Bridge Structure Health Detection Method and System Based on Fuzzy C-Means Clustering Algorithm

Abstract

The present invention discloses a bridge structure health detection method and system based on the fuzzy C-means clustering algorithm, which is applied to the field of bridge structure detection technology. The method includes the following steps: S1, collecting acceleration response signals on the bridge; S2, identifying the acceleration response signals to obtain the results of the stabilization diagram; S3, defining the modal parameter results corresponding to each stabilization diagram result as the parameter results of frequency, damping ratio, and vibration mode; S4, adopting the FCM fuzzy C-means step-by-step clustering method to perform clustering analysis on all sets of data for frequency, damping ratio, and modal vibration mode respectively, and finally obtaining the true modal results after clustering; S5, comparing and analyzing the changes in the modal parameter results after clustering to judge the health state of the bridge; the system is a software / hardware system for executing the detection method and can execute the steps of the detection method; the present invention can eliminate human subjectivity, realize the intelligent identification of true and false modes, improve the efficiency of parameter identification, and quickly judge the health state of the bridge structure.

Description

Technical Field

[0001] The present invention relates to the technical field of bridge structure detection, and particularly to a bridge structure health detection method and system based on the fuzzy C-means clustering algorithm. Background Art

[0002] With the rapid development of bridge technology in China, the types and quantities of bridge structures have been increasing year by year. However, with the increasing aging of bridge structures, damage and aging of varying degrees will inevitably occur in different parts, and in severe cases, it will directly affect the normal use of bridge structures. Therefore, a new research field has emerged, namely the health detection system of bridge structures. At the present stage, certain mathematical algorithms can be used to obtain the modal parameter results of the structure at different times, including natural frequency, damping ratio, and modal vibration mode; and by analyzing the changes of these three parameters over time, it is possible to indirectly identify whether the structure is in a good health state.

[0003] At the present stage, the stochastic subspace algorithm is widely used in the modal identification of bridge structures. The main advantages of this algorithm are that it can not only directly use the time-domain signals collected by sensors as input, but also effectively avoid problems such as frequency resolution errors, and the parameter results obtained by identification can well meet the requirements of actual engineering. However, with continuous research on it, it is found that the main drawback of this algorithm is that manual participation is required in the identification of true and false modes in the stabilization diagram, which greatly reduces the efficiency of parameter identification.

[0004] In summary, it can be seen that how to efficiently implement the health detection of existing bridge structures is an urgent problem to be solved. Summary of the Invention

[0005] The purpose of the present invention is to overcome the above-mentioned deficiencies in the prior art, such as the low efficiency of identifying true and false modes in bridge health detection, and to provide a bridge structure health detection method and system based on the fuzzy C-means clustering algorithm, which can eliminate human subjectivity, and through mathematical methods, enable parameters to automatically find similar classes and perform clustering, realizing the intelligent identification of true and false modes, improving the efficiency of parameter identification, and quickly judging the health state of bridge structures.

[0006] In order to achieve the above-mentioned invention purpose, the present invention provides the following technical solutions:

[0007] A bridge structure health detection method based on the fuzzy C-means clustering algorithm, which includes the following steps:

[0008] S1. Collect the acceleration response signals of the same measurement structure on the bridge at different times;

[0009] S2. Use the acceleration response signal as the input signal for modal parameter identification, and a large number of parameter results are identified. The parameter results in the same time period are grouped as a set and saved as the stable diagram results.

[0010] S3. Define the modal parameter results corresponding to each stable diagram result as X i ={f i (a,b), ξ i (a,b), Ψ

[0011] i (a,b,q)}, i = 1, 2, …, T; a = 1, 2, …, A; b = 1, 2, …, B;

[0012] Among them, T represents the total number of groups of modal parameter results, f represents the frequency results, which are (m×n) matrix data, ξ represents the damping ratio results, which are (m×n) matrix data, Ψ represents the modal shape results, which are (m×n×c) matrix data, and c is the number of clusters; A represents the system order of the bridge measurement structure, B represents the number of columns of the vector in the parameter results, and q represents the total number of sensors arranged on the bridge measurement structure.

[0013] S4. Adopt the FCM fuzzy C-means step-by-step clustering method to cluster the adjacent front and back two stable diagrams in the T groups of stable diagrams. First, divide different clusters according to the membership degree. By finding the membership matrix and the clustering center, complete the clustering analysis of all group data sets for frequency, damping ratio, and modal shape respectively. Plot the modes whose clustering groups of frequency values, damping ratios, and modal shapes exceed the effective number of groups in the final stable diagram as stable modes, and then obtain the true modal results after clustering.

[0014] S5. Compare and analyze the changes in the modal parameter results after clustering of the same structure of the bridge in consecutive time periods. If the modal parameter results after clustering change, it is judged that the bridge is in an unhealthy state; if the modal parameter results after clustering do not change, it is judged that the bridge is in a healthy state.

