the mode shape.

[0131] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the technical solutions of the present invention, and all such modifications or substitutions should be covered within the scope of the claims of the present invention.

Claims

1. A method for identifying bridge structural damage using a test vehicle based on synchronization theory, characterized in that, Includes the following steps: Step 1: Install two sensors on the middle of the two axles of a test vehicle. The test vehicle can be a current type of transportation vehicle or a self-designed vehicle. Step 2: The test vehicle passes over the bridge under test at a constant speed, and the acceleration response signal is collected simultaneously until the test vehicle has completely left the bridge. Step 3: Filter the obtained signal to obtain the mode response signal of the nth order. Step 4: Cluster the acceleration signals of the front and rear wheels of the test vehicle according to the measurement point values ​​required by the synchronization theory; Step 5: Calculate the required nth mode shape using the clustered measurement point values ​​according to synchronization theory; Step 6: For the obtained nth-order frequency and mode of the bridge, the improved direct stiffness method is used to perform stiffness inversion in order to identify the cross-sectional bending stiffness of each element node. In steps three and four, the obtained bridge signals are solved using the modal superposition method, and the vertical displacement of the bridge is expressed as: （4） in, For the bridge's first n First vibration mode, For the first n The generalized coordinates corresponding to the first vibration mode, because, for a simply supported beam, its vibration mode is... Therefore, by filtering the signal... k After the first frequency, only the first frequency is present in the obtained signal. k The step signal will be collected from the front and rear axles at certain vehicle intervals and speeds. n The signal, after being filtered to a certain frequency, can be expressed by formula (4): (5) （6） in, No. k First mode of vibration n Vibration mode values ​​at each point location, No. k Step t The generalized coordinates corresponding to the vibration mode at time 1; Analysis of the test vehicle's movement process shows that the front and rear wheels of the test vehicle will successively pass through the same points; From formulas (5) and (6), it can be seen that the ratio of the two wheel axle signals at the same moment is And a car-distance time interval from that moment △ t At the same time, there are also By analogy, we can obtain the time required to travel one car length along the bridge. △ t mode ratio Observations show that, based on the existence of mode shape components at the same time for two adjacent components, a certain mode shape value can be assumed. By obtaining these points and normalizing them, the desired bridge mode shape can be obtained. This method is called the synchronous theory for acquiring bridge modal information through bridge motion. Furthermore, to obtain more accurate bridge mode shapes, when calculating the ratio of two wheel axle signals at the same time, a clustering method is used to cluster the signals at the same time. By synchronously moving the test vehicle until information about the entire bridge is obtained, the final result of the bridge structure is determined. n The first mode, using the obtained first mode n The bridge unit node stiffness is obtained through an improved direct stiffness method. The basic principle is to obtain the modal curvature by using the central difference method for the test mode, and to understand the mode as the displacement vector generated by the modal inertial force. Then, the modal bending moment and modal curvature at the corresponding test mode and the corresponding frequency are obtained. The bridge node stiffness is then obtained through equation (7) to achieve the purpose of stiffness identification. （7） in, EI Indicates the bending stiffness of the cross section. Indicates the bridge's first n First mode, M The bending moment of the section, For modal curvature.

2. The method for identifying bridge structural damage using a test vehicle based on synchronization theory according to claim 1, characterized in that: In steps one and two, the test vehicle passes through the bridge under test at a constant speed. The equations of motion for the bridge structure and the test vehicle are as follows: （1） （2） In the formula: This represents the vertical displacement of the bridge. for To obtain the partial derivative with respect to time; for To obtain the partial derivative with respect to the displacement; , x and t For Diclave function, horizontal displacement, and time of action; To ensure uniform mass of the bridge, This represents the load application function, which in this case indicates that two discrete moving loads are acting on the beam. This represents the unit step function, and the definitions of the remaining parameters are as follows: （3） here t Indicates travel time. L The length of the bridge. v Indicates vehicle speed. For vehicle body mass, It is the acceleration due to gravity. p is the time it takes for a single axle to travel across the entire bridge. k Indicates the first k The position of each wheel axle from the vehicle's center of gravity; t k Indicates the first k The time it takes for each wheel to enter the bridge.

3. The method for identifying bridge structural damage using a test vehicle based on synchronization theory according to claim 1, characterized in that: In step three, the collected acceleration response needs to be filtered to include only the first-order vertical acceleration mode response of the structure.

4. The method for identifying bridge structural damage using a test vehicle based on synchronization theory according to claim 1, wherein... The characteristic is that the clustering method is least squares and statistical moments.

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