An automatic identification method of high arch dam modal parameters based on strong earthquake monitoring data

Abstract

A high arch dam modal parameter automatic identification method based on strong earthquake monitoring data, comprising: based on high arch dam strong earthquake monitoring data, using random subspace identification method algorithm to identify high arch dam modal parameter, taking self-vibration frequency and modal confidence criterion as coordinates, and the maximum value of power spectrum of all measuring points as background curve to draw stability diagram; combining local outlier factor and kernel density estimation to identify abnormal poles in stability diagram, eliminating false modes, and then using sparrow search algorithm to search for the optimal combination of K-means clustering algorithm to obtain the initial clustering center of stability diagram; using K-means algorithm to cluster and analyze effective poles in stability diagram, and realizing automatic identification of modal parameters. The present application combines SSI, SSA, LOF, KDE and K-means clustering algorithm, can significantly suppress noise under low signal-to-noise ratio condition, eliminate false modes, and automatically and accurately identify high arch dam modal parameters without human intervention.

Description

Technical Field

[0001] This invention relates to the field of safety monitoring of hydraulic structures, specifically a method for automatic identification of modal parameters of high arch dams based on strong earthquake monitoring data. Background Technology

[0002] Modal parameter identification is a crucial component of structural health monitoring. For large and complex structures like high arch dams, operational modal analysis under environmental excitation can ensure structural safety while reducing maintenance and management costs. Strong earthquake monitoring of high arch dams utilizes strong-motion seismographs installed on the dam and in a free field to measure the dynamic response of the "dam-reservoir-foundation" system under seismic excitation, providing a unique type of structural vibration monitoring data. Strong earthquake excitation is typically treated as stationary white noise. Based on this input assumption and the premise of linear structural analysis, modal parameters of high arch dams can be identified solely through the output response.

[0003] Because high arch dams are massive engineering structures with high degrees of freedom and dense modalities, they are significantly affected by environmental disturbances, posing considerable challenges to modal analysis. Therefore, automatically identifying the modal parameters of high arch dams based on strong earthquake monitoring data is an urgent problem to be solved. Summary of the Invention

[0004] To address the problems existing in the prior art, this invention provides an automatic identification method for modal parameters of high arch dams based on strong earthquake monitoring data. This method uses the natural frequency of the high arch dam identified by SSI (Self-Sensitive Indexing) as the abscissa, the modal confidence criterion calculated from the mode shape as the ordinate, and the maximum power spectrum as the background curve to plot a reliable stability diagram. Furthermore, to address the issue that single clustering algorithms often fail to achieve optimal clustering results, this invention combines LOF (Local Outlier Factor), KDE (Kernel Density Estimation), SSA (Sparrow Search Algorithm), and K-means clustering algorithms. By integrating the advantages of these methods, a new SSA-KMK clustering algorithm is proposed, overcoming the shortcomings of the K-means algorithm, such as sensitivity to initial cluster centers and outliers and susceptibility to local convergence. Ultimately, this method achieves automatic identification of modal parameters of high arch dams.

[0005] The technical solution adopted by this invention to solve its technical problem is as follows:

[0006] An automatic identification method for modal parameters of high arch dams based on strong earthquake monitoring data includes the following steps:

[0007] S1: Stability plotting: SSI (Scattered Subspace Identification) was used to perform preliminary analysis on the strong earthquake monitoring data of the high arch dam to identify the natural frequencies and mode shapes of different orders. The natural frequencies and MAC (Modal Confidence Criterion) that meet the tolerance were calculated. The natural frequencies that meet the tolerance were used as the x-axis, MAC as the y-axis, and the maximum power spectrum of all measuring points was used as the background curve to plot the stability plot. The poles in the stability plot were analyzed by the LOF (Local Outlier Factor) algorithm and KDE (Kernel Density Estimation) method to eliminate spurious modes.

[0008] S2: Parameter initialization: Set the population size, number of iterations, warning value, discoverer ratio, and scout ratio of SSA (Sparrow Search Algorithm), and initialize the sparrow population with K cluster centers;

[0009] S3: Cluster center update: For each cluster center, according to the minimum distance principle, the extreme points in the stable graph that have been removed from the outliers are assigned to the cluster with the smallest distance, and the average value of the elements in each cluster is calculated as the new center of the cluster.