[0015] By collecting a large number of acceleration response signals of the bridge structure, sufficient data can be utilized to analyze the bridge structure response signals more accurately, improve the recognition accuracy of modal parameter results and stability diagrams. By defining each stability diagram as a comprehensive result of frequency, damping ratio, and mode shape, frequency, damping ratio, and mode shape can be considered comprehensively to more comprehensively reflect the actual damage condition of the bridge structure. Through the step-by-step clustering method, all stability diagrams are clustered and identified. By finding the clustering center, the modal parameter results are automatically identified. When identifying similarity, the manual division method is changed. Compared with the rigid division of the ordinary C-means algorithm, the clustering division method of the present invention is relatively flexible. The clustering process does not require manual intervention, avoiding the problem of threshold setting, that is, avoiding the similarity artificially stipulated by human subjective consciousness, and providing a flexible division method. Through mathematical calculation, the modal parameters automatically find the clustering center point and similar classes. Only by inputting the set classification can the clustering division be automatically completed. Moreover, this clustering method considers the "both this and that" multi-result nature of each modal parameter belonging to each class, can classify the data overlap between various classes, and has good convergence. This clustering method improves the efficiency of parameter identification; by selecting the stability diagrams corresponding to the modal parameter results greater than 0.8T, the effectiveness of the results is improved. Through the intuitive continuous change of modal parameter results, the health state of the bridge structure can be quickly judged, and the intelligent identification of true and false modes can be realized; and the FCM clustering method has low complexity and is easy to implement, improves the identification effectiveness, and the obtained results are closer to the real situation.

[0016] In a preferred embodiment of the present invention, in the above step S4, when performing clustering analysis on frequency, it includes:

[0017] S41. Select f1(a, b) and f2(a, b) as the data set X for FCM clustering;

[0018] S42. Determine the number of clusters c = 2 and determine the maximum number of iterations m = A / 2;

[0019] S43. Define the objective function J and constraints of clustering;

[0020] S44. Based on the membership matrix and the clustering center, by continuously iteratively verifying the clustering center for the data set X, find the membership matrix and the clustering center that minimize the objective function;

[0021] S45. Cluster the modes of each order of f1(a, b) and f2(a, b), judge whether the frequencies of each order are in the same class, and if they are in the same class, calculate the updated frequency values of each order.

[0022] Adopt the FCM clustering method. By selecting the dataset, determining the number of clusters and the maximum number of iterations, determine the parameters of the iterative calculation. Through f1(a, b) and f2(a, b), cluster the two consecutive stable graphs. The clustering process is to cluster the two consecutive stable graphs in the modal parameter results of group T in sequence. First, identify the first and the second graphs, then the second and the third graphs, and so on; by only extracting the group of data with the most concentrated clustering from the data, and the input data is only f1(a, b) and f2(a, b), thus determine that the number of clusters is 2; when continuously iterating, first assume that the data point A is the clustering center, then calculate the Euclidean distance of all points from the data point A through the membership matrix and the clustering center, and judge whether the point A is the clustering center. If the point A is not the clustering center, then re-assume that the data point B is the clustering center, and so on, for continuous iteration; when judging the same class, judge the number of rows of the matrix of the set f1(a, b) and the set f2(a, b), use the number of rows of the matrix as the length, and then calculate the membership degree according to the membership matrix, so as to determine the membership matrix with the minimum value; by adopting the FCM clustering algorithm of S41~S45, effectively cluster and divide the modal parameter results of multiple collected stable graphs, and realize the intelligent identification of true and false modes.

[0023] In a preferred embodiment of the present invention, the above objective function J is:

[0024]

[0025] where, u ij is the membership degree of each sample j belonging to a certain class i;

[0026] The constraint conditions are:

[0027]

[0028] where, m is the maximum number of iterations, and the value range is m ∈ [1, ∞], ||x j - c i || represents the Euclidean distance between the data object x j and the i-th clustering center; by establishing the objective function and its constraint conditions, a series of data can be quickly obtained through the objective function, which is convenient to quickly find the minimum value from these data to find the clustering center.

[0029] In a preferred embodiment of the present invention, the above membership degree is calculated by the following formula:

[0030]

[0031] where, u ijis the membership degree, representing the membership degree of each sample j in the dataset X belonging to the i-th cluster center; by comprehensively considering the membership matrix, the objective function J can be accurately determined to obtain the clustering result.

[0032] In a preferred embodiment of the present invention, the above-mentioned cluster center is calculated by the following formula:

[0033]

[0034] where c i is the cluster center, representing the i-th cluster center when the dataset X is divided into c cluster centers; by comprehensively considering the cluster center, the objective function J can be accurately determined to obtain the clustering result.

[0035] In a preferred embodiment of the present invention, when performing clustering judgment in the above step S45:

[0036] Perform clustering identification on the first-order frequency. When f1(a,1) and f2(a,1) belong to the same class, calculate the updated first-order frequency value f 1,2 (a,1) = (f1(a,1) + f2(a,1)) / 2;

[0037] And so on to complete the clustering analysis of all order frequency values in the two frequency matrices of f1(a,b) and f2(a,b), and form a new frequency result f 1,2 (a,b1) with the new clustered modes and the unclustered modes; since both f1(a,b) and f2(a,b) contain a total of b-order modes, the FCM clustering needs to be used to cluster each order of modes respectively. By performing frequency clustering on all orders of modes, the possible true modes of all datasets can be identified, realizing high-precision identification of modes and improving the anti-noise performance of clustering identification.

[0038] In a preferred embodiment of the present invention, in the above step S4, when performing clustering analysis on the damping ratio, it includes:

[0039] Assume f 1,2 (a,b1) where f1(a,1) and f2(a,1) are of the same class in terms of frequency. According to the methods of steps S41 - S45, perform clustering analysis on ξ1(a,1) and ξ2(a,1) for the damping ratio, and finally construct a new damping ratio matrix result ξ 1,2 (a,bb1); because the points on the stable axis in the stability diagram need to be stable not only in terms of frequency but also in terms of the damping ratio result, it is necessary to perform frequency identification on f 1,2(a, b1) Cluster identification of damping ratios for modes of the same frequency category; by clustering the damping ratios of all orders of modes, the possible true modes of all data sets can be identified, achieving high-precision identification of modes and improving the noise resistance performance of cluster identification.

