Bridge damage identification method, system, device and medium of multi-scale gaussian filtering residual

Abstract

This invention discloses a bridge damage identification method, system, electronic device, and storage medium based on multi-scale Gaussian filter residuals. The bridge damage identification method comprises the following steps: acquiring displacement response data of a simply supported beam of the bridge under test under moving load; performing principal component analysis (PCA) on the displacement response data and extracting key principal components using cumulative contribution rate (CCR); using a moving average filter (MAF) to filter out the high-frequency components in the dynamic components and obtaining low-frequency damage mode shapes; then using a Gaussian filter (GF) to simultaneously eliminate high-frequency dynamic components and most of the modal abrupt changes caused by damage, i.e., using a Gaussian function as a weighting kernel to reduce noise in the signal; and by analyzing the filtering residuals of the two filters, introducing an exponential function to amplify local peak values, effectively extracting damage features, thereby completing the structural damage identification and determining its specific location.

Description

Technical Field

[0001] This invention belongs to the field of bridge damage location and identification technology, specifically relating to a bridge damage identification method, system, electronic device, and storage medium based on multi-scale Gaussian filter residuals. Background Technology

[0002] Among various structural health monitoring technologies, vibration-based damage detection is a field currently under extensive research. This method detects and locates structural damage by analyzing changes in vibration-based characteristics, and can be broadly categorized into three types: time-domain methods, time-frequency domain methods, and frequency-domain methods. Time-domain methods analyze the instantaneous response of a structure under external loads, while time-frequency domain methods integrate both time and spectral information, providing a comprehensive characterization of the structure's dynamic behavior. However, both time-domain and time-frequency domain methods remain sensitive to noise and external excitations. Moreover, their damage indices often fluctuate under different load conditions, which may affect the reliability of the detection. Furthermore, frequency-domain methods detect damage by identifying shifts in modal parameters derived from the vibration response spectrum, but they also face significant challenges in practical engineering applications.

[0003] To address the shortcomings of these three types of methods, recent research has explored damage identification methods using high-resolution mode shapes, which are generally categorized into baseline-based and baseline-free methods. Despite significant progress in this area, two major limitations remain. First, in-service structures often lack complete baseline data, which is often unavailable in practice. Therefore, the applicability of baseline-based methods in real-world engineering scenarios is greatly limited. Second, while baseline-free methods eliminate the need for reference data, they typically rely on idealized assumptions that may not hold under complex real-world conditions or involve additional computational complexity, thus affecting their practical feasibility.

[0004] Therefore, there is a need for an engineering-reliable, easy-to-implement, and cost-effective method for applying to medium- and short-span bridges. To meet this need, it is necessary to develop a bridge damage identification method based on multi-scale Gaussian filter residuals. Summary of the Invention

[0005] The main objective of this invention is to overcome the shortcomings and deficiencies of the prior art and provide a bridge damage identification method, system, electronic device, and storage medium based on multi-scale Gaussian filter residuals.

[0006] To achieve the above objectives, the present invention adopts the following technical solution:

[0007] In a first aspect, the present invention provides a bridge damage identification method based on multi-scale Gaussian filter residuals, comprising the following steps:

[0008] In a first aspect, the present invention provides a bridge damage identification method based on multi-scale Gaussian filter residuals, comprising the following steps:

[0009] S1. Arrange 7 ≥ M ≥ 2 displacement sensors at equal intervals on the bridge to be tested. Obtain the displacement response of the bridge under a uniform vehicle load using the displacement sensors. Assume the time it takes for the vehicle to pass over the bridge is t, and the sampling frequency of the displacement sensors is f. s That is, to collect displacement response signals x of length K from M displacement sensors respectively. km x km Let represent the displacement response signal of the m-th displacement sensor at the k-th sampling time, where k = 1, 2, ..., K, m = 1, 2, ..., M, and obtain the displacement response matrix. , ;

[0010] S2, Regarding the displacement response matrix Principal component analysis was performed to obtain the modal components. and dynamic component The principal component matrix G is formed by linear superposition, i.e. The order N of the dominant principal component is determined by the cumulative contribution rate (CCR), where Obtain the nth order mode shape components at the kth sampling time. and the nth order dynamic component at the kth sampling time The principal component matrix column vector G is formed by linear superposition. n , ,

[0011] Take the column vectors of the principal component matrix G n As the nth principal component, where n = 1, 2, ..., N, the column vector G of this principal component matrix is... n Used for damage identification;

[0012] S3, convert the column vectors of the principal component matrix G n The nth modal component at the kth sampling time Decomposed into undamaged column vectors and damaged column vector The linear superposition, i.e. ,

[0013] in The nth undamaged mode shape component at the kth sampling time. The local deformation of the nth mode shape at the kth sampling time caused by the damage;

[0014] S4. Use a moving average filter (MAF) to filter out the column vectors of the principal component matrix G. n The nth dynamic component at the kth sampling time Obtain the nth modal components with local damage information at the kth sampling time. ;

[0015] S5. Simultaneously filter out the column vectors of the principal component matrix G using a low-pass Gaussian filter GF. n The nth dynamic component at the kth sampling time and the nth order mode shape components Local deformation of the mode shape caused by the nth order damage at the kth sampling time Obtain the nth modal components without local damage information at the kth sampling time. ;

[0016] S6. The nth modal component with local damage information at the kth sampling time. and the nth order mode shape component without local damage information at the kth sampling time. Calculate the difference to obtain the filter residual. ;

[0017] S7. Filter residual The damage index is obtained by performing an exponential function amplification. μ R For the filter residual The average value.

