Engineering structure modal identification method based on Monte Carlo method and multilevel clustering

Abstract

The invention belongs to the field of structure safety monitoring, and discloses an engineering structure modal recognition method based on a Monte Carlo method and multi-level clustering, which comprises the following steps: acquiring a Fourier spectrogram of structure dynamic time history response, and acquiring an estimated value of structure fundamental frequency; a plurality of groups of random integers are generated through Monte Carlo simulation to serve as user-defined parameters of the SSI-COV modal identification method, and corresponding modal parameter identification is carried out. And carrying out stability discrimination on the identification modal points of each group of parameters, and adding the discriminated modal points to the stability graph to form a stability graph with multiple identification results. And estimating a probability density map of frequency characteristics in the stability map by adopting a kernel density clustering method. And in the probability density map, screening out a plurality of modal point clusters based on a frequency prominent peak threshold, applying a DBSCAN clustering algorithm to the modal point clusters to obtain a plurality of clustering clusters, and calculating a modal parameter average value of the clusters to obtain structural modal parameters.

Description

Technical Field

[0001] The present invention belongs to the technical field of structural safety monitoring, and in particular relates to an engineering structure modal identification method based on Monte Carlo method and multi-level clustering. Background Art

[0002] The importance of large-scale infrastructure in national production activities is evident, especially large dams and wind turbine structures. Most of my country's large dams are located in the southwest, which is characterized by high-frequency and high-intensity earthquakes. Over the long term, concrete dams are subject to loads such as earthquakes and flood discharges, which can damage their structures. Furthermore, concrete materials age during long-term freeze-thaw cycles, affecting their load-bearing capacity. Both of these factors can alter the dynamic characteristics of the structure. Structural modal parameter identification can track changes in dynamic characteristics, which helps improve our understanding of the dynamic behavior of structures.

[0003] However, the traditional modal parameter identification algorithm has the following problems: (1) Classical modal identification algorithms in the time domain, such as the Stochastic Subspace Identification - Covariance Driven (SSI-COV) method, have identification structures that are very sensitive to user-defined parameters, and the accuracy of identification is highly dependent on the selection of parameters.

[0004] (2) For the stability diagram generated by the SSI-COV method, the current clustering algorithm cannot distinguish the physical and false modes of the stability diagram well, and cannot distinguish the physical dense modes therein well. Summary of the Invention

[0005] The objective of the present invention is to address the above-mentioned problems and provide a modal identification method for engineering structures based on the Monte Carlo method and multi-level clustering, which obtains the Fourier spectrum of the structural dynamic time-history response and obtains the estimated value of the structural fundamental frequency; generates multiple groups of random integers through Monte Carlo simulation as user-defined parameters of the SSI-COV modal identification method, and performs corresponding modal parameter identification; identifies modal points for each group of parameters and adds them to the stability diagram after stability judgment; performs a first and a second clustering of the modal points using the kernel density estimation method (KDN) and the density-based spatial clustering of applications with noise (DBSCAN) algorithm, respectively, to obtain modal point clusters, calculates the modal parameter averages of the clusters, and obtains the structural modal parameters; and forms a closed-loop modal identification framework by organically combining SSI-COV, β distribution statistics, and DBSCAN clustering to solve the problems of strong parameter dependence and weak noise resistance in traditional methods.

[0006] In order to achieve the above object, in a first aspect, the present invention provides an engineering structure modal identification method based on Monte Carlo method and multi-level clustering, comprising the following steps: S1. Obtain the dynamic response of the engineering structure under environmental excitation, perform Fourier spectrum analysis, and obtain an estimated value of the structural basic frequency; based on the estimated frequency value, determine the value range of the user-defined parameter group; S2. Based on the value range of the user-defined parameter group, a Monte Carlo method is used to generate multiple user-defined parameter groups; S3. Apply the SSI-COV modal identification algorithm to each user-defined parameter group, use the stability judgment criterion to screen the modal points, add the screened modal points to the stability diagram, and add the modal points identified by all user-defined parameter groups to the same stability diagram; S4. Based on a kernel density estimation method, a Gaussian kernel is selected to scan the frequency features in the stability map to generate a probability density map for identifying frequencies; S5. Fitting all frequency points using a beta distribution to generate a frequency prominence threshold; selecting based on the frequency prominence threshold in the probability density map to form multiple modal point clusters; S6. Applying the DBSCAN clustering algorithm to the modal point clusters obtained in step S5 to form modal point clusters; calculating an average value of the modal parameters of each modal point cluster to obtain the modal parameters of the engineering structure.