[0040] In a preferred embodiment of the present invention, in the above step S4, when performing cluster analysis on the mode shapes, it includes:

[0041] Assume ξ 1,2 (a, bb1) ξ1(a, 1) and ξ2(a, 1) in (a, bb1) belong to the same category in terms of frequency and damping ratio. According to the methods of steps S41 - S45, perform cluster analysis on Ψ1(a, 1, q) and Ψ2(a, 1, q) for the mode shapes, and finally construct a new mode shape matrix result Ψ 1,2 (a, bbb1, q); since the points on the stable axis in the stability diagram need to be stable not only in terms of frequency and damping ratio, but also ensure the stability of the mode shapes. It is necessary to perform cluster analysis on the corresponding two-order modes in Ψ1(a, b, q) and Ψ2(a, b, q). By performing cluster analysis on the mode shapes of all orders of modes, the possible true modes of all data sets can be identified, achieving high-precision identification of modes and improving the noise resistance performance of cluster identification.

[0042] In a preferred embodiment of the present invention, when judging the health state in the above step S5, when the results of the natural frequencies of each order at the measured structure of the bridge change at a certain moment, and the changes in the results of each order of frequencies continue to exist after that moment, it is determined that the bridge has certain damage; through the changes and the existence of changes in the results of each order of natural frequencies, the bridge damage can be intuitively judged, and the health status of the bridge can be quickly judged.

[0043] A bridge structure health detection system based on the fuzzy C - means clustering algorithm, which adopts the above-mentioned bridge structure health detection method based on the fuzzy C - means clustering algorithm. The system includes a memory and a processor. The memory stores computer code that can run on the processor. The computer code includes the steps S1 - S5 of executing the bridge structure health detection method based on the fuzzy C - means clustering algorithm according to any one of claims 1 - 9; through this system, the steps of the bridge structure health detection method based on the fuzzy C - means clustering algorithm can be executed, and the health status of the bridge can be detected based on the detection method, eliminating manual operations, quickly outputting results, facilitating the implementation of the detection method and the detection operation, and quickly judging the health state of the bridge structure.

[0044] Compared with the prior art, the beneficial effects of the present invention:

[0045] 1. This detection method saves the collected acceleration response signals as stable diagrams. Each stable diagram is defined as the comprehensive result of frequency, damping ratio, and vibration mode, which can comprehensively consider frequency, damping ratio, and vibration mode, and more comprehensively reflect the actual damage situation of the bridge structure. Through FCM fuzzy C-means clustering, it changes the way of manual division. Compared with the rigid division of the ordinary C-means algorithm, the clustering division method of the present invention is relatively flexible. The clustering process does not require manual intervention, avoiding the problem of threshold setting, that is, avoiding the similarity artificially stipulated by human subjective consciousness, and providing a flexible division method. Through mathematical calculation, the modal parameters automatically find the clustering center points and similar classes. Just input the set classification, and the clustering division can be automatically completed, realizing the intelligent identification of true and false modes, improving the efficiency of parameter identification, and being able to quickly judge the health status of the bridge structure.

[0046] 2. This system stores the computer code for executing steps through a memory, and through a processor, it quickly processes and performs the detection method, and can execute the steps of the bridge structure health detection method including the fuzzy C-means clustering algorithm. Based on the detection method, it conducts bridge health condition detection, eliminating manual operations, quickly outputting results, facilitating the implementation of the detection method and the detection operation, and quickly judging the health status of the bridge structure. Description of the Drawings

[0047] Figure 1 It is the execution flowchart of the bridge structure health detection method based on the fuzzy C-means clustering algorithm of the present invention;

[0048] Figure 2 It is the standard cross-sectional view of the simply supported beam structure of the bridge of the present invention;

[0049] Figure 3 It is the 3D calculation model structure diagram established by the CSIBRIDGE software in the embodiment;

[0050] Figure 4 It is the time history curve diagram of white noise excitation within 60 s in the embodiment;

[0051] Figure 5 It is the time history curve diagram of the acceleration response signal corresponding to a certain simply supported beam span in the embodiment;

[0052] Figure 6 It is the stable diagram result of a certain simply supported beam span in the embodiment;

[0053] Figure 7 It is the clustering stable diagram result of a certain simply supported beam span in the embodiment;

[0054] Figure 8 It is the time history curve diagram of the first 4-order frequency values of a certain simply supported beam span within 30 days in the embodiment;

[0055] Figure 9 Bridge span layout plan of a cable-stayed bridge in the embodiment;

[0056] Figure 10 Time history curve graph of the dynamic response signal collected by sensors at the mid-span of a cable-stayed bridge in the embodiment;

[0057] Figure 11 Vehicle jumping free vibration spectrum diagram of a cable-stayed bridge in the embodiment;

[0058] Figure 12 Clustering stability graph of a cable-stayed bridge in the embodiment;

[0059] Figure 13 First three order modal vibration mode diagrams of a cable-stayed bridge in the embodiment;

[0060] Markings in the figure: 1 - bridge, 2 - bent cap, 3 - T-beam, 4 - acceleration sensor. Specific implementation manner

[0061] The present invention will be further described in detail below in combination with test examples and specific implementation manners. However, it should not be understood that the scope of the above-mentioned subject matter of the present invention is limited to the following embodiments only. All technologies implemented based on the content of the present invention belong to the scope of the present invention.

[0062] Embodiment 1

[0063] This embodiment provides a bridge structure health detection method based on the fuzzy C-means clustering algorithm. The bridge data detected in this embodiment is as follows: The total length of the entire bridge structure 1 is 1.3 km, and there are a total of 44 spans of prestressed reinforced concrete simply supported beams, including 7 spans of 25 m beams, 30 spans of 30 m beams, and 7 spans of 35 m beams; Each span of simply supported beam consists of 4 T-beams 3, and the transverse connection between the 4 T-beams 3 is increased by pouring a 25 cm thick reinforced concrete slab on the top slab to improve the overall stability of the structure.