[0018] Furthermore, in step S1, 7≥M≥2 displacement sensors are arranged at equal intervals on the bridge to be tested. On the one hand, principal component analysis requires displacement response signals obtained from at least two displacement sensors. On the other hand, for small and medium span bridges, no more than 7 displacement sensors are needed, which avoids processing a large amount of complex displacement response data. Compared with the traditional dynamic fingerprint method, which requires a large number of sensors, the cost is reasonably controlled.

[0019] Furthermore, in step S2, the cumulative contribution rate of the first n principal components in the principal component matrix G is calculated. Determine the order N of the dominant principal component, where n = 1, 2, ..., N. At that time, the column vectors of the principal component matrix G n As the nth principal component, the above steps can capture most of the damage information in the original displacement response data, simplify the data processing process, and the processed displacement response data can be used for subsequent filtering and damage identification analysis.

[0020] Furthermore, step S3 is as follows:

[0021] Principal component analysis (PCA) is used to reduce the dimensionality of displacement response data, thereby reducing the amount of data to be calculated and obtaining the column vectors of the principal component matrix. As can be seen from the expression, the column vectors of the principal component matrix G n From the nth order mode shape part With the nth order dynamic component The superposition of these elements has a clear physical meaning, as shown in the expression. The line density of the bridge to be measured. The calculated span of the bridge to be tested is... Let n be the nth natural angular frequency of the bridge under test. Let be the angular frequency of the nth order external excitation. The velocity of the moving load along the length of the structure. For the time-domain function of the moving external load;

[0022] When the bridge under test is in an undamaged state, G n It should include two complete mechanical properties: the bridge's modal vibration mode component and the dynamic component component, that is, the nth order modal vibration mode component at the kth sampling time. and the nth order dynamic component at the kth sampling time Linear superposition, represented as ;

[0023] When the bridge under test is in a damaged state, G n It should include damage identification information after bridge damage; therefore, G n The modal vibration mode is partially decomposed into a linear superposition of the undamaged and damaged parts, that is, the nth order modal vibration mode component at the kth sampling time. Decompose the nth order undamaged mode shape components at the kth sampling time. The local deformation of the nth mode shape at the kth sampling time caused by damage The linear superposition of these is expressed as This step facilitates more precise filtration by the two subsequent filters, improving the intuitiveness and effectiveness of the damage identification process.

[0024] Furthermore, step S4 is as follows:

[0025] Using a moving average filter (MAF) to filter out the column vectors of the principal component matrix G n The nth dynamic component at the kth sampling time Obtain the nth modal components with local damage information at the kth sampling time. This process can be represented as: ,

[0026] in, This represents the filtering operation function of the moving average filter (MAF). The column vector of the principal component matrix at the k-th sampling time. f n Principal component matrix column vector G n The natural frequency. Filtering out dynamic components in this step is to more accurately identify changes in the modal components of the bridge under test. These changes are more sensitive to local damage than the original displacement response signal, which helps in the detection of early damage.

[0027] Furthermore, step S5 is as follows:

[0028] S51. Local deformation of the modal shape caused by the nth-order damage at the kth sampling time. The high-frequency components are filtered out to obtain the nth-order mode shape component without local information at the kth sampling time. , where ε represents the degree of damage retained in the high-resolution mode shape after processing by the low-pass Gaussian filter GF. In order to ensure the accuracy of subsequent calculation of the filter residual, it is necessary to ensure that 1≥ε≥0.

[0029] S52. Using a low-pass Gaussian filter GF to filter out the column vectors of the principal component matrix G. n The nth dynamic component at the kth sampling time and the nth order mode shape components Local deformation of the mode shape caused by the nth order damage at the kth sampling time This process is represented as:

[0030] ,

[0031] In the formula, This represents the GF filtering operation function for a low-pass Gaussian filter, where Gaussian kernel is used. Represented as:

[0032] .

[0033] in Gaussian kernel standard deviation , .

[0034] This step combines a low-pass Gaussian filter (GF) to remove dynamic components and high-frequency components of high-resolution mode shapes. Compared with existing methods that process data using a single filter, this not only preserves the characteristics of local damage to the bridge under test but also enhances the smoothing effect of mode shape components.

[0035] Furthermore, in step S7, the filtered residual... The local peak values ​​are amplified to make the obtained damage indicators more intuitive and effective in locating the damage location; the filter residual is first taken. The average value μR Then, the damage index is obtained by introducing an exponential function. The damage index calculated in this step more easily reveals the location of damage and more prominently displays the degree of damage than other methods, and the process of calculating the damage index only uses... and μ R Two parameters, eliminating the need to rely on adjusting a large number of parameters.

[0036] Secondly, the present invention provides a bridge damage identification system based on multi-scale Gaussian filter residuals, used to execute the aforementioned bridge damage identification method based on multi-scale Gaussian filter residuals, wherein the bridge damage identification system based on multi-scale Gaussian filter residuals includes:

[0037] The displacement response signal acquisition module is used to arrange 7 ≥ M ≥ 2 displacement sensors at equal intervals on the bridge under test. The displacement sensors acquire the displacement response of the bridge under a uniform vehicle load. Assuming the time it takes for the vehicle to pass over the bridge is t, and the sampling frequency of the displacement sensors is f... s That is, to collect displacement response signals x of length K from M displacement sensors respectively. km x km Let represent the displacement response signal of the m-th displacement sensor at the k-th sampling time, where k = 1, 2, ..., K, m = 1, 2, ..., M, and obtain the displacement response matrix. ;