[0007] Preferably, in step S1, the Fourier spectrum is obtained based on the dynamic response of the engineering structure under environmental excitation to determine the estimated value of the fundamental frequency of the engineering structure.f ;by f Based on this, calculate the threshold constant of the user-defined parameter group α , ; in, f s is the sampling frequency of the engineering structure.

[0008] Preferably, in step S1, the value range of the user-defined parameter group is: ; ; ; in, N max is the maximum system order, i is the forward time window parameter, and j is the backward time window parameter.

[0009] Preferably, in step S2, K groups of user-defined parameter groups are generated based on Monte Carlo simulation to form a parameter set [θ 1 ,θ 2 , ... ,θ K-1 ,θ K ],in , s =1,2...K.

[0010] Preferably, in step S3, the user-defined parameter group Apply the SSI-COV modal identification method to obtain the modal point set Ψ s =[ γ 1 , γ 2 ,..., γ N ],in γ h =[ , ξ h , ], h =1,2,..., N They correspond to the natural frequency, damping ratio, and mode shape of the hth modal point, respectively, and N is the number of modal points; When a modal point meets the following screening conditions, it is retained in the stable diagram; ; ; ; in, Hrepresents the Hermitian transpose operator; MAC( ) represents the function corresponding to the modal determination criterion; 、 and are the acceptance thresholds for frequency, damping ratio, and mode shape, respectively; 、 Respectively represent the frequencies of the modal points at orders 2n and 2n+2; 、 Respectively represent the damping ratios of the modal points at orders 2n and 2n+2; 、 They represent the vibration mode vectors of the modal point at orders 2n and 2n+2 respectively.

[0011] Preferably, in step S3, the threshold is specifically set to 、 and .

[0012] In step S4, the x-axis of the stability diagram is the frequency, and the y-axis is the order of the model, ranging from [10, N max ].

[0013] In step S4, a Gaussian function is selected as the kernel function of the kernel density estimation method to estimate the probability density function of the frequency feature; The frequency estimate is calculated as: ; ; in, is the estimated value of the frequency value, K( ) represents the kernel function; is the frequency value to be estimated for a certain item in the stability diagram, is the number of modal points in the stability diagram, is the frequency value of each modal point in the stability diagram, is a user-defined smoothing parameter.

[0014] Preferably, in step S4, the improved Sheather–Jones algorithm is used to calculate , to avoid errors caused by user customization.

[0015] Preferably, in step S5, a β distribution is applied to fit all frequency points, and a frequency prominence threshold t is determined based on a 99% confidence criterion. Based on the frequency prominence threshold t, p prominence clusters are selected from the frequency probability density curve as modal point clusters.

[0016] Preferably, in step S6, the DBSCAN clustering algorithm is applied to the p modal point clusters in S5 to obtain q clusters, and the modal parameter average of each cluster in the q clusters is calculated to obtain the modal parameters of the structure.

[0017] In a second aspect, the present invention provides an engineering structure modal identification system based on the Monte Carlo method and multi-level clustering, comprising the following modules: Structural foundation frequency estimation module: used to obtain the dynamic response of the engineering structure under environmental excitation, perform Fourier spectrum analysis, and obtain the estimated value of the structural foundation frequency; User-defined parameter module: Determines the value range of the user-defined parameter group based on the frequency estimation value output by the structural basic frequency estimation module; uses the Monte Carlo method to generate multiple user-defined parameter groups; Stability diagram module: applies the SSI-COV modal identification algorithm to each user-defined parameter group output by the user-defined parameter module, uses the stability judgment criterion to screen the modal points, and adds the screened modal points to the stability diagram; The first clustering module: Based on the kernel density estimation method, a Gaussian kernel is selected to scan the frequency features in the stability map obtained by the stability map module to generate a probability density map for identifying frequencies; Modal point cluster generation module: using β Distribution fitting is performed on all frequency points to generate a frequency prominence threshold. Based on the frequency prominence threshold, selection is performed in the probability density map obtained by the first clustering module to form multiple modal point clusters. The second clustering module: uses the DBSCAN algorithm to cluster the modal point clusters output by the modal point cluster generation module to form modal point clusters; Modal parameter calculation module: used to calculate the average value of the modal point clusters to obtain the modal parameters of the engineering structure.