[0010] S4: Calculation of optimal fitness value and individual sparrow: Calculate the fitness value of individuals in the sparrow population, sort all individual sparrow fitness values, find the current best and worst fitness values, update the positions of discoverers, joiners, and scouts, calculate the population fitness value of sparrows, update the population position of sparrows, and determine whether the algorithm has reached the maximum number of iterations. If not, return to step S3; if so, output the optimal fitness value and individual sparrow.

[0011] S5: Obtaining the best cluster centers and cluster partitions: Using the best sparrow individuals obtained in step S4 as the initial cluster centers, the K-means clustering algorithm is used to perform cluster analysis on the extreme points in the stable graph after outliers have been removed, to obtain the final cluster centers and cluster partitions.

[0012] S6: Modal parameter determination: The parameters contained in the poles closest to the final cluster centers are determined as the final modal parameters.

[0013] The specific steps for drawing the stability diagram in step S1 are as follows:

[0014] S11. For monitoring data of strong earthquakes involving high arch dams, the discrete stochastic state-space model is as follows:

[0015]

[0016] In the formula: x k ∈R n×1 y k ∈R l×1 Let x and y be the values ​​of the system's discrete-time state vector and output vector y at time k, respectively, and l be the number of system outputs; A ∈ R n×n , C∈Rl×n These are the state matrix and output matrix of the system's state-space equations, respectively; w k ∈R n×l v k ∈R l×1 Let w and v be the values ​​of the system modeling process noise and the measurement noise at time k, respectively, which are white noise with zero mean.

[0017] S12. Construct the Toeplitz matrix:

[0018]

[0019] In the formula: R is the covariance matrix of the output vector. i for:

[0020] S13, Toeplitz matrix decomposition:

[0021] For the Toeplitz matrix T 1|i SVD decomposition yields:

[0022]

[0023] In the formula: U1∈R li×n V1∈R li×n All are orthogonal matrices, and S1 is a diagonal matrix of n principal singular values ​​arranged in descending order;

[0024] S14. The eigenvalues ​​of the system matrix are decomposed as follows:

[0025] A = ΨΛΨ -1 (4)

[0026] In the formula, Λ is a pole of the discrete-time system μ i The diagonal matrix formed by these elements, Ψ, is the eigenvector of the state matrix A in the system's state-space equations.

[0027] S15, Passing through the poles μ of the discrete system i Calculate the eigenvalues ​​λ of a continuous system i for:

[0028]

[0029] In the formula: Δt is the sampling time interval;

[0030] S16, the calculated results for natural frequency, damping ratio, and mode shape are as follows:

[0031]

[0032] In the formula: f i ξ i Φ iLet represent the natural frequency, damping ratio, and mode shape of the i-th mode, respectively.

[0033] S17. Calculate the natural frequency and MAC that satisfy the tolerance:

[0034]

[0035] (1-MAC(n,n+1))×100%<2% (8)

[0036] In the formula: f is the calculated natural frequency, n is the order of the model, and MAC is the Modal Assurance Criterion.

[0037]

[0038] In the formula: Φ represents the mode shape, and the MAC value is between 0 and 1, indicating the correlation of the mode shape.

[0039] A stability graph is plotted with the natural frequency that meets the tolerance as the x-axis and MAC as the y-axis, and the maximum power spectrum of all measurement points is used as the background curve of the stability graph.

[0040] S18. For a dataset of poles in a stable graph, X = [x1, x2, ..., x...] N ]∈R M×N x i The k nearest neighbors of (i = 1, 2, ..., N) are:

[0041]

[0042] x i With x j The reachable distance is represented as:

[0043] reach_dist(x i x j )=max{k_dist(x j ), dist(x i x j (11)

[0044] In the formula: k_dist(x i ) is x i The Euclidean distance between it and its k-th nearest neighbor;

[0045] x i The locally attainable density is:

[0046]

[0047] In the formula: NK(x) i ) is xi The neighborhood set;

[0048] x i The local outlier factor is:

[0049]

[0050] S19. Using the KDE method, determine the probability density function of the local outlier LOF calculated in step S18. Set the significance level to 5% and calculate the control value. If LOF(x) i If the value is higher than the control value determined by KDE, then x is determined to be higher. i To eliminate abnormal poles in the stability graph, spurious modes related to high arch dams are removed.