[0038] Principal component analysis module is used to analyze the displacement response matrix. Principal component analysis was performed to obtain the modal components. and dynamic component The principal component matrix G is formed by linear superposition, i.e. The order N of the dominant principal component is determined by the cumulative contribution rate (CCR), where Obtain the nth order mode shape components at the kth sampling time. and the nth order dynamic component at the kth sampling time The principal component matrix column vector G is formed by linear superposition. n Take the column vectors of the principal component matrix G n As the nth principal component, where n = 1, 2, ..., N, the column vector G of this principal component matrix is... n Used for damage identification;

[0039] The modal component decomposition module is used to process the column vectors of the principal component matrix G. n The nth modal component at the kth sampling time Decomposed into undamaged column vectors and damaged column vector The linear superposition of, where The nth undamaged mode shape component at the kth sampling time. The local deformation of the nth mode shape at the kth sampling time caused by the damage;

[0040] The dynamic component filtering module is used to filter out the column vectors G of the principal component matrix using a moving average filter (MAF). n The nth dynamic component at the kth sampling time Obtain the nth modal components with local damage information at the kth sampling time. ;

[0041] The modal component acquisition module is used to simultaneously filter out the column vectors G of the principal component matrix using a low-pass Gaussian filter GF. n The nth dynamic component at the kth sampling time and the nth order mode shape components Local deformation of the mode shape caused by the nth order damage at the kth sampling time Obtain the nth modal components without local damage information at the kth sampling time. ;

[0042] The filter residual acquisition module obtains the nth-order modal components with local damage information at the kth sampling time. and the nth order mode shape component without local damage information at the kth sampling time. Calculate the difference to obtain the filter residual. ;

[0043] The damage index acquisition module processes the filtered residuals. The damage index is obtained by performing an exponential function amplification. , For the filter residual The average value.

[0044] Thirdly, the present invention provides an electronic device, including a processor and a memory for storing a processor-executable program, wherein when the processor executes the program stored in the memory, it implements the above-mentioned bridge damage identification method based on multi-scale Gaussian filter residuals.

[0045] Fourthly, the present invention provides a storage medium storing a program, which, when executed by a processor, implements the above-mentioned bridge damage identification method based on multi-scale Gaussian filter residuals.

[0046] The present invention has the following advantages and beneficial effects compared with the prior art:

[0047] (1) This invention belongs to the data-driven method. It only requires a small amount of sensor displacement data to accurately locate the bridge damage location. It has the advantages of low cost, easy installation and simple maintenance. It is of great significance for establishing a structural health detection system for small and medium span bridges.

[0048] (2) This invention retains the advantages of principal component analysis and uses a combination of two filters, the moving average filter (MAF) and the Gaussian filter (GF), to process the data. This further filters out the high-frequency part of the high-resolution modal shape in the displacement response data after dimensionality reduction by principal component analysis. Compared with existing methods, the calculation results are more accurate and the process is more convenient.

[0049] (3) The exponential function introduced in this invention amplifies the local peak value of the filter residual, thereby improving the effectiveness and intuitiveness of damage identification. The calculation of damage index does not depend on a large number of parameter adjustments. Attached Figure Description

[0050] To more clearly illustrate the technical solutions in the embodiments of this application, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0051] Figure 1 This is a flowchart of the bridge damage identification method based on multi-scale Gaussian filter residuals disclosed in this invention.

[0052] Figure 2 This is a simplified diagram of the bridge model in Example 1;

[0053] Figure 3 This is a diagram showing the single-damage identification results of the combined data from sensors 1 and 7 in Example 1;

[0054] Figure 4 This is a schematic diagram of the simply supported steel beam model in Example 2;

[0055] Figure 5 This is a schematic diagram of the simply supported steel beam in Example 2;

[0056] Figure 6 This is a diagram showing the single-damage identification results of the sensor combination data in Example 2;

[0057] Figure 7 This is a structural block diagram of the bridge damage identification system based on multi-scale Gaussian filter residuals in Embodiment 3 of the present invention;

[0058] Figure 8 This is a structural block diagram of the electronic device in Embodiment 4 of the present invention. Detailed Implementation

[0059] To enable those skilled in the art to better understand the present application, the technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are merely some embodiments of the present application, and not all embodiments. All other embodiments obtained by those skilled in the art based on the embodiments of the present application without creative effort are within the scope of protection of the present application.

[0060] In this application, the reference to "embodiment" means that a specific feature, structure, or characteristic described in connection with an embodiment may be included in at least one embodiment of this application. The appearance of this phrase in various places throughout the specification does not necessarily refer to the same embodiment, nor is it a mutually exclusive, independent, or alternative embodiment. It will be explicitly and implicitly understood by those skilled in the art that the embodiments described in this application can be combined with other embodiments.

[0061] Example 1

[0062] like Figure 1 The flowchart shown is for a bridge damage identification method based on multi-scale Gaussian filter residuals. The beam bridge model used in this embodiment is as follows: Figure 2 As shown. The model beam length L is 10m, and the sampling frequency is... The frequency was 200Hz, the vehicle speed was 0.5m / s, and the damage was located at 0.4L of the beam length. The bridge damage levels were no damage, 5%, 10%, 20%, and 30%, respectively. Seven sensors were used to represent the effects of different installation locations, and marker points indicated the damage locations. The specific implementation process is as follows:

[0063] S1. Seven measuring points are set up on the bridge, corresponding to eight equal division points of the bridge, and displacement sensors are installed to measure the displacement response of the bridge when a vehicle load passes over the bridge surface at a constant speed. The time required for the vehicle to travel on the bridge surface is 20 seconds, and the sampling frequency is 200Hz. Displacement response signals x of length K are collected from M=7 displacement sensors. km x km Let represent the displacement response signal of the m-th displacement sensor at the k-th sampling time, where k = 1, 2, ..., K, m = 1, 2, ..., M, and obtain the displacement response matrix. ,