[0064] Please refer to Figure 1 , and the detection method includes the following steps:

[0065] S1. Collect the acceleration response signals of the same measurement structure on the bridge at different time periods; To collect the acceleration response signals, it is necessary to install acceleration sensors 4 at the structures to be measured on the bridge structure 1 in advance, and collect the acceleration dynamic response signals of the bridge structure 1 at each time period under ambient excitation through the acceleration sensors 4; The sensors use acceleration sensors 4, and vibration sensors or other sensors capable of measuring vibration signals can also be used. The sensors are installed on each span of the bridge structure 1, such as Figure 2, the T-beam 3 is arranged on the top of the capping beam 2 of the bridge structure 1. Three acceleration sensors 4 are arranged at the bottom of the structure of each span of the T-beam 3, respectively at the 1 / 4 span and the mid-span. Among them, the acceleration sensor 4 is arranged at the bottom of the reinforced concrete slab of the top plate. The entire bridge structure 1 of this embodiment is not yet completed and is in the construction stage of the bridge deck system. In order to clearly show how the present invention realizes the health detection of the bridge structure 1, the following will use the CSIBRIDGE software to establish a simply supported beam model with a span of 35m to realize the simulation. As Figure 3 .

[0066] Simulate the environmental excitation situation. Use the Randn function in the mathematical software MATLAB to generate a set of data with a mean of 0 and a variance of 1 as white noise excitation to simulate the real environmental excitation, and add each group of data signals to the three sensor positions corresponding to each span of the simply supported beam. As Figure 4 is the time history curve of the white noise excitation within a certain 60s.

[0067] S2. Take the acceleration response signal as the input signal for modal parameter identification, and a large number of parameter results are identified. The parameter results in the same time period are taken as a group and saved as the stable diagram results; by collecting a large number of acceleration response signals of the bridge structure 1, sufficient data can be used to more accurately analyze the response signals of the bridge structure 1 and improve the identification accuracy of the modal parameter results and the stable diagram. The identification method in this step refers to the patent CN202111414693.5, an intelligent detection method and system for bridge structure damage.

[0068] Collect the structural response signals corresponding to each acceleration sensor 4 under the train operation condition, and store all the response signal data with the information of the time point of the collected signal, bridge name, bridge span, bridge span number, mid-span mileage and sensor code as labels, and store all the input data for subsequent review; since this patent uses the acceleration response signal as the input data of the stochastic subspace algorithm, the type of sensor used is the acceleration sensor 4, and the sampling frequency is 20Hz, that is, 20 data collections are performed per second. The time history curve of the collected acceleration response signal is as Figure 4 .

[0069] When identifying the stable diagram results from the response signal data, the following steps are included:

[0070] S21. Decompose and reconstruct the signals collected by all acceleration sensors 4 using the Ensemble Empirical Mode Decomposition (EEMD) algorithm, and store the reconstructed signals. The reason for not using the Empirical Mode Decomposition (EMD) algorithm for signal decomposition in this embodiment is mainly that, compared with the EMD algorithm, the EEMD decomposition algorithm adds equal-amplitude random white noise to the original signal multiple times during the decomposition process, making the distribution of extreme points in the original signal more uniform, thereby avoiding the influence brought by intermittent high-frequency components.

[0071] S22. Use the Data-Driven Stochastic Subspace Identification (DATA-SSI) method to identify the reconstructed signals corresponding to the acceleration response signals of the bridge structure 1 by all sensors in each time period, and obtain the corresponding stabilization diagram results and store them.

[0072] 1) Assume that in the time period t1 (in hours), the acceleration response signal collected by the sensor numbered N1 is

[0073] 2) Use the EEMD decomposition algorithm to perform noise reduction and reconstruction processing to obtain the reconstructed signal

[0074] 3) Use the reconstructed signal to establish a Hankel matrix, and the formula is:

[0075]

[0076] where: Y p is the output data matrix at a past time point, and Y f is the input data matrix at a corresponding future time point.

[0077] 4) Solve Y o / 2i-1 to obtain the orthogonal projection matrix O i , and perform SVD decomposition on O i to obtain the extended observable matrix Γ i and the product of the Kalman filter state sequence ; Based on Γ i and solve for the state matrix A and the output matrix C to obtain the modal parameter results of the bridge structure 1. The formula is as follows:

[0078]

[0079] In the formula: U and V are orthogonal matrices; S is a singular diagonal matrix.

[0080] 5) Finally, a stable diagram of the bridge structure 1 in the time period t1 is obtained. Similarly, the stable diagrams of the structure in each time period can be obtained, and all the stable diagram results are stored, assumed to be where M represents the total number of time periods.

[0081] 6) Considering that each sensor has an independent number, based on the above principle, the stable diagrams of all sensors in each time period are obtained, and all the stable diagram results are stored, assumed to be where M represents the total number of time periods and N represents the total number of sensors.

[0082] Finally, the corresponding stable diagram results are obtained, such as Figure 6 , from the stable diagram results in a certain 1-hour time period, it can be seen that there are a large number of false modes. If manual participation is used to identify the true and false modes in the stable diagram, there will be modal misjudgment caused by subjective reasons.