[0051] The specific steps for parameter initialization in step S2 are as follows:

[0052] S21. Set the population size, number of iterations, warning value, discoverer ratio, and scout ratio in the Sparrow Algorithm;

[0053] S22. Based on the stability graph in step S1 after removing spurious modes, determine the K dominant natural frequencies of the high arch dam monitoring data, and initialize the sparrow population at the K cluster centers of the poles in the stability graph.

[0054] The specific steps for updating cluster centers in step S3 are as follows:

[0055] S31. For each group of cluster centers determined in step S2, calculate the Euclidean distance between each pole in the stable graph determined in step S1 and these cluster centers.

[0056] S32. Based on the Euclidean distance calculated in step S31 and the minimum distance principle, the poles in the stable graph that have been removed from outliers are assigned to the clusters with the smallest distances.

[0057] S33. Calculate the average value of the elements in each cluster as the new cluster center for that cluster.

[0058] The specific steps for calculating the optimal fitness value and individual sparrows in step S4 are as follows:

[0059] S41. Calculate the fitness value of individuals in the sparrow population, sort all sparrow individual fitness values, and find the current best and worst fitness values;

[0060] S42. The formula for updating the discoverer's location is:

[0061]

[0062] In the formula: This indicates the position of the i-th sparrow in generation t+1; C is a constant representing the maximum number of iterations.ξ ∈(0,1) is a random number; R2∈[0,1] and ST∈[0,1] represent the warning value and the safety value, respectively; C Q Let L be a random number that follows a normal distribution; L is a single-row multidimensional matrix with all elements equal to 1.

[0063] S43. The formula for updating the position of newcomers is:

[0064]

[0065] In the formula: X P X is the optimal location for the current discoverer. worst A represents the current worst-case position globally; A is a single-row multidimensional matrix where each element is either 1 or -1. + =A T (AA T );

[0066] S44. The formula for updating the scout's position is:

[0067]

[0068] In the formula: It is the current global best position; C β It is the step size control parameter; C K ∈(0,1) is a random number; f i It is the current fitness value of the sparrow, f g and f w These are the current best and worst fitness values; C ε It is a constant used to avoid the denominator being zero, and is set to 10e-10;

[0069] S45. Calculate the sparrow population fitness value and update the sparrow population location;

[0070] S46. Determine if the algorithm has reached the maximum number of iterations. If not, return to step S3. If it has, output the optimal fitness value and the individual sparrow.

[0071] The specific steps for obtaining the optimal cluster centers and cluster partitions in step S5 are as follows:

[0072] S51. Use the best sparrow individual obtained by the sparrow algorithm as the initial cluster center;

[0073] S52. Calculate the Euclidean distance between the poles of the stable graph determined in step S1 after removing outliers and the initial cluster centers, and divide the graph according to the minimum distance to form K cluster regions.

[0074] S53. Calculate the mean of all objects in each cluster domain and use it as the new cluster center for that class.

[0075] S54 and the Davies-Bouldin index are used as clustering evaluation indicators, and their specific calculation formulas are as follows:

[0076]

[0077] In the formula, C i w represents the average distance from the data within cluster i to the cluster centroid. i For cluster class C i The cluster centroid, ||·||2 represents the Euclidean distance;

[0078] S55. If the termination condition is met, the algorithm ends; otherwise, return to step S52 to obtain the final cluster centers and cluster partitions.

[0079] The present invention has the following beneficial effects:

[0080] (1) This invention proposes a new stability diagram, which uses the natural frequency that meets the tolerance as the horizontal axis, the mode guarantee criterion as the vertical axis, and the maximum power spectrum as the background curve. This makes each pole in the stability diagram contain two stable modal parameters: the natural frequency and the mode guarantee criterion, thus avoiding the influence of unstable damping ratio and facilitating the automatic identification of modal parameters.