[0064] ;

[0065] S2, Regarding the displacement response matrix Principal component analysis was performed to obtain the modal components. and dynamic component The principal component matrix G is formed by linear superposition, i.e. The order N of the dominant principal component is determined by the cumulative contribution rate (CCR), where Obtain the nth order mode shape components at the kth sampling time. and the nth order dynamic component at the kth sampling time The principal component matrix column vector G is formed by linear superposition. n ,

[0066] ,

[0067] Take the column vectors of the principal component matrix As the nth principal component, where n = 1, 2, ..., N, the column vector G of this principal component matrix is... n Used for damage identification;

[0068] S3, convert the column vectors of the principal component matrix G n The nth modal component at the kth sampling time Decomposed into undamaged column vectors and damaged column vector The linear superposition, i.e.

[0069] ,

[0070] in The nth undamaged mode shape component at the kth sampling time. The local deformation of the nth mode shape at the kth sampling time caused by the damage;

[0071] S4. Use a moving average filter (MAF) to filter out the column vectors of the principal component matrix G. n The nth dynamic component at the kth sampling time Obtain the nth modal components with local damage information at the kth sampling time. ;

[0072] S5. Simultaneously filter out the column vectors of the principal component matrix G using a low-pass Gaussian filter GF. n The nth dynamic component at the kth sampling time and the nth order mode shape components Local deformation of the mode shape caused by the nth order damage at the kth sampling time Obtain the nth modal components without local damage information at the kth sampling time. ;

[0073] S6. The nth modal component with local damage information at the kth sampling time. and the nth order mode shape component without local damage information at the kth sampling time. Calculate the difference to obtain the filter residual. ;

[0074] S7. Filter residual The damage index is obtained by performing an exponential function amplification. μ R For the filter residual The average value.

[0075] In this embodiment, the specific process of step S2 above is as follows:

[0076] S21, Regarding the displacement response matrix Principal component analysis is performed to obtain the principal component matrix G, the eigenvalue matrix Λ, and the eigenvector matrix D, i.e. ,in, This represents the principal component analysis operation function.

[0077] ;

[0078] S22, Regarding the displacement response matrix Perform principal component analysis to obtain the principal component matrix G. This process can be represented as follows:

[0079] ,

[0080] Pick As the column vector of the principal component matrix, the nth order mode shape component at the kth sampling time Represented as:

[0081] ,

[0082] The nth dynamic component at the kth sampling time Represented as:

[0083] ,

[0084] In the formula, The line density of the bridge to be measured. The calculated span of the bridge to be tested is... Let n be the nth natural angular frequency of the bridge under test. Let be the angular frequency of the nth order external excitation. The velocity of the moving load along the length of the structure. For the time-domain function of the moving external load;

[0085] S23. Calculate the cumulative contribution rate of the first n principal components in the principal component matrix G. Determine the order N of the dominant principal component when When, take the column vector G of the principal component matrix. nAs the nth principal component, where n=1,2,…,N.

[0086] In this embodiment, the specific process of step S4 above is as follows:

[0087] Using a moving average filter (MAF) to filter out the column vectors of the principal component matrix G n The nth dynamic component at the kth sampling time Obtain the nth modal components with local damage information at the kth sampling time. This process can be represented as:

[0088]

[0089] in, This represents the filtering operation function of the moving average filter (MAF). The column vector f at the k-th sampling time of the principal component matrix n Principal component matrix column vector G n Its natural frequency.

[0090] In this embodiment, the specific process of step S5 above is as follows:

[0091] S51. Local deformation of the modal shape caused by the nth-order damage at the kth sampling time. The high-frequency components are filtered out to obtain the nth-order mode shape component without local information at the kth sampling time. , where ε represents the degree of damage retained in the high-resolution modal shape after processing with a low-pass Gaussian filter GF.

[0092] S52. Using a low-pass Gaussian filter GF to filter out the column vectors of the principal component matrix G. n The nth dynamic component at the kth sampling time and the nth order mode shape components Local deformation of the mode shape caused by the nth order damage at the kth sampling time This process is represented as: ,

[0093] In the formula, This represents the GF filtering operation function for a low-pass Gaussian filter, where Gaussian kernel is used. Represented as:

[0094] .

[0095] in Gaussian kernel standard deviation , .

[0096] Figure 3 This is a diagram showing the single-damage identification results based on combined data from sensors 1 and 7. From... Figure 3 The peak value of the curve indicates that the bridge damage location is 4m, which is 2 / 5 of the beam length. The bridge structural damage identification method in this embodiment 1 accurately locates the bridge damage location without affecting its accuracy.

[0097] Example 2

[0098] To further illustrate the effectiveness of the bridge damage identification method proposed in this invention, the steel beam model used in this embodiment is shown in the figure below. Figure 5 As shown. The steel beam is 6m long (L), and the sampling frequency is... The frequency was 200Hz, the vehicle speed was 0.5m / s, the damage was located at 0.58L of the beam length, and the bridge damage depths were 3mm and 5mm. Five sensors were used to represent the effects of different installation locations, and marker points indicated the damage locations. The specific implementation process is as follows:

[0099] S1. Five measuring points are set up on the bridge, corresponding to six equal divisions of the bridge, and displacement sensors are installed to measure the displacement response of the bridge when a vehicle load passes over the bridge surface at a constant speed. The time required for the vehicle to travel across the bridge surface is 20 seconds, and the sampling frequency is 200Hz. Displacement response signals x of length K are collected from M=5 displacement sensors. km x km Let represent the displacement response signal of the m-th displacement sensor at the k-th sampling time, where k = 1, 2, ..., K, m = 1, 2, ..., M, and obtain the displacement response matrix. ,

[0100] ;

[0101] S2, Regarding the displacement response matrix Principal component analysis was performed to obtain the modal components. and dynamic component The principal component matrix G is formed by linear superposition, i.e. The order N of the dominant principal component is determined by the cumulative contribution rate (CCR), where Obtain the nth order mode shape components at the kth sampling time. and the nth order dynamic component at the kth sampling time The principal component matrix column vector G is formed by linear superposition. n , ,

[0102] Take the column vectors of the principal component matrix As the nth principal component, where n = 1, 2, ..., N, the column vector G of this principal component matrix is... n Used for damage identification;

[0103] S3, convert the column vectors of the principal component matrix G n The nth modal component at the kth sampling time Decomposed into undamaged column vectors and damaged column vector The linear superposition, i.e.

[0104] ,

[0105] in The nth undamaged mode shape component at the kth sampling time. The local deformation of the nth mode shape at the kth sampling time caused by the damage;

[0106] S4. Use a moving average filter (MAF) to filter out the column vectors of the principal component matrix G. n The nth dynamic component at the kth sampling time Obtain the nth modal components with local damage information at the kth sampling time. ;

[0107] S5. Simultaneously filter out the column vectors of the principal component matrix G using a low-pass Gaussian filter GF. n The nth dynamic component at the kth sampling time and the nth order mode shape components Local deformation of the mode shape caused by the nth order damage at the kth sampling time Obtain the nth modal components without local damage information at the kth sampling time. ;

[0108] S6. The nth modal component with local damage information at the kth sampling time. and the nth order mode shape component without local damage information at the kth sampling time. Calculate the difference to obtain the filter residual. ;

[0109] S7. Filter residual The damage index is obtained by performing an exponential function amplification. μ R For the filter residual The average value.

[0110] In this embodiment, the specific process of step S2 above is as follows:

[0111] S21, Regarding the displacement response matrix Principal component analysis is performed to obtain the principal component matrix G, the eigenvalue matrix Λ, and the eigenvector matrix D, i.e. ,in, This represents the principal component analysis operation function.

[0112] ;

[0113] S22, Regarding the displacement response matrix Perform principal component analysis to obtain the principal component matrix G. This process can be represented as follows:

[0114] ,

[0115] Pick As the column vector of the principal component matrix, the nth order mode shape component at the kth sampling time Represented as:

[0116] ,

[0117] The nth dynamic component at the kth sampling time Represented as:

[0118] ,

[0119] In the formula, The line density of the bridge to be measured. The calculated span of the bridge to be tested is... Let n be the nth natural angular frequency of the bridge under test. Let be the angular frequency of the nth order external excitation. The velocity of the moving load along the length of the structure. For the time-domain function of the moving external load;

[0120] S23. Calculate the cumulative contribution rate of the first n principal components in the principal component matrix G. Determine the order N of the dominant principal component when When, take the column vector G of the principal component matrix. n As the nth principal component, where n=1,2,…,N.

[0121] In this embodiment, the specific process of step S4 above is as follows:

[0122] Using a moving average filter (MAF) to filter out the column vectors of the principal component matrix G n The nth dynamic component at the kth sampling time Obtain the nth modal components with local damage information at the kth sampling time. This process can be represented as: ,

[0123] in, This represents the filtering operation function of the moving average filter (MAF). The column vector f at the k-th sampling time of the principal component matrix n Principal component matrix column vector G n Its natural frequency.

[0124] In this embodiment, the specific process of step S5 above is as follows:

[0125] S51. Local deformation of the modal shape caused by the nth-order damage at the kth sampling time. The high-frequency components are filtered out to obtain the nth-order mode shape component without local information at the kth sampling time. , where ε represents the degree of damage retained in the high-resolution modal shape after processing with a low-pass Gaussian filter GF.

[0126] S52. Using a low-pass Gaussian filter GF to filter out the column vectors of the principal component matrix G. n The nth dynamic component at the kth sampling time and the nth order mode shape components Local deformation of the mode shape caused by the nth order damage at the kth sampling time This process is represented as: ,

[0127] In the formula, This represents the GF filtering operation function for a low-pass Gaussian filter, where Gaussian kernel is used. Represented as:

[0128] .

[0129] in Gaussian kernel standard deviation , .

[0130] Figure 3 This is a diagram showing the single-damage identification results based on combined data from sensors 1 and 7. From... Figure 3 The peak value of the curve indicates that the bridge damage location is 4m, or 0.4L. In this embodiment 1, the bridge structural damage identification method accurately locates the bridge damage location without affecting its accuracy.

[0131] like Figure 6 This is a diagram showing the single-damage identification results based on combined data from sensors 1 and 5. From... Figure 3 The peak value of the curve indicates that the bridge damage location is 4m, or 0.58L. In this embodiment 2, the bridge structural damage identification method accurately locates the bridge damage location without affecting its accuracy.

[0132] In summary, the structural damage identification method for bridges disclosed in this example only requires the installation of a small number of displacement sensors on the bridge. By analyzing the filtering residuals of the moving average filter (MAF) and the Gaussian filter (GF), structural damage identification can be completed and its specific location can be determined.

[0133] The above embodiments are preferred embodiments of the present invention, but the embodiments of the present invention are not limited to the above embodiments. Any changes, modifications, substitutions, combinations, or simplifications made without departing from the spirit and principle of the present invention shall be considered equivalent substitutions and shall be included within the protection scope of the present invention.