[0083] S3. Define each stable diagram result The corresponding modal parameter result is X i ={f i (a,b), ξ i (a,b), Ψ i (a,b,q)}, i = 1, 2, …, T; a = 1, 2, …, A; b = 1, 2, …, B; By defining each stable diagram as a comprehensive result of frequency, damping ratio, and mode shape, the frequency, damping ratio, and mode shape can be considered comprehensively, and the actual damage condition of the bridge structure 1 can be reflected more comprehensively.

[0084] Among them, T represents the total number of groups of modal parameter results, f represents the frequency result, which is (m×n) matrix data, ξ represents the damping ratio result, which is (m×n) matrix data, Ψ represents the modal mode shape result, which is (m×n×c) matrix data, and c is the number of clusters; A represents the system order of the bridge measurement structure, B represents the number of columns of the vector in the parameter result, and q represents the total number of sensors arranged on the bridge measurement structure. Among them, the system order A is the system order size determined by the stable diagram order determination method, and the stable diagram order determination method is a method that can be used in the existing modal parameter identification of the bridge structure 1.

[0085] S4. Adopt the FCM fuzzy C-means step-by-step clustering method to cluster the adjacent two stable graphs in the T groups of stable graphs. The clustering process is to cluster the two adjacent stable graphs in the modal parameter results of each of the T groups in turn. First, identify the first and the second graphs, then the second and the third graphs, and so on. Considering that it is difficult to determine the number of clusters clearly if the parameter results of the T groups are clustered at one time, the step-by-step clustering method is adopted to identify the frequency results in the two adjacent stable graphs of all the stable graphs. By finding the clustering center, the modal parameter results are automatically identified. When identifying the similarity, the way of artificial division is changed. Compared with the rigid division of the ordinary C-means algorithm, the clustering division method of the present invention is relatively flexible. The clustering process does not require manual intervention, avoiding the problem of threshold setting, that is, avoiding the similarity artificially stipulated by human subjective consciousness, and providing a flexible division method. Through mathematical calculation, the modal parameters automatically find the clustering center point and similar classes. Only by inputting the set classification can the clustering division be completed automatically. Moreover, this clustering method takes into account the "both this and that" multi-result nature of each modal parameter belonging to various classes, can classify the data overlap between various classes, has good convergence, and improves the efficiency of parameter identification.

[0086] In order to determine from how many stable graphs the real modal clustering can be achieved, in this embodiment, the clustering analysis is carried out with a step difference of 1 stable graph. Finally, it is determined that when the number of stable graphs is 8, the real modal clustering can be achieved, and a clear real modal axis can be obtained. First, different clusters are divided according to the membership degree. By finding the membership matrix and the clustering center, the clustering analysis of all groups of data sets is completed for the frequency, damping ratio, and modal vibration mode respectively. The modes with the number of clustering groups of the frequency value, damping ratio, and modal vibration mode exceeding the effective number of groups are plotted in the final stable graph as stable modes, and then the real modal results after clustering are obtained.

[0087] Specifically, when performing the clustering analysis, it is carried out in the order of frequency value, damping ratio, and modal vibration mode.

[0088] When first performing the clustering analysis on the frequency, it includes:

[0089] S41. Select f1(a, b) and f2(a, b) as the data set X for FCM clustering;

[0090] S42. Determine the number of clusters c = 2 and determine the maximum number of iterations m. By only extracting the most concentrated group of data in the data, and the input data is only f1(a, b) and f2(a, b), the number of clusters is determined to be 2. When determining m, since the maximum number of rows of each data matrix in the modal parameter results is half of the maximum order number in the stable graph, so m = A / 2;

[0091] S43. Define the objective function J and the constraints for clustering;

[0092] The objective function J is:

[0093]

[0094] where u ij is the membership degree of each sample j belonging to a certain class i;

[0095] The constraints are:

[0096]

[0097] where m is the maximum number of iterations, and the value range is m ∈ [1, ∞]. ||x j -c i || represents the Euclidean distance between the data object x j and the i-th cluster center. By establishing the objective function and its constraints, a series of data can be quickly obtained through the objective function, which is convenient for quickly finding the minimum value from these data to search for the cluster center.

[0098] S44. Based on the membership matrix and the cluster centers, by continuously iteratively validating the cluster centers for the dataset X. During continuous iteration, first assume that the data point A is the cluster center, and then calculate the Euclidean distance between all points and the data point A through the membership matrix and the cluster centers to determine whether point A is the cluster center. If point A is not the cluster center, then re-assume that the data point B is the cluster center, and so on, and perform continuous iteration to find the membership matrix and the cluster centers that minimize the objective function;

[0099] The membership degree is calculated by the following formula:

[0100]

[0101] where u ij is the membership degree, representing the membership degree of each sample j in the dataset X belonging to the i-th cluster center. By comprehensively considering the membership matrix, the objective function J can be accurately determined to obtain the clustering result.

[0102] The cluster center is calculated by the following formula:

[0103]

[0104] where c i is the cluster center, representing the i-th cluster center when the dataset X is divided into c cluster centers. By comprehensively considering the cluster centers, the objective function J can be accurately determined to obtain the clustering result.

[0105] S45. Cluster the modes of each order of f1(a, b) and f2(a, b), determine whether each order of frequency belongs to the same class. When determining the same class, judge the number of rows of the matrices of set f1(a, b) and set f2(a, b). Take the number of rows of the matrix as the length, and then calculate the membership degree according to the membership degree matrix, so as to determine the membership degree matrix of the minimum value. If it is the same class, then calculate the updated frequency values of each order.

[0106] Since both f1(a, b) and f2(a, b) contain a total of b orders of modes, it is necessary to use FCM clustering to cluster the modes of each order respectively. Cluster and identify the first-order frequency. When f1(a, 1) and f2(a, 1) belong to the same class, calculate the updated first-order frequency value f 1,2 (a, 1) = (f1(a, 1) + f2(a, 1)) / 2;

[0107] And so on, complete the clustering analysis of all order frequency values in the two frequency matrices of f1(a, b) and f2(a, b), and form a new frequency result f 1,2 (a, b1) by combining the new modes after clustering and the unclustered modes. By performing frequency clustering on the modes of all orders, it is possible to identify the possible true modes of all data sets, achieving high-precision identification of the modes and improving the anti-noise performance of the clustering identification.

[0108] When performing clustering analysis on the damping ratio in this step, since the points on the stable axis in the stability diagram need to be stable not only in frequency but also ensure the stability of the damping ratio results, it is necessary to perform clustering identification of the damping ratio on the modes with the same frequency in f 1,2 (a, b1) obtained by frequency identification, including:

[0109] Assume that f 1,2 (a, b1) where f1(a, 1) and f2(a, 1) are of the same class in frequency. According to the methods of steps S41 - S45, perform clustering analysis on ξ1(a, 1) and ξ2(a, 1) for the damping ratio;

[0110] When ξ1(a, 1) and ξ2(a, 1) are classified as the same class, then take the average value as the new first-order damping ratio result: ξ 1,2 (a, 1) = (ξ1(a, 1) + ξ2(a, 1)) / 2; Otherwise, split f 1,2 (a, 1) into the original f1(a, 1) and f2(a, 1), and construct a new frequency matrix ff 1,2 (a, 1).

[0111] And so on, complete the clustering analysis of ξ1(a, b) and ξ2(a, b), and finally construct the new damping ratio matrix result ξ 1,2(a, bb1); By clustering the damping ratios of all orders of modes, the possible true modes of all data sets can be identified, achieving high-precision identification of modes and improving the noise resistance performance of clustering identification.

[0112] When performing clustering analysis on the mode shapes in this step, since the points on the stable axis in the stability diagram need to be stable not only in terms of frequency and damping ratio but also ensure the stability of the mode shapes, it is necessary to perform mode shape clustering on the corresponding two-order modes in Ψ1(a, b, q) and Ψ2(a, b, q), including:

[0113] Assume ξ 1,2 (a, bb1) in which ξ1(a, 1) and ξ2(a, 1) belong to the same category in terms of frequency and damping ratio. According to the method in steps S41 - S45, perform clustering analysis on Ψ1(a, 1, q) and Ψ2(a, 1, q);

[0114] When Ψ1(a, 1, q) and Ψ2(a, 1, q) are classified into the same category, take the average value as the new first-order mode shape result: Ψ 1,2 (a, 1, q) = (Ψ1(a, 1, q) + Ψ2(a, 1, q)) / 2; otherwise, split f 1,2 (a, 1) into the original f1(a, 1) and f2(a, 1), split ξ 1,2 (a, 1) into the original ξ1(a, 1) and ξ2(a, 1), and construct a new frequency matrix ff 1,2 (a, 1) and damping ratio matrix ξξ 1,2 (a, 1).

[0115] By analogy, complete the clustering analysis of Ψ1(a, 1, q) + Ψ2(a, 1, q), and finally construct a new mode shape matrix result Ψ 1,2 (a, bbb1, q); By performing mode shape clustering on all orders of modes, the possible true modes of all data sets can be identified, achieving high-precision identification of modes and improving the noise resistance performance of clustering identification.

[0116] Define the updated frequency result f 1,2 (a, b1), damping ratio result ξ 1,2 (a, bb1) and mode shape result Ψ 1,2 (a, bbb1, q) as the new second set of modal parameter results ξ 1,2 (a, bb1), Ψ 1,2 (a, bbb1, q)} and complete the analysis of the same category for and X3 based on the steps in S41 - S45 to obtain the updated third set of modal parameter results By analogy, complete the clustering analysis of all groups of numbers (T) to obtain the final modal parameter results By adopting the FCM clustering algorithm of S41 - S45, the modal parameter results of multiple collected stable diagrams are effectively clustered and divided to achieve the intelligent identification of true and false modes.

[0117] In order to screen out the modes that are stable in terms of frequency value, damping ratio, and modal vibration shape, the number of effective group modal parameters for each clustering mode in can be first counted. In this embodiment, the effective number of groups is the modal parameter results of all groups that can reflect the true mode. In this embodiment, the effective number of groups is taken as 0.8T; by selecting the stable diagrams corresponding to the modal parameter results greater than 0.8T, the effectiveness of the results is improved. Through the continuous change of the intuitive modal parameter results, the health state of the bridge structure 1 can be quickly judged, and the FCM clustering method has low complexity and is easy to implement, improving the recognition effectiveness and making the obtained results closer to the real situation.

[0118] Please refer to Figure 7 , through the clustering stable diagrams within 8 consecutive hours, the first 4 natural frequency values of the simply supported beam structure of this span can be known. Among them, the first-order modal frequency value is 2.07Hz, the second-order modal frequency value is 8.21Hz, the third-order modal frequency value is 16.67Hz, and the fourth-order modal frequency value is 31.06Hz.

[0119] S5. Compare and analyze the change situation of the modal parameter results after clustering of the same structure of the bridge in consecutive time periods. If the modal parameter results after clustering change, it is judged that the bridge is in an unhealthy state. If the modal parameter results after clustering do not change, it is judged that the bridge is in a healthy state.

[0120] When judging the health state, when the natural frequency results of each order at the measured structure of the bridge change at a certain moment and the change of the frequency results of each order exists after that moment, it is determined that the bridge has certain damage and relevant technical personnel need to be arranged to conduct a comprehensive inspection on it; through the change and the existence of the change of the natural frequency results of each order, the bridge damage can be intuitively judged and the health condition of the bridge can be quickly judged.

[0121] In this embodiment, the health state of a 35m simply supported beam of a certain span of the bridge structure 1 is detected continuously for 1 month. Based on steps S1 - S5, with time as the X-axis and frequency value as the Y-axis, finally, the time history curve graph of the first 5 natural frequency values of this simply supported beam within 30 days is obtained every day; by comparing and analyzing the percentage difference between each natural frequency value and the average value of each order of frequency, when the percentage difference exceeds 5%, it can be preliminarily determined that this simply supported beam may be damaged, and relevant professionals need to be arranged to conduct a more detailed inspection on it; such as Figure 8 , according to the time history curve graph of the first 5 natural frequency values of a 35m simply supported beam of a certain span within a certain 30 days, it can be seen from this graph that the percentage error of the first 5 natural frequency values is within 5%, which indicates that the structure of this simply supported beam is in good health within these 30 days and no damage has occurred.

[0122] Embodiment 2

[0123] This embodiment provides a bridge structure health detection method based on the fuzzy C-means clustering algorithm, adopting steps S1 - S5 of the detection method in Embodiment 1. The difference is that: the bridge targeted in this embodiment is a real cable-stayed bridge structure, a certain suspension system cable-stayed bridge in Chongqing, and the parameter results of its main girder are identified by clustering. The layout of this cable-stayed bridge is as Figure 9 , the main span length of this cable-stayed bridge is 330m, the side span length is 149m, and there are 411 acceleration sensors installed on the main girder in total. The sampling frequency of the acceleration sensor 4 is 80Hz, as Figure 10 , the acceleration response signals collected by the mid-span sensor within any 50 seconds, a total of 4000 data points, and the general range of the acceleration value is between [-0.02, 0.02].

[0124] Relevant detection units obtain the natural frequency of this cable-stayed bridge itself by means of vehicle jumping excitation, as Figure 11 , the abscissa in the figure represents the frequency value of the structure, and the ordinate represents the acceleration value. It can be seen from this figure that the first-order modal frequency value of this cable-stayed bridge is 0.421Hz, the second-order modal frequency value is 0.861Hz, the third-order modal frequency value is 1.087Hz, the fourth-order modal frequency value is 1.666Hz, the fifth-order modal frequency value is 1.868Hz, and the sixth-order modal frequency value is 2.057Hz.

[0125] Collect the acceleration signals of this cable-stayed bridge every day in August 2020 through 11 sensors on the main girder, and take the data volume per 1 hour as the input data of the DATA-SSI algorithm, then 720 stable graphs can be identified. Using these 720 sets of modal parameter results as the input of the FCM clustering algorithm, and combining with Figure 1 the flowchart shown to realize the intelligent screening of the real mode and obtain the final clustering stable graph, as Figure 12As shown in the figure. It can be seen from the figure that the first six-order frequency values of the cable-stayed bridge identified by the method according to this embodiment are 0.432 Hz, 0.882 Hz, 1.039 Hz, 1.643 Hz, 1.824 Hz, and 2.011 Hz respectively.

[0126] Table 1 is Figure 12 a comparative analysis table between the true modal values and the theoretical values obtained by vehicle jumping. It can be seen that the first six-order frequency values identified by the algorithm proposed in this embodiment are very close to the theoretical values, and the percentage range of the error values is [-4.4%, 2.6%], further verifying the credibility of the identification effect of the proposed clustering algorithm.

[0127] Table 1 Comparative analysis table of frequency results

[0128]

[0129] In order to further verify that the detection method of this embodiment can effectively identify the modal vibration mode diagram of the bridge structure 1, the Figure 13 shown modal vibration mode diagram is obtained. The MAC value of the modal vibration mode matching degree quantization index of the first three-order modal vibration mode diagrams in the figure is 0.96, indicating that the obtained modal vibration mode results have a very high matching degree with the theoretical modal vibration mode diagram.

[0130] Embodiment 3

[0131] This embodiment provides a system for bridge structure health detection based on the fuzzy C-means clustering algorithm, which adopts the bridge structure health detection method based on the fuzzy C-means clustering algorithm in Embodiment 1. The system includes a memory and a processor, and the system can be implemented based on hardware, software, or a combination of software and hardware.

[0132] The memory of this embodiment uses a disk memory, and can also use a CD-ROM, optical memory, or other forms of memory. The memory stores computer code that can run on the processor. The computer code includes steps S1 to S5 of executing the bridge structure health detection method based on the fuzzy C-means clustering algorithm in Embodiment 1, and can execute each step according to the Figure 1 process in it. It includes each process, block, or their combination in it, and provides these computer program instructions to the processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing device to generate a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate for realizing in the process Figure 1 one process or multiple processes and / or blocks Figure 1Apparatus for the functions specified in one or more boxes; computer program instructions can also be stored in a computer-readable memory capable of guiding a computer or other programmable data processing device to work in a specific manner, so that the instructions stored in the computer-readable memory produce a manufactured article including an instruction device, and the instruction device implements the process Figure 1 One process or more processes and / or boxes Figure 1 The functions specified in one box or more boxes; through this system, it is possible to execute the steps of a bridge structure health detection method based on the fuzzy C-means clustering algorithm, detect the health status of the bridge based on the detection method, eliminate manual operations, quickly output results, facilitate the implementation of the detection method and the detection operation, and quickly judge the health status of the bridge structure 1.

[0133] The above are only the preferred embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principles of the present invention shall be included in the protection scope of the present invention.

Claims

1. A bridge structure health detection method based on the fuzzy C - means clustering algorithm, characterized in that, It includes the following steps: S1. Collect the acceleration response signals of the same measurement structure on the bridge at different time periods; S2. Take the acceleration response signals as the input signals for modal parameter identification, and identify a large number of parameter results. The parameter results of the same time period are grouped as a set and retained as the stability diagram results; S3. Define the modal parameter result corresponding to each stable graph result as X i ={f i (a,b), ξ i (a,b), Ψ i (a, b, q)}, i = 1, 2, …, T; a = 1, 2, …, A; b = 1, 2, …, B; Where, T represents the total number of groups of modal parameter results, f represents the frequency results, which are (m×n) matrix data, ξ represents the damping ratio results, which are (m×n) matrix data, Ψ represents the modal shape results, which are (m×n×c) matrix data, and c is the number of clusters; A represents the system order of the bridge measurement structure, B represents the number of columns of the vector in the parameter results, and q represents the number of sensors arranged on the bridge measurement structure; S4. Adopt the FCM fuzzy C-means step-by-step clustering method to cluster the adjacent front and back stability diagrams in the T groups of stability diagrams. First, divide different clusters according to the membership degree. By finding the membership matrix and the cluster center, complete the clustering analysis of all groups of data sets for frequency, damping ratio, and modal shape respectively. Plot the modes whose clustering groups of frequency values, damping ratios, and modal shapes exceed the effective number of groups in the final stability diagram as stable modes, and then obtain the true modal results after clustering; S5. Compare and analyze the changes in the modal parameter results after clustering of the same structure of the bridge in consecutive time periods. If the modal parameter results after clustering change, it is judged that the bridge is in an unhealthy state. If the modal parameter results after clustering do not change, it is judged that the bridge is in a healthy state.

2. The bridge structure health detection method based on the fuzzy C - means clustering algorithm according to claim 1, characterized in that, In step S4, when performing clustering analysis on frequency, it includes: S41. Select f1(a,b) and f2(a,b) as the data set X for FCM clustering; S42. Determine the number of clusters c = 2 and the maximum number of iterations m = A / 2; S43. Define the objective function J and the constraints of the clustering; S44. Based on the membership matrix and the cluster center, find the membership matrix and the cluster center that minimize the objective function by continuously iteratively verifying the cluster center for the data set X; S45. Cluster the modes of each order of f1(a,b) and f2(a,b), and judge whether the frequencies of each order are in the same class. If they are in the same class, calculate the updated frequency values of each order.

3. The bridge structure health detection method based on the fuzzy C - means clustering algorithm according to claim 2, characterized in that, The objective function J is: where, u ij is the membership degree of each sample j belonging to a certain class i; The constraints are: where m is the maximum number of iterations, with the value range m ∈ [1, ∞], ||x j - c i || represents the Euclidean distance between the data object x j and the i-th cluster center.

4. The bridge structure health detection method based on the fuzzy C - means clustering algorithm according to claim 2, characterized in that, The membership degree is calculated by the following formula: where, u ij is the membership degree, representing the membership degree of each sample j in the dataset X belonging to the i-th cluster center.

5. The bridge structure health detection method based on the fuzzy C - means clustering algorithm according to claim 2, characterized in that, The cluster center is calculated by the following formula: Among them, c i is the clustering center, indicating the i-th clustering center of the c clustering centers into which the dataset X is divided.

6. The bridge structure health detection method based on the fuzzy C - means clustering algorithm according to claim 2, characterized in that, When performing clustering judgment in step S45: Cluster identification is performed on the first-order frequency. When f1(a,1) and f2(a,1) belong to the same class, the updated first-order frequency value f 1,2 (a,1) = (f1(a,1) + f2(a,1)) / 2; And so on, complete the clustering analysis of all order frequency values in the two frequency matrices of f1(a, b) and f2(a, b), and form a new frequency result f by combining the new modes after clustering with the unclustered modes 1,2 (a, b1).

7. The bridge structure health detection method based on the fuzzy C - means clustering algorithm according to claim 6, wherein, In step S4, when performing clustering analysis on the damping ratio, it includes: Assume f 1,2 (f1(a, 1) and f2(a, 1) in (a, b1) are of the same kind in terms of frequency. According to the method of steps S41 - S45, clustering analysis of the damping ratios of ξ1(a, 1) and ξ2(a, 1) is carried out, and finally a new damping ratio matrix result ξ is constructed.) 1,2 (a, bb1).

8. The bridge structure health detection method based on the fuzzy C - means clustering algorithm according to claim 6, wherein, In step S4, when performing clustering analysis on the modal shape, it includes: Assume ξ 1,2 (In (a, bb1), ξ1(a, 1) and ξ2(a, 1) are of the same kind in terms of frequency and damping ratio. According to the method of steps S41 to S45, perform clustering analysis on the modal vibration modes of Ψ1(a, 1, q) and Ψ2(a, 1, q), and finally construct a new vibration mode matrix result Ψ 1,2 (a, bbb1, q).

9. The bridge structure health detection method based on the fuzzy C - means clustering algorithm according to claim 1, wherein, When judging the health state in step S5, when the natural frequency results of each order at the measurement structure of the bridge change at a certain moment and the changes in the frequency results of each order continue to exist after that moment, it is determined that the bridge has certain damage.

10. The system for bridge structure health detection based on the fuzzy C - means clustering algorithm, wherein, Adopt the bridge structure health detection method based on the fuzzy C-means clustering algorithm according to any one of claims 1-9. The system includes a memory and a processor. The memory stores computer code that can run on the processor. The computer code includes steps S1 to S5 of executing the bridge structure health detection method based on the fuzzy C-means clustering algorithm according to any one of claims 1-9.

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