A method and system for structural operational modal parameter identification and damping ratio calculation

Abstract

The application relates to the technical field of structural dynamics modal parameter identification, in particular to a method and system for structural operating modal parameter identification and damping ratio calculation. The method comprises the following steps: obtaining multi-channel acceleration response data of a structure under random excitation; performing frequency domain decomposition on the multi-channel acceleration response data to obtain frequency domain modes and corresponding singular values of each frequency point; clustering each frequency point based on the frequency domain modes and the singular values to obtain candidate modal clusters by using a hierarchical density clustering algorithm; fusing the amplitude domain and the shape domain based on D-S evidence theory, and removing false modes from the candidate modal clusters to obtain modal frequencies and modal shapes of real modes; performing spatial filtering on the acceleration response data to obtain single-degree-of-freedom generalized coordinate responses; resampling the single-degree-of-freedom generalized coordinate responses, constructing a frequency domain optimization objective function, and performing parameter optimization to obtain the damping ratios of the real modes. The method solves the problems of low automation degree and limited damping ratio identification accuracy in existing methods.

Description

Technical Field

[0001] This application relates to the field of structural dynamics modal parameter identification technology, specifically to a method and system for identifying structural working modal parameters and calculating damping ratio. Background Technology

[0002] Operational Modal Analysis (OMA) identifies the modal parameters (including modal frequencies, mode shapes, and damping ratios) of a structure by measuring its response data under random environmental excitations. It is widely used in the dynamic characteristic assessment and health monitoring of bridges, high-rise buildings, major equipment, and aerospace structures.

[0003] Frequency domain decomposition (FDD) is a commonly used method in working modal analysis. This method typically involves decomposing the structural response data in the frequency domain to obtain the frequency mode shapes and singular values ​​at each frequency point. The modal frequencies are then determined by manually identifying the peak positions on the singular value spectrum. Based on human experience, the identified modes are screened to distinguish between true and false modes. Finally, the damping ratio is extracted using the half-power bandwidth method or enhanced frequency domain decomposition.

[0004] However, the existing methods described above have the following problems: In the modal identification stage, modal peak identification and modal selection typically rely on human experience for judgment. Operators must manually pick peaks on the singular value spectrum and judge whether each peak corresponds to a real physical mode based on experience. This reliance on human experience results in a low degree of automation in the analysis process, and the analysis results are affected by the operator's subjective factors, making it difficult to meet the needs of online monitoring and automated processing.

[0005] In the damping ratio extraction stage, traditional half-power bandwidth methods or enhanced frequency domain decomposition methods are limited by frequency resolution and affected by spectral leakage, resulting in deviations in the damping ratio identification results. When the frequency resolution is insufficient, the estimated half-power bandwidth deviates from the true value; spectral leakage will interfere with the enhanced frequency domain decomposition method based on autocorrelation function truncation, causing the damping ratio estimate to deviate further from the true value.

[0006] Therefore, existing frequency domain modal analysis methods suffer from low automation levels due to reliance on human experience in modal peak identification and mode selection, and limited accuracy in damping ratio identification due to spectral leakage and frequency resolution limitations. Summary of the Invention

[0007] To address the aforementioned issues, this application provides a method for identifying structural operating modal parameters and calculating damping ratios, thereby resolving the problems of low automation levels in existing frequency domain operating modal analysis methods due to reliance on manual experience for modal peak identification and mode selection, as well as limited accuracy in damping ratio identification.

[0008] To achieve the above objectives, the technical solution adopted in this application is as follows: A method for identifying structural operating modal parameters and calculating damping ratios is provided, including: Acquire multi-channel acceleration response data of the structure under random excitation; The multi-channel acceleration response data is decomposed in the frequency domain to obtain the frequency domain mode shape and the corresponding singular value at each frequency point; Based on the frequency domain mode shape and the singular value, a hierarchical density clustering algorithm is used to cluster each frequency point to obtain candidate mode clusters; Based on the DS evidence theory, the amplitude domain and morphological domain information are fused and false modes are eliminated from the candidate mode clusters to obtain the modal frequencies and mode shapes of the true modes; Using the mode shapes of the actual modes as weights, spatial filtering is performed on the multi-channel acceleration response data to obtain the single-degree-of-freedom generalized coordinate response; Using the modal frequency of the true mode as a reference, the single-degree-of-freedom generalized coordinate response is resampled, a local frequency band centered on the modal frequency is extracted, and the parameters of the frequency domain optimization objective function are optimized to obtain the damping ratio of the true mode.