[0134] Example 3

[0135] Reference Figure 7 This embodiment provides a bridge damage identification method system based on multi-scale Gaussian filter residuals, used to execute the bridge damage identification method based on multi-scale Gaussian filter residuals disclosed in the above embodiment. This multi-scale Gaussian filter residual bridge damage identification method system includes, in sequence: a displacement response signal acquisition module 701, a principal component analysis module 702, a modal component decomposition processing module 703, a dynamic component filtering module 704, a modal component acquisition module 705, a filter residual acquisition module 706, and a damage index acquisition module 707, wherein:

[0136] The displacement response signal acquisition module 701 is used to arrange 7 ≥ M ≥ 2 displacement sensors at equal intervals on the bridge under test. The displacement sensors acquire the displacement response of the bridge under a uniform vehicle load. Assuming the time it takes for the vehicle to pass over the bridge is t, and the sampling frequency of the displacement sensors is f... s That is, to collect displacement response signals x of length K from M displacement sensors respectively. km x km Let represent the displacement response signal of the m-th displacement sensor at the k-th sampling time, where k = 1, 2, ..., K, m = 1, 2, ..., M, and obtain the displacement response matrix. ;

[0137] Principal component analysis module 702 is used for analyzing the displacement response matrix. Principal component analysis was performed to obtain the modal components. and dynamic component The principal component matrix G is formed by linear superposition, i.e. The order N of the dominant principal component is determined by the cumulative contribution rate (CCR), where Obtain the nth order mode shape components at the kth sampling time. and the nth order dynamic component at the kth sampling time The principal component matrix column vector G is formed by linear superposition. nTake the column vectors of the principal component matrix As the nth principal component, where n = 1, 2, ..., N, the column vector G of this principal component matrix is... n Used for damage identification;

[0138] Modal component decomposition processing module 703 is used to process the column vectors of the principal component matrix G. n The nth modal component at the kth sampling time Decomposed into undamaged column vectors and damaged column vector The linear superposition of, where The nth undamaged mode shape component at the kth sampling time. The local deformation of the nth mode shape at the kth sampling time caused by the damage;

[0139] The dynamic component filtering module 704 is used to filter out the column vectors G of the principal component matrix using a moving average filter (MAF). n The nth dynamic component at the kth sampling time Obtain the nth modal components with local damage information at the kth sampling time. ;

[0140] The modal component acquisition module 705 is used to simultaneously filter out the column vectors G of the principal component matrix using a low-pass Gaussian filter GF. n The nth dynamic component at the kth sampling time and the nth order mode shape components Local deformation of the mode shape caused by the nth order damage at the kth sampling time Obtain the nth modal components without local damage information at the kth sampling time. ;

[0141] The filter residual acquisition module 706 obtains the nth-order modal components with local damage information at the kth sampling time. and the nth order mode shape component without local damage information at the kth sampling time. Calculate the difference to obtain the filter residual. ;

[0142] Damage index acquisition module 707, for filtering residuals The damage index is obtained by performing an exponential function amplification. , For the filter residual The average value.

[0143] Example 4

[0144] This embodiment provides an electronic device, which can be a computer, such as... Figure 8 As shown, the system bus 801 connects a processor 802, a memory, an input device 803, a display 804, and a network interface 805. The processor provides computing and control capabilities. The memory includes a non-volatile storage medium 806 and internal memory 807. The non-volatile storage medium 806 stores the operating system, computer programs, and a database. The internal memory 807 provides an environment for the operation of the operating system and computer programs in the non-volatile storage medium. When the processor 802 executes the computer program stored in the memory, it implements the bridge damage identification method based on multi-scale Gaussian filter residuals proposed in Embodiment 1. The bridge damage identification method includes the following steps:

[0145] S1. Arrange 7 ≥ M ≥ 2 displacement sensors at equal intervals on the bridge to be tested (the specific values ​​follow the reference values ​​in Examples 1 and 2, and the values ​​within the range meet the requirements). Obtain the displacement response of the bridge under uniform vehicle load through the displacement sensors. Assume the time for the vehicle to pass over the bridge is t, and the sampling frequency of the displacement sensors is f. s That is, to collect displacement response signals x of length K from M displacement sensors respectively. km x km Let represent the displacement response signal of the m-th displacement sensor at the k-th sampling time, where k = 1, 2, ..., K, m = 1, 2, ..., M, and obtain the displacement response matrix. ;

[0146] S2, Regarding the displacement response matrix Principal component analysis was performed to obtain the modal components. and dynamic component The principal component matrix G is formed by linear superposition, i.e. The order N of the dominant principal component is determined by the cumulative contribution rate (CCR), where Obtain the nth order mode shape components at the kth sampling time. and the nth order dynamic component at the kth sampling time The principal component matrix column vector G is formed by linear superposition. n Take the column vectors of the principal component matrix As the nth principal component, where n = 1, 2, ..., N, the column vector G of this principal component matrix is... n Used for damage identification;

[0147] S3, convert the column vectors of the principal component matrix G n The nth modal component at the kth sampling time Decomposed into undamaged column vectors and damaged column vector The linear superposition of, where The nth undamaged mode shape component at the kth sampling time. The local deformation of the nth mode shape at the kth sampling time caused by the damage;

[0148] S4. Use a moving average filter (MAF) to filter out the column vectors of the principal component matrix G. n The nth dynamic component at the kth sampling time Obtain the nth modal components with local damage information at the kth sampling time. ;

[0149] S5. Simultaneously filter out the nth-order dynamic component at the kth sampling time in the column vector Gn of the principal component matrix using a low-pass Gaussian filter GF. and the nth order mode shape components Local deformation of the mode shape caused by the nth order damage at the kth sampling time Obtain the nth modal components without local damage information at the kth sampling time. ;

[0150] S6. The nth modal component with local damage information at the kth sampling time. and the nth order mode shape component without local damage information at the kth sampling time. Calculate the difference to obtain the filter residual. ;

[0151] S7. Filter residual The damage index is obtained by performing an exponential function amplification. μ R For the filter residual The average value.

[0152] Example 5

[0153] This embodiment provides a storable medium, which is a computer-readable storage medium, storing a computer program. When the computer program is executed by a processor, it implements a bridge damage identification method based on multi-scale Gaussian filter residuals proposed in Embodiment 1 above. The bridge damage identification method includes the following steps:

[0154] S1. Arrange 7 ≥ M ≥ 2 displacement sensors at equal intervals on the bridge to be tested (the specific values ​​follow the reference values ​​in Examples 1 and 2, and the values ​​within the range meet the requirements). Obtain the displacement response of the bridge under uniform vehicle load through the displacement sensors. Assume the time for the vehicle to pass over the bridge is t, and the sampling frequency of the displacement sensors is f. sThat is, to collect displacement response signals x of length K from M displacement sensors respectively. km x km Let represent the displacement response signal of the m-th displacement sensor at the k-th sampling time, where k = 1, 2, ..., K, m = 1, 2, ..., M, and obtain the displacement response matrix. ;

[0155] S2, Regarding the displacement response matrix Principal component analysis was performed to obtain the modal components. and dynamic component The principal component matrix G is formed by linear superposition, i.e. The order N of the dominant principal component is determined by the cumulative contribution rate (CCR), where Obtain the nth order mode shape components at the kth sampling time. and the nth order dynamic component at the kth sampling time The principal component matrix column vector G is formed by linear superposition. n Take the column vectors of the principal component matrix As the nth principal component, where n = 1, 2, ..., N, the column vector G of this principal component matrix is... n Used for damage identification;

[0156] S3, convert the column vectors of the principal component matrix G n The nth modal component at the kth sampling time Decomposed into undamaged column vectors and damaged column vector The linear superposition of, where The nth undamaged mode shape component at the kth sampling time. The local deformation of the nth mode shape at the kth sampling time caused by the damage;

[0157] S4. Use a moving average filter (MAF) to filter out the column vectors of the principal component matrix G. n The nth dynamic component at the kth sampling time Obtain the nth modal components with local damage information at the kth sampling time. ;

[0158] S5. Simultaneously filter out the column vectors of the principal component matrix G using a low-pass Gaussian filter GF. n The nth dynamic component at the kth sampling time and the nth order mode shape components Local deformation of the mode shape caused by the nth order damage at the kth sampling time Obtain the nth modal components without local damage information at the kth sampling time. ;

[0159] S6. The nth modal component with local damage information at the kth sampling time. and the nth order mode shape component without local damage information at the kth sampling time. Calculate the difference to obtain the filter residual. ;

[0160] S7. Filter residual The damage index is obtained by performing an exponential function amplification. μ R For the filter residual The average value.

[0161] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0162] The above embodiments are preferred embodiments of the present invention, but the embodiments of the present invention are not limited to the above embodiments. Any changes, modifications, substitutions, combinations, or simplifications made without departing from the spirit and principle of the present invention shall be considered equivalent substitutions and shall be included within the protection scope of the present invention.

Claims

1. A bridge damage identification method using multi-scale Gaussian filter residuals, characterized in that, The bridge damage location and identification method includes the following steps: S1. Arrange 7 ≥ M ≥ 2 displacement sensors at equal intervals on the bridge to be tested. Obtain the displacement response of the bridge under a uniform vehicle load using the displacement sensors. Assume the time it takes for the vehicle to pass over the bridge is t, and the sampling frequency of the displacement sensors is f. s That is, to collect displacement response signals x of length K from M displacement sensors respectively. km x km Let represent the displacement response signal of the m-th displacement sensor at the k-th sampling time, where k = 1, 2, ..., K, m = 1, 2, ..., M, and obtain the displacement response matrix. , ; S2, Regarding the displacement response matrix Principal component analysis was performed to obtain the modal components. and dynamic component The principal component matrix G is formed by linear superposition, i.e. The order N of the dominant principal component is determined by the cumulative contribution rate (CCR), where Obtain the nth order mode shape components at the kth sampling time. and the nth order dynamic component at the kth sampling time The principal component matrix column vector G is formed by linear superposition. n , , Take the column vectors of the principal component matrix As the nth principal component, where n = 1, 2, ..., N, the column vector G of this principal component matrix is... n Used for damage identification; S3, convert the column vectors of the principal component matrix G n The nth modal component at the kth sampling time Decomposed into undamaged column vectors and damaged column vector The linear superposition, i.e. , in The nth undamaged mode shape component at the kth sampling time. The local deformation of the nth mode shape at the kth sampling time caused by the damage; S4. Use a moving average filter (MAF) to filter out the column vectors of the principal component matrix G. n The nth dynamic component at the kth sampling time Obtain the nth modal components with local damage information at the kth sampling time. ; S5. Simultaneously filter out the column vectors of the principal component matrix G using a low-pass Gaussian filter GF. n The nth dynamic component at the kth sampling time and the nth order mode shape components Local deformation of the mode shape caused by the nth order damage at the kth sampling time Obtain the nth modal components without local damage information at the kth sampling time. ; S6. The nth modal component with local damage information at the kth sampling time. and the nth order mode shape component without local damage information at the kth sampling time. Calculate the difference to obtain the filter residual. ; S7. Filter residual The damage index is obtained by performing an exponential function amplification. μ R For the filter residual The average value.