[0018] Compared with the prior art, the present invention has the following beneficial effects: 1) This paper organically combines SSI-COV, Monte Carlo sampling, ISJ kernel density estimation, β distribution statistics and DBSCAN clustering to form a closed-loop modal identification framework, which achieves accurate and efficient identification of modal parameters of large-scale engineering structures, and solves the problems of strong parameter dependence and weak noise immunity in traditional methods. It also optimizes modal extraction by jointly using statistical methods (β distribution confidence threshold) and data-driven methods (DBSCAN), taking into account both physical rationality and data adaptability.

[0019] 2) This invention improves the accuracy of structural modal identification. By integrating multiple parameter groups and implementing strict screening criteria, it significantly reduces the rate of false positives (such as the introduction of false modes), ensuring accurate identification of frequency, damping ratio, and mode shape. The improved ISJ algorithm optimizes kernel density estimation, accurately capturing multimodal distribution characteristics and avoiding over-smoothing or under-smoothing issues.

[0020] 3) The structural modal identification method proposed in this paper enhances adaptability to environmental excitations and is suitable for long-term health monitoring of engineering structures that rely solely on environmental excitations (without artificial excitation), such as bridges and large buildings. The Monte Carlo parameter generation is combined with the SSI-COV algorithm, which is robust to non-stationary noise and low signal-to-noise ratio data.

[0021] 4) This invention automates the entire process of engineering structure modal identification (parameter generation → modal identification → statistical screening → clustering fusion), reducing manual intervention, operational complexity, and subjective errors. The β-distributed confidence threshold and DBSCAN clustering method enable automatic mode extraction and verification, making it suitable for large-scale data processing.

[0022] 5) This invention is compatible with modal analysis of structures with multiple measurement points and multiple degrees of freedom, supporting complex engineering scenarios (such as multi-order modes and dense modal separation), enhancing engineering practicality. Visual output of stability diagrams and probability density plots facilitates intuitive verification of modal results. BRIEF DESCRIPTION OF THE DRAWINGS

[0023] The present invention will be further described below with reference to the accompanying drawings.

[0024] Figure 1 Schematic diagram of the flow of the engineering structure modal identification method of embodiment 1.

[0025] Figure 2 This is the frequency peak selection diagram of the high arch dam response data at a certain hour under the first clustering in Example 2.

[0026] Figure 3 This is the frequency-order stability diagram of the high arch dam response data at a certain hour in Example 2 under the first clustering.

[0027] Figure 4 This is the frequency-damping ratio stability diagram of the high arch dam response data at a certain hour in Example 2 under the first clustering.

[0028] Figure 5 This is the frequency-damping ratio stability diagram of the high arch dam response data at a certain hour in Example 2 under the second clustering.

[0029] Figure 6 This is a frequency peak selection diagram of the wind turbine tower response data in a half-hour under the first clustering in Example 2.

[0030] Figure 7 This is the frequency-order stability diagram of the wind turbine tower response data for a half-hour under the first clustering in Example 2.

[0031] Figure 8 This is the frequency-damping ratio stability diagram of the wind turbine tower response data for a certain half-hour under the first clustering in Example 2.

[0032] Figure 9 This is the frequency-damping ratio stability diagram of the wind turbine tower response data for a half-hour under the second clustering in Example 2. DETAILED DESCRIPTION

[0033] Example 1 like Figure 1 As shown in FIG, the engineering structure modal identification method based on the Monte Carlo method and multi-level clustering includes the following steps: S1. Obtain the dynamic response of the structure under environmental excitation, perform Fourier spectrum analysis, and obtain the estimated value of the structural fundamental frequency f .by f Based on, build user-defined parameter group [ N max ,i,j ] value range.

[0034] S2, based on the user-defined parameter value range given in S1, use the Monte Carlo method to generate multiple user-defined parameter groups [ N max ,i,j ].

[0035] S3. Apply the SSI-COV modal identification algorithm to each parameter group. Use the stability criteria to filter modal points and add the filtered modal points to the stability diagram. Add the modal points identified by all parameter groups to the same stability diagram.

[0036] S4. Based on the kernel density estimation method, the frequency features in the Gaussian kernel scanning stability map are selected to generate a probability density map of the recognition frequency.

[0037] S5. Adoption β Distribution fitting is performed on all frequency points, and a frequency prominence threshold is generated based on a 99% confidence level. t Frequency-based highlight threshold t , select in the probability density map to form p A cluster of modal points.

[0038] S6, yes p The DBSCAN clustering algorithm is applied to the modal point clusters to form q The modal parameters of each cluster are averaged to obtain the modal parameters of the structure.

[0039] In step S1, the Fourier spectrum is obtained based on the structural dynamic response under environmental excitation to determine the estimated fundamental frequency of the structure. f .by f Based on the threshold constant of the parameter group α： ; in f s Where is the sampling frequency of the structure, from which the value range of the user-defined parameter group is derived as follows: ; ; .

[0040] In step S2, K groups of user-defined parameter groups are generated based on Monte Carlo simulation to form a parameter set [θ 1 ,θ 2 , ... ,θ K-1 ,θ K ],in , s =1,2...K.

[0041] In step S3, the user-defined parameter group Apply the SSI-COV modal identification method to obtain the modal point Ψ s =[ γ 1 , γ 1 ,..., γ n ],in γ h =[ , ξ h , ], corresponding to the natural frequency, damping ratio, and mode shape, respectively. When a modal point meets the following screening conditions, it is retained in the stability diagram.

[0042] ; ; ; Among them, the superscript H is the Hermitian transpose operator. MAC is the modal determination criterion; 、 and are the acceptance thresholds for frequency, damping ratio, and mode shape.

[0043] In the embodiment, respectively set to 、 and Repeat the above steps for K groups of user-defined parameter groups to form the final stability diagram.

[0044] In the generated stability diagram, the x-axis is the frequency and the y-axis is the order of the model, ranging from 10- N max .

[0045] In step S4, the Gaussian function is selected as the kernel function of the kernel density estimation to estimate the probability density function of the frequency feature. as follows: ; ; in is the frequency value to be estimated for a certain item in the stability diagram, is the number of modal points in the stability diagram, is the frequency value of each modal point in the stability diagram, is a user-defined smoothing parameter. To avoid errors caused by user-defined smoothing, it is calculated using the improved Sheather–Jones (ISJ) algorithm.

[0046] In step S5, apply β Distribution fitting is performed on all frequency points, and the frequency threshold is determined based on a 99% confidence criterion. t Frequency-based highlight threshold t , selected in the probability density curve of frequency p The prominent clusters are used as modal point clusters.

[0047] In step S6, the p The modal point clusters are clustered using the DBSCAN algorithm, and we get q Clusters. Calculate q The modal parameters of the structure are obtained by averaging the modal parameters of each cluster in the clusters.

[0048] The present invention does not require manual customization of the user-defined parameter group. N max ,i,j ] for selection. Monte Carlo simulations were used to generate multiple parameter groups within a reasonable range, each of which was identified using the SSI-COV method. Physical modal points were selected from all simulation results based on the fact that stable physical modal points have little correlation with the custom parameter groups.

[0049] The multi-level clustering method proposed in this invention is well adapted to the stability diagram generated based on Monte Carlo simulation. The amount of stability diagram data generated by this method is very large, and the first level of clustering has the characteristics of fast speed. For the stability diagram with a large number of modal points, it can quickly generate p The second-level DBSCAN clustering algorithm can incorporate frequency and vibration mode factors into the clustering metric to generate q modal point clusters, where q ≤ p The vibration mode is the most critical factor in determining whether a modal point is a physical modal point.

[0050] Example 2 Based on the response signal of a high arch dam under environmental excitation, identification is performed. In this embodiment, seven accelerometers are selected from the dam top and are symmetrically distributed on the left and right. The sampling frequency of each accelerometer is 200 Hz.

[0051] The measured acceleration response data comes from a certain time period of 1 hour. Using the engineering structure modal identification method based on Monte Carlo method and multi-level clustering in Example 1, the frequency peak selection diagram and the corresponding frequency-order diagram and frequency-damping ratio diagram of the structure under the first clustering (KDE clustering) are obtained, as shown in Figure 1. Figure 2 、 Figure 3 and Figure 4 As shown. It can be seen that the total recognition p =9 clusters, which does not conform to physical laws. After the second clustering (DBSCAN clustering), the frequency-damping Figure 5 As shown, it can be seen that there are 3 clusters, namely q =3, corresponding to the first three modes of the structure. Table 1 shows the modal parameters obtained by this method and the modal parameters obtained by the SSI-COV method with fixed user-defined parameters. The results show that the modal identification method proposed in this paper not only eliminates the tedious process of selecting user-defined parameters, but also shows good consistency in identification results with traditional methods.

[0052] Table 1 Comparison of modal parameters identified for a high arch dam

[0053] Example 3 Based on the response signal of a wind turbine tower under environmental excitation, identification is performed. In this embodiment, five accelerometers are selected from the inner wall of the tower and are evenly distributed up and down. The sampling frequency of each accelerometer is 100 Hz.

[0054] The measured acceleration response data is from a certain time period of 30 minutes. Using the engineering structure modal identification method based on Monte Carlo method and multi-level clustering in Example 1, the frequency peak selection diagram and the corresponding frequency-order diagram, as well as the frequency-damping ratio diagram of the structure under the first clustering (KDE clustering) are obtained as shown in the following figure: Figure 6 、 Figure 7 and Figure 8 As shown. It can be seen that the total recognition p = 4 clusters. After the second clustering (DBSCAN clustering), the frequency-damping Figure 9 As shown, it can be seen that it contains q =4 clusters, corresponding to the FA and SS directions of the first two modes of the wind turbine tower structure. Table 2 shows the modal parameters obtained by this method and the modal parameters obtained by the SSI-COV method with fixed user-defined parameters. The results show that the modal identification method proposed in this paper has good recognition results for different structures. At the same time, the two levels of clustering do not conflict with each other and complement each other, screening out physical modal points from the identified modal points, showing good robustness.

[0055] Table 2 Comparison of modal parameters for wind turbine tower identification

[0056] Example 4 This embodiment provides an engineering structure modal identification system based on the Monte Carlo method and multi-level clustering based on the method of the first embodiment, including the following modules: Structural foundation frequency estimation module: used to obtain the dynamic response of the engineering structure under environmental excitation, perform Fourier spectrum analysis, and obtain the estimated value of the structural foundation frequency; User-defined parameter module: Determines the value range of the user-defined parameter group based on the frequency estimation value output by the structural basic frequency estimation module; uses the Monte Carlo method to generate multiple user-defined parameter groups; Stability diagram module: applies the SSI-COV modal identification algorithm to each user-defined parameter group output by the user-defined parameter module, uses the stability judgment criterion to screen the modal points, and adds the screened modal points to the stability diagram; The first clustering module: Based on the kernel density estimation method, a Gaussian kernel is selected to scan the frequency features in the stability map obtained by the stability map module to generate a probability density map for identifying frequencies; Modal point cluster generation module: using β Distribution fitting is performed on all frequency points to generate a frequency prominence threshold. Based on the frequency prominence threshold, selection is performed in the probability density map obtained by the first clustering module to form multiple modal point clusters. The second clustering module: uses the DBSCAN algorithm to cluster the modal point clusters output by the modal point cluster generation module to form modal point clusters; Modal parameter calculation module: used to calculate the average value of the modal point clusters to obtain the modal parameters of the engineering structure.

Claims

1. The engineering structure modal identification method based on Monte Carlo method and multi-level clustering is characterized by: The following steps are involved: S1. Obtain the dynamic response of the engineering structure under environmental excitation, perform Fourier spectrum analysis, and obtain the estimated value of the structural foundation frequency; Determining a value range of a user-defined parameter group based on the frequency estimate; S2. Based on the value range of the user-defined parameter group, a Monte Carlo method is used to generate multiple user-defined parameter groups; S3. Apply the SSI-COV modal identification algorithm to each user-defined parameter group, use the stability judgment criterion to screen the modal points, add the screened modal points to the stability diagram, and add the modal points identified by all user-defined parameter groups to the same stability diagram; S4. Based on the kernel density estimation method, a Gaussian kernel is selected to scan the frequency features in the stability map to generate a probability density map of the recognition frequency; S5, fitting all frequency points using β distribution to generate a frequency prominence threshold; Based on a frequency prominence threshold, selection is performed in the probability density map to form a plurality of modal point clusters; S6. Applying the DBSCAN clustering algorithm to the modal point clusters obtained in step S5 to form modal point clusters; calculating an average value of the modal parameters of each modal point cluster to obtain the modal parameters of the engineering structure.

2. The engineering structure modal identification method based on Monte Carlo method and multi-level clustering according to claim 1 is characterized in that: In step S1, the Fourier spectrum is obtained based on the dynamic response of the engineering structure under environmental excitation to determine the estimated value of the fundamental frequency of the engineering structure. f ; by f Based on this, calculate the threshold constant of the user-defined parameter group α , ； in, f s is the sampling frequency of the engineering structure.

3. The engineering structure modal identification method based on Monte Carlo method and multi-level clustering according to claim 2 is characterized in that: In step S1, the value range of the user-defined parameter group is: ； ； ； in N max is the maximum system order, i is the forward time window parameter, and j is the backward time window parameter.

4. The engineering structure modal identification method based on Monte Carlo method and multi-level clustering according to claim 3 is characterized in that: In step S3, the user-defined parameter group Apply the SSI-COV modal identification method to obtain the modal point set Ψ s =[ γ 1 , γ 2 ,..., γ N ],in γ h =[ , ξ h , ], h =1,2,..., N They correspond to the natural frequency, damping ratio, and mode shape of the hth modal point, respectively, and N is the number of modal points; When a modal point meets the following screening conditions, it is retained in the stable diagram; ； ； ； in, H represents the Hermitian transpose operator; MAC( ) represents the function corresponding to the modal determination criterion; 、 and are the acceptance thresholds for frequency, damping ratio, and mode shape, respectively; 、 Respectively represent the frequencies of the modal points at orders 2n and 2n+2; 、 Respectively represent the damping ratios of the modal points at orders 2n and 2n+2; 、 They represent the vibration mode vectors of the modal point at orders 2n and 2n+2 respectively.

5. The engineering structure modal identification method based on Monte Carlo method and multi-level clustering according to claim 4 is characterized in that: In step S3, the threshold is specifically set to 、 and .

6. The engineering structure modal identification method based on Monte Carlo method and multi-level clustering according to claim 5 is characterized in that: In step S4, the x-axis of the stability diagram is the frequency, and the y-axis is the order of the model, ranging from [10, N max ].

7. The engineering structure modal identification method based on Monte Carlo method and multi-level clustering according to claim 6 is characterized in that: In step S4, a Gaussian function is selected as the kernel function of the kernel density estimation method to estimate the probability density function of the frequency feature; The frequency estimate is calculated as: ； ； in, is the estimated value of the frequency value, K( ) represents the kernel function; is the frequency value to be estimated for a certain item in the stability diagram, is the number of modal points in the stability diagram, is the frequency value of each modal point in the stability diagram, is a user-defined smoothing parameter.

8. The engineering structure modal identification method based on Monte Carlo method and multi-level clustering according to claim 7 is characterized in that: In step S4, the improved Sheather–Jones algorithm is used to calculate , to avoid errors caused by user customization.

9. The engineering structure modal identification method based on Monte Carlo method and multi-level clustering according to claim 8, characterized in that: In step S5, apply β Distribution fitting is performed on all frequency points, and the frequency threshold is determined based on a 99% confidence criterion. t ; Frequency-based highlight threshold t , selected in the probability density curve of frequency p The prominent clusters are used as modal point clusters.

10. The modal identification system of the engineering structure modal identification method according to any one of claims 1 to 9, characterized in that: Includes the following modules: Structural foundation frequency estimation module: used to obtain the dynamic response of the engineering structure under environmental excitation, perform Fourier spectrum analysis, and obtain the estimated value of the structural foundation frequency; User-defined parameter module: Determines the value range of the user-defined parameter group based on the frequency estimation value output by the structural basic frequency estimation module; uses the Monte Carlo method to generate multiple user-defined parameter groups; Stability diagram module: applies the SSI-COV modal identification algorithm to each user-defined parameter group output by the user-defined parameter module, uses the stability judgment criterion to screen the modal points, and adds the screened modal points to the stability diagram; The first clustering module: Based on the kernel density estimation method, a Gaussian kernel is selected to scan the frequency features in the stability map obtained by the stability map module to generate a probability density map for identifying frequencies; Modal point cluster generation module: using β Distribution fitting is performed on all frequency points to generate frequency prominence thresholds; Based on the frequency prominence threshold, multiple modal point clusters are formed by selecting from the probability density map obtained by the first clustering module; The second clustering module: uses the DBSCAN algorithm to cluster the modal point clusters output by the modal point cluster generation module to form modal point clusters; Modal parameter calculation module: used to calculate the average value of the modal point clusters to obtain the modal parameters of the engineering structure.

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