[0081] (2) This invention uses LOF and KDE methods to identify outlier poles and remove spurious modes in the stability graph; then it optimizes the K-means algorithm clustering process through SSA to automatically determine the globally approximate optimal cluster center; finally, it uses the cluster center as the initial center of the K-means algorithm to perform local search to obtain the optimal cluster center and cluster partition, and automatically identifies the modal parameters of the high arch dam; this method can make up for the shortcomings of the K-means algorithm in being sensitive to the initial cluster center and outlier points and being prone to local convergence, and finally realizes the automatic identification of the modal parameters of the high arch dam. Attached Figure Description

[0082] Figure 1 This is a flowchart of one embodiment of the method for identifying modal parameters of high arch dams based on strong earthquake monitoring data according to the present invention;

[0083] Figure 2 This is a field layout diagram of the strong-motion seismometer monitoring system used in the embodiments of the present invention;

[0084] Figure 3 This is a diagram of a strong-motion seismometer monitoring system;

[0085] Figure 4 These are the radial strong earthquake acceleration monitoring data and corresponding power spectrum of the high arch dam at an elevation of 527m according to an embodiment of the present invention;

[0086] Figure 5This is a stability diagram of radial strong earthquake monitoring data for a high arch dam according to an embodiment of the present invention;

[0087] Figure 6 The results of identifying abnormal poles in the stability diagram of a high arch dam based on LOF and KDE in this embodiment of the invention are shown in (a) as a two-dimensional diagram and (b) as a three-dimensional diagram.

[0088] Figure 7 This is a convergence trajectory diagram of the existing PSO-KM clustering algorithm and the SSA-KM clustering algorithm of this invention;

[0089] Figure 8 These are stability diagrams of high arch dams using the existing PSO-KM clustering algorithm and the SSA-KM clustering algorithm of this invention.

[0090] Figure 9 This is a stability diagram of a high arch dam using the SSA-KMK clustering algorithm according to an embodiment of the present invention;

[0091] Figure 10 This is a comparison chart of the identification results of the eight vibration modes in front of the high arch dam using the traditional SSI and the SSI-SSA-KMK embodiment of the present invention. Detailed Implementation

[0092] The technical solutions of the present invention will now be clearly and completely described with reference to the accompanying drawings.

[0093] Please refer to Figure 1 This embodiment provides an automatic identification method for modal parameters of high arch dams based on strong earthquake monitoring data, including the following steps:

[0094] S1: Stability plotting;

[0095] To analyze and verify the effectiveness of the proposed method, radial strong-motion acceleration monitoring data from five strong-motion seismographs (QZY13~QZY17) at an elevation of 527m on January 23, 2021, were analyzed, assuming a magnitude 4.7 earthquake occurred 56.55 km from the Xiluodu arch dam with a focal depth of 10 km. The strong-motion seismograph monitoring system was deployed on-site as follows: Figure 2 As shown, the strong-motion seismometer monitoring system is as follows: Figure 3 As shown. Radial strong earthquake monitoring data and corresponding power spectra at an elevation of 527m are shown below. Figure 4 .

[0096] With frequency and mode shape errors set at 1% and 2% respectively, and a maximum system order of 40, SSI was used for preliminary analysis of strong earthquake monitoring data of high arch dams. Natural frequencies and mode shapes of different orders were identified, and the tolerable natural frequencies and MAC were calculated. Using the tolerable natural frequencies as the x-axis and MAC as the y-axis, and the maximum power spectrum of all measuring points as the background curve, a stability diagram was plotted. The stability diagram of the strong earthquake monitoring data of high arch dams is shown below. Figure 5 .from Figure 4 and Figure 5 The power spectrum shows that there are eight dominant frequencies in the radial strong earthquake monitoring data of high arch dams. The results of anomaly identification in the stability plot based on the LOF algorithm and KDE method are shown below. Figure 6 .

[0097] S2: Parameter initialization;

[0098] The population size was set to 40, the number of iterations to 300, the warning value to 0.6, the discoverer ratio to 70%, and the scout ratio to 20%. To compare the superiority of the sparrow algorithm, the particle swarm optimization (PSO) algorithm was used to optimize the K-means clustering algorithm. The learning factor of the PSO algorithm was set to 0.2, and the inertia weight decreased linearly from 0.9 to 0.4. The sparrow population and particle population with 8 cluster centers were randomly initialized.

[0099] S3: Cluster center update;

[0100] Three clustering algorithms, K-means, PSO-KM (short for PSO-K-means) and SSA-KM (short for SSA-K-means), were used to test the poles in the stable graph drawn in step S1. For each cluster center of each clustering algorithm, the poles in the stable graph that have been removed from the outliers were assigned to the cluster with the smallest distance according to the minimum distance principle. The average value of the elements in each cluster was calculated as the new center of the cluster.

[0101] S4: Optimal fitness value and sparrow individual calculation;

[0102] Calculate the fitness value of individuals in the sparrow population, sort all sparrow individual fitness values, find the current best and worst fitness values, update the positions of discoverers, joiners and scouts, calculate the sparrow population fitness value, update the sparrow population position, and determine whether the algorithm has reached the maximum number of iterations. If not, return to step S3; if so, output the best fitness value and sparrow individual.

[0103] The KM, PSO-KM, and SSA-KM clustering algorithms were tested 10 times, and the average optimal value of the 10 tests was calculated. Due to the sensitivity of the KM algorithm to the initial centers and its local convergence characteristics, the KM algorithm could not obtain 8 cluster centers in every test. The optimization iteration process of the PSO-KM and SSA-KM algorithms is described in [link to optimization process]. Figure 7 The calculation results are shown in Figure 8 .from Figure 7 It can be seen that the average optimal fitness value of the SSA-KM method is better than that of the PSO-KM algorithm. From... Figure 8 It can be seen that, compared with the PSO-KM algorithm, the initial cluster centers identified by the SSA-KM algorithm are closer to the peak frequency positions of the power spectrum curves of the strong earthquake acceleration signal, and the MAC value of the initial cluster centers is closer to 1, indicating that the clustering effect of the SSA-KM algorithm is better than that of the PSO-KM algorithm.

[0104] S5: Obtaining the optimal cluster centers and cluster partitions;

[0105] The best sparrow individual obtained by the sparrow algorithm optimization is used as the initial cluster center. The KM clustering algorithm is used to perform cluster analysis on the extreme points in the stable graph after removing outliers to obtain the final cluster centers and cluster divisions.

[0106] Based on the initial cluster center calculation, the K-means algorithm is then used for cluster analysis. Analysis revealed that the initial cluster centers obtained by the PSO-KM algorithm cannot yield the predicted 8 cluster centers using the K-means algorithm. The stable graph finally obtained by the SSA-KMK (short for SSA-KM-K-means) clustering algorithm is shown below. Figure 9 , Figure 9 Different colored poles represent different clusters. The modal frequencies of the eight cluster centers are basically consistent with the peak frequency of the power spectrum of the strong earthquake acceleration response, indicating that the identified modal frequencies are relatively accurate.

[0107] S6: Determination of modal parameters;

[0108] Sure Figure 9 The parameters contained in the poles closest to the cluster center are the final modal parameters. Based on the strong earthquake monitoring data of high arch dams, a comparative analysis was conducted using the traditional SSI and the SSI-SSA-KMK clustering algorithm proposed in this invention, which integrates SSI and SSA-KMK. The comparison of the natural frequency identification results of high arch dams is shown in Table 1.

[0109] Table 1 Comparison of Natural Frequency Identification Results for High Arch Dams

[0110]

[0111] The modal modes of high arch dams identified by the two methods are shown in the figure. Figure 10From Table 1 and Figure 10 It can be seen that the modal recognition accuracy of the SSI-SSA-KMK algorithm proposed in this invention is similar to that of the SSI method. However, the SSI method requires human judgment of false modes, which has subjective uncertainty. In contrast, SSI-SSA-KMK can automatically eliminate false modes and intelligently identify the optimal structural modal parameters.

[0112] Through the implementation and experimental analysis of this invention, the following conclusions can be drawn:

[0113] 1. The steady-state diagram proposed in this invention, which combines MAC, natural frequency, and maximum power spectrum based on SSI modal parameter identification, avoids the influence of damping ratio of unstable modal parameters and provides a foundation for accurate identification of modal parameters of high arch dams.

[0114] 2. The LOF and KDE fusion method proposed in this invention can effectively identify abnormal poles in the stability graph and eliminate spurious modes of high arch dams.

[0115] 3. This invention integrates the SSI-SSA-KMK algorithm, which combines SSI, SSA, and K-means clustering analysis, and can effectively improve the accuracy and intelligence of modal parameter estimation, automatically searching for the true modes from the stability graph.

[0116] In summary, the automatic identification method for modal parameters of high arch dams based on strong earthquake monitoring data proposed in this invention is effective. Compared with the traditional SSI method, it has higher modal parameter identification accuracy and can realize the automation and intelligence of modal parameter identification of high arch dams under strong earthquake excitation in complex environments with strong noise interference. Therefore, it is recommended to promote its application in actual engineering monitoring.

[0117] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A high arch dam modal parameter automatic identification method based on strong earthquake monitoring data, characterized by comprising the following steps: S1: stable figure drawing: using the random subspace identification method to preliminarily analyze the high arch dam strong earthquake monitoring data, identifying the natural frequency and mode shape of different orders, calculating the natural frequency and modal confidence criterion meeting the tolerance, taking the natural frequency meeting the tolerance as the abscissa, the modal confidence criterion as the ordinate, and the maximum value of the power spectrum of all measuring points as the background curve, drawing the stable figure, analyzing the poles in the stable figure by the local outlier factor and kernel density estimation method, and eliminating the false modes; S2: parameter initialization: setting the population size, iteration number, early warning value, discoverer proportion, and scout proportion of the sparrow search algorithm, and initializing the sparrow population of K cluster centers; S3: cluster center updating: for each cluster center, the poles in the stable figure with the abnormal points removed are divided into the cluster with the minimum distance according to the minimum distance principle, and the average value of the elements in each cluster is calculated as the new cluster center of the cluster; S4: best fitness value and sparrow individual calculation: calculating the individual fitness value in the sparrow population, sorting all sparrow individual fitness values, finding the current best and worst fitness values, updating the positions of the discoverer, joiner, and scout, calculating the sparrow population fitness value, updating the sparrow population position, judging whether the algorithm reaches the maximum iteration number, returning to step S3 if not satisfied, and outputting the best fitness value and the best sparrow individual corresponding to the best fitness value if satisfied; S5: best cluster center and cluster division acquisition: taking the best sparrow individual obtained in step S4 as the initial cluster center, using the K-means clustering algorithm to perform clustering analysis on the poles in the stable figure with the abnormal points removed, and obtaining the final cluster center and cluster division; S6: modal parameter determination: determining the parameters contained in the pole closest to the final cluster center as the final modal parameters; The specific steps of drawing the stable figure in step S1 are as follows: S11, for the high arch dam strong earthquake monitoring data, the discrete random state space model is: S12, construct a Toeplitz matrix: (1)； where: , are the state vector and the output vector of the system at time , are the values of the state vector and the output vector of the system at time , is the number of outputs of the system; , are the state matrix and the output matrix of the system state space equation, respectively; , are the system modeling process noise and measurement noise at time , which are white noise with zero mean. S13, Toeplitz matrix decomposition: (2)； In the formula: Covariance matrix of the output vector is: ; S14, the eigenvalue decomposition of the system matrix is: On Toeplitz matrices The SVD decomposition gives: (3)； wherein: , are orthogonal matrices, is a diagonal matrix of the largest singular values in descending order; S16, the calculation results of the natural frequency, damping ratio, and mode shape are: (4)； wherein is a diagonal matrix composed of poles of the discrete-time system is a characteristic vector of the state matrix of the system state space equation of the system state space equation S15, poles of a discrete system computing eigenvalues of a continuous system are: (5)； In the formula: is a sampling time interval; S17, calculate the frequency and MAC meeting the tolerance: ， ， (6)； wherein: , , respectively represent the natural frequency, damping ratio and mode shape of the mode. Take the frequency meeting the tolerance as the abscissa and the MAC as the ordinate, draw the stable figure, and take the maximum value of the power spectrum of all measuring points as the background curve of the stable figure; (7)； (8)； where: is the calculated frequency, is the order of the model, is the modal confidence criterion: (9)； wherein: is the modal shape, is a value between 0 and 1, representing the correlation of the modal shape; The specific steps of parameter initialization in step S2 are as follows: S18, For the data set of the pole in the stability diagram , All nearest neighbors are: (10)； The reachable distance of the UE is expressed as: The reachable distance of the UE is expressed as: (11)； wherein: is and the Euclidean distance between its first nearest neighbors; The local reachable density of is: (12)； In the formulae: is a neighborhood set of The local outlier factor for each point is: (13)； S19, determining the local outlier factor calculated in step S18 by using the KDE method , setting the significance level to 5%, calculating the control value, and determining , if the control value is higher than the control value determined by the KDE, as an abnormal pole in the stable diagram, eliminating the false mode of the high arch dam. ​ 2. The method for automatically identifying modal parameters of a high arch dam based on strong motion monitoring data according to claim 1, characterized in that, S21, set the population size, iteration number, early warning value, discoverer proportion, and scout proportion in the sparrow algorithm; S22, according to the stable figure with the false modes removed in step S1, determine the K dominant frequencies of the high arch dam monitoring data, and initialize the sparrow population of K cluster centers of the poles in the stable figure. The specific steps of cluster center updating in step S3 are as follows:

3. The method of claim 1, wherein the method further comprises: S31, for each cluster center determined in step S2, calculate the Euclidean distance between each pole in the stable figure determined in step S1 and these cluster centers; ​ S32, the stable graph is divided into clusters according to the Euclidean distance calculated in step S31 and the minimum distance principle; S33, the average value of the elements in each cluster is calculated as the new cluster center of the cluster.

4. The method of claim 1, wherein, The specific steps of calculating the best fitness value and sparrow individual in step S4 are as follows: S41, the fitness value of each individual in the sparrow population is calculated, and the fitness values of all sparrow individuals are sorted to find the current best and worst fitness values; S42, the position of the finder is updated, and the formula is: (14)； In the formula: represents in the first only sparrow position; is a constant, indicating the maximum number of iterations; is a random number; , respectively represent the early warning value and the safety value; is a random number subject to normal distribution; is a one-dimensional multi-dimensional matrix, and all elements are 1; S43, the position of the joiner is updated, and the formula is: (15)； wherein: is the best position of the current discoverer; denotes the current global worst position; is a row vector of dimensionality n, whose elements are either 1 or -1, ; S44, the position of the scout is updated, and the formula is: (16)； wherein: is the current global best position; is a step size control parameter; is a random number; is the fitness value of the current sparrow; and are the current best fitness value and the worst fitness value; is a constant to avoid division by zero, set to 10e-10; S45, the fitness value of the sparrow population is calculated, and the position of the sparrow population is updated; S46, it is judged whether the algorithm reaches the maximum number of iterations, if not, it returns to step S3, if yes, the best fitness value and the best sparrow individual corresponding to the best fitness value are output.

5. The method of claim 1, wherein, The specific steps of obtaining the best cluster center and cluster division in step S5 are as follows: S51, the best sparrow individual optimized by the sparrow algorithm is taken as the initial cluster center; S52, the Euclidean distance between the extreme points in the stable graph determined in step S1 and the initial cluster center is calculated, and the minimum distance is used for division to form K cluster domains; S53, the average value of all objects in each cluster domain is calculated as the new cluster center point of the class; S54, Davies-Bouldin index is taken as the cluster evaluation index, and the specific calculation formula is as follows: (17)； wherein denotes a cluster the average distance of the data within the cluster to the cluster centroid, is a cluster class the cluster centroid of the cluster class, denotes the Euclidean distance; S55, if the termination condition is met, the algorithm ends, otherwise, it returns to step S52 to obtain the final cluster center and cluster division.

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