2. The bridge damage identification method based on multi-scale Gaussian filter residuals according to claim 1, characterized in that, The process in step S2 is as follows: S21, Regarding the displacement response matrix Principal component analysis is performed to obtain the principal component matrix G, the eigenvalue matrix Λ, and the eigenvector matrix D, i.e. ,in, This represents the principal component analysis operation function. ; S22, Regarding the displacement response matrix Perform principal component analysis to obtain the principal component matrix G. This process can be represented as follows: ， ， Pick As the column vector of the principal component matrix, the nth order mode shape component at the kth sampling time Represented as: ， The nth dynamic component at the kth sampling time Represented as: ， In the formula, The line density of the bridge to be measured. The calculated span of the bridge to be tested is... Let n be the nth natural angular frequency of the bridge under test. Let be the angular frequency of the nth order external excitation. The velocity of the moving load along the length of the structure. For the time-domain function of the moving external load; S23. Calculate the cumulative contribution rate of the first n principal components in the principal component matrix G. Determine the order N of the dominant principal component when When, take the column vector G of the principal component matrix. n As the nth principal component, where n=1,2,…,N.

3. The bridge damage identification method based on multi-scale Gaussian filter residuals according to claim 1, characterized in that, The process of step S4 is as follows: Using a moving average filter (MAF) to filter out the column vectors of the principal component matrix G n The nth dynamic component at the kth sampling time Obtain the nth modal components with local damage information at the kth sampling time. This process can be represented as: , in, This represents the filtering operation function of the moving average filter (MAF). The column vector of the principal component matrix at the k-th sampling time. f n Principal component matrix column vector G n Its natural frequency.

4. The bridge damage identification method based on multi-scale Gaussian filter residuals according to claim 3, characterized in that, The process of step S5 is as follows: S51. Local deformation of the modal shape caused by the nth-order damage at the kth sampling time. The high-frequency components are filtered out to obtain the nth-order mode shape component without local information at the kth sampling time. , where ε represents the degree of damage retained in the high-resolution mode shape after processing with a low-pass Gaussian filter GF; S52. Using a low-pass Gaussian filter GF to filter out the column vectors of the principal component matrix G. n The nth dynamic component at the kth sampling time and the nth order mode shape components Local deformation of the mode shape caused by the nth order damage at the kth sampling time This process is represented as: , In the formula, This represents the GF filtering operation function for a low-pass Gaussian filter, where Gaussian kernel is used. Represented as: ， in Gaussian kernel standard deviation , .

5. The bridge damage identification method based on multi-scale Gaussian filter residuals according to claim 4, characterized in that, In step S6, the filter residual is obtained by subtraction. .

6. A bridge damage identification system based on multi-scale Gaussian filter residuals, used to execute the bridge damage identification method based on multi-scale Gaussian filter residuals as described in any one of claims 1 to 5, characterized in that, The bridge damage identification system based on the multi-scale Gaussian filter residuals includes: The displacement response signal acquisition module is used to arrange 7 ≥ M ≥ 2 displacement sensors at equal intervals on the bridge under test. The displacement sensors acquire the displacement response of the bridge under a uniform vehicle load. Assuming the time it takes for the vehicle to pass over the bridge is t, and the sampling frequency of the displacement sensors is f... s That is, to collect displacement response signals x of length K from M displacement sensors respectively. km x km Let represent the displacement response signal of the m-th displacement sensor at the k-th sampling time, where k = 1, 2, ..., K, m = 1, 2, ..., M, and obtain the displacement response matrix. ; Principal component analysis module is used to analyze the displacement response matrix. Principal component analysis was performed to obtain the modal components. and dynamic component The principal component matrix G is formed by linear superposition, i.e. The order N of the dominant principal component is determined by the cumulative contribution rate (CCR), where Obtain the nth order mode shape components at the kth sampling time. and the nth order dynamic component at the kth sampling time The principal component matrix column vector G is formed by linear superposition. n Take the column vectors of the principal component matrix As the nth principal component, where n = 1, 2, ..., N, the column vector G of this principal component matrix is... n Used for damage identification; The modal component decomposition module is used to process the column vectors of the principal component matrix G. n The nth modal component at the kth sampling time Decomposed into undamaged column vectors and damaged column vector The linear superposition of, where The nth undamaged mode shape component at the kth sampling time. The local deformation of the nth mode shape at the kth sampling time caused by the damage; The dynamic component filtering module is used to filter out the column vectors G of the principal component matrix using a moving average filter (MAF). n The nth dynamic component at the kth sampling time Obtain the nth modal components with local damage information at the kth sampling time. ; The modal component acquisition module is used to simultaneously filter out the nth-order dynamic component at the kth sampling time in the column vector Gn of the principal component matrix using a low-pass Gaussian filter GF. and the nth order mode shape components Local deformation of the mode shape caused by the nth order damage at the kth sampling time Obtain the nth modal components without local damage information at the kth sampling time. ; The filter residual acquisition module obtains the nth-order modal components with local damage information at the kth sampling time. and the nth order mode shape component without local damage information at the kth sampling time. Calculate the difference to obtain the filter residual. ; The damage index acquisition module processes the filtered residuals. The damage index is obtained by performing an exponential function amplification. , For the filter residual The average value.

7. An electronic device comprising a processor and a memory for storing a processor-executable program, characterized in that, When the processor executes the program stored in the memory, it implements the bridge damage identification method based on the multi-scale Gaussian filter residuals as described in any one of claims 1 to 5.

8. A storable medium storing a program, characterized in that, When the program is executed by the processor, it implements the bridge damage identification method based on the multi-scale Gaussian filter residuals as described in any one of claims 1 to 5.

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