[0009] This technique uses multiple accelerometers deployed on a structure to synchronously acquire vibration signals under random environmental excitation, obtaining multi-channel acceleration response data. Frequency domain decomposition is performed on the multi-channel acceleration response data, and singular value decomposition is performed on the power spectral density matrix at each frequency point to obtain the frequency domain mode shape and singular values. Based on the frequency domain mode shape and singular values, a hierarchical density clustering algorithm is used to cluster the frequency points, grouping those with similar mode shapes and frequencies into the same group to obtain candidate mode clusters. Based on DS evidence theory, amplitude domain evidence is established using the magnitude of logarithmic singular values, and morphological domain evidence is established using the attenuation degree and prominence on both sides of the peak value. The two types of evidence are fused to screen the candidate mode clusters, eliminating spurious modes caused by noise, and obtaining the modal frequencies and mode shapes of the true modes. Using the mode shapes of the true modes as weights, the multi-channel acceleration response data is weighted and summed to obtain a single-degree-of-freedom generalized coordinate response containing only the vibration component of that mode. Using the modal frequencies of the true modes as a reference, the single-degree-of-freedom generalized coordinate response is resampled, and a local frequency band near the modal frequency is extracted. A frequency domain optimization objective function is constructed to optimize the parameters and obtain the damping ratio of the true modes.

[0010] Further, the step of performing frequency domain decomposition on the multi-channel acceleration response data to obtain the frequency domain mode shapes and corresponding singular values ​​at each frequency point includes: Based on the physical characteristics of the multi-channel acceleration response data, the optimal parameters for frequency domain decomposition are determined by Welch self-power spectrum estimation and normalized bias error requirements. Based on the optimal parameters, the superposition spectrum of the self-power spectrum of the multi-channel acceleration response is solved and the logarithm is taken; Based on the logarithmic power spectrum, the noise baseline is extracted and resonance peaks are identified to determine the analysis frequency band; The frequency domain mode shapes and corresponding singular values ​​of each frequency point within the analysis band are extracted by singular value decomposition.

[0011] This technique utilizes the sampling frequency and structural physical characteristics of multi-channel acceleration response data to determine the optimal parameters for Welch autopower spectrum estimation by adjusting the normalized bias error requirement, thus balancing frequency resolution and averaging order. Based on these optimal parameters, Welch autopower spectrum estimation is performed on the multi-channel acceleration response data to obtain the global logarithmic power spectrum. A moving median filter is then used to extract the noise baseline from the global logarithmic power spectrum, relative salience is calculated, resonance peaks are identified, and the analysis frequency band is determined. Singular value decomposition is performed on the data within the analysis frequency band at each frequency point to obtain the frequency domain mode shapes and corresponding singular values ​​for each frequency point.

[0012] Furthermore, the step of clustering each frequency point using a hierarchical density clustering algorithm based on the frequency domain mode shape and the singular values ​​includes: Based on the frequency domain mode shape, calculate the frequency similarity and mode shape confidence. Based on the relative magnitude of the singular values, calculate the singular value amplitude weight (i.e., spectral line amplitude weight). Construct the frequency similarity, the mode shape confidence, and the singular value amplitude weight into a pairwise distance. The mutual reachability distance is calculated based on the pairwise distance, and a minimum spanning tree is constructed based on the mutual reachability distance; The minimum spanning tree is hierarchically split and noise points are removed to extract stable clusters as candidate mode clusters.

[0013] This technique calculates frequency similarity based on the frequency difference between two frequency points, modal confidence based on the modal confidence criterion (MAC) between the corresponding mode shape vectors of the two frequency points, and singular value amplitude weights based on the sum of the ratios of the normalized first singular value to the normalized median across the entire frequency band. These three terms are then combined through a product to form a pairwise distance. The mutual reachability distance is calculated based on the pairwise distances, and a minimum spanning tree is constructed using the Prim algorithm. The edges of the minimum spanning tree are sorted by weight and then disconnected sequentially. Subclusters with fewer nodes than the minimum cluster size limit are removed as noise points, while subclusters with the required number of nodes are retained as stable clusters, resulting in candidate modal clusters.

[0014] Furthermore, the step of fusing amplitude domain and morphological domain information based on DS evidence theory and performing false mode elimination on the candidate mode cluster includes: Extract candidate peak points from the candidate mode cluster; The global noise floor value is measured based on the median absolute deviation. An amplitude domain evidence source is established based on the global noise floor value. The true modal confidence and false modal confidence of each candidate peak point are calculated based on the amplitude domain evidence source. Based on the attenuation degree and prominence of the candidate peak points on both sides of the singular value, a morphological domain evidence source is established, and the true modal confidence and false modal confidence of each candidate peak point are calculated based on the morphological domain evidence source. The conflict coefficient is calculated based on the confidence levels of the amplitude domain evidence sources and the morphological domain evidence sources, and orthogonalization and fusion are performed to obtain the joint confidence level of each candidate peak point; The candidate peak points are screened based on the joint confidence level, and the candidate peak points that meet the true mode decision criteria are retained. The corresponding candidate mode clusters are determined as true modes, and the modal frequencies and mode shapes of the true modes are obtained.

[0015] This technique extracts the frequency point with the largest singular value from the candidate mode cluster as the candidate peak point. The absolute median difference of the global frequency singular value ratio sequence is calculated as the global noise floor, establishing an amplitude domain evidence source. Linear interpolation is used to calculate the true mode confidence and false mode confidence of each candidate peak point. A sub-interval of a certain width is truncated on both sides of the candidate peak point, and the attenuation of the minimum values ​​on both sides relative to the peak point is calculated. The peak prominence is calculated by merging the two sub-intervals, establishing a morphological domain evidence source, and the true mode confidence and false mode confidence of each candidate peak point are calculated. The conflict coefficient between the amplitude domain evidence and the morphological domain evidence is calculated, and the joint confidence of each candidate peak point is obtained through orthogonality and fusion. Candidate peak points whose joint confidence satisfies the true mode decision criterion are retained, and their corresponding candidate mode clusters are determined as true modes, obtaining the modal frequencies and mode shapes of the true modes.

[0016] Further, the step of resampling the single-degree-of-freedom generalized coordinate response based on the modal frequency of the true mode, constructing a frequency domain optimization objective function for parameter optimization, and obtaining the damping ratio of the true mode includes: The single-degree-of-freedom generalized coordinate response is resampled based on the modal frequencies; The resampled single-degree-of-freedom generalized coordinate response is subjected to frequency domain transformation, and a local frequency band centered on the modal frequency is extracted to obtain the power spectral density of the local frequency band. Based on the power spectral density of the local frequency band, a frequency domain optimization objective function is constructed to optimize the parameters and obtain the damping ratio of the true mode.

[0017] This technique uses the mode shapes of the actual modes as weights to perform weighted projection on the multi-channel acceleration response data matrix, merging the multi-channel signals into a single-channel signal to obtain the single-degree-of-freedom generalized coordinate response. The target sampling frequency is calculated based on the modal frequencies, and the single-degree-of-freedom generalized coordinate response is resampled. A frequency domain transformation is performed on the resampled single-degree-of-freedom generalized coordinate response, and a local frequency band centered on the modal frequencies is extracted to obtain the power spectral density of that local band. A frequency domain optimization objective function is constructed to minimize the deviation between the theoretical and actual power spectral densities. The damping ratio of the actual mode is obtained by solving for the minimum value of the objective function.

[0018] Furthermore, the step of resampling the single-degree-of-freedom generalized coordinate response based on the modal frequency includes: The target sampling frequency is calculated based on the modal frequency, and the resampling scale factor is determined by rational fraction approximation. The single-degree-of-freedom generalized coordinate response is then resampled based on the resampling scale factor.

[0019] This technique calculates a safe target sampling frequency for the target modal frequency, ensuring the sampling frequency is a fixed multiple of the target frequency. A rational fraction approximation is used to extract the simplest coprime scaling factor, making the resampled frequency approximate the target sampling frequency. Based on the resampling scaling factor, the single-degree-of-freedom generalized coordinate response is resampled, reducing the sampling frequency while retaining effective information about the target resonance peak.

[0020] Further, the steps of performing frequency domain transformation on the resampled single-degree-of-freedom generalized coordinate response, extracting a local frequency band centered on the modal frequency to obtain the power spectral density of the local frequency band, and constructing a frequency domain optimization objective function based on the power spectral density of the local frequency band to perform parameter optimization and obtain the damping ratio of the true mode include: Construct a theoretical single-degree-of-freedom power spectral density function, and construct a logarithmic domain residual sum of squares error function based on the deviation between the power spectral density of the local frequency band and the theoretical single-degree-of-freedom power spectral density function; The initial parameter vector is derived inversely based on the modal frequency, the minimum and peak power spectral density of the local frequency band; Based on the initial parameter vector, the minimum value of the error function is solved using the simplex method to obtain the damping ratio of the true mode.

[0021] This technique constructs a theoretical single-degree-of-freedom power spectral density function. The logarithm of the theoretical function is subtracted from the logarithm of the actual local band power spectral density, and the sum of squared residuals is calculated to construct a logarithmic domain residual sum of squared error function. Initial natural frequencies are determined based on the discrete frequency points corresponding to local peaks. The minimum local band power spectral density is taken as the initial value of the floor noise. The initial value of the amplitude factor is derived by inversely based on the condition that the amplitude at the resonance peak equals the actual peak value, and the empirical damping ratio is used as the initial value of the damping ratio. These combinations yield an initial parameter vector. Based on this initial parameter vector, the simplex method is used to search for the minimum value of the error function, and the damping ratio is extracted from the optimization results.

[0022] On the other hand, a system for identifying structural operating modal parameters and calculating damping ratios is provided, including: The data acquisition module is used to acquire multi-channel acceleration response data of the structure under random excitation; The data preprocessing module is used to process multi-channel acceleration response data to obtain the optimal resolution and analysis frequency band; The frequency domain decomposition module is used to perform frequency domain decomposition on the multi-channel acceleration response data to obtain the frequency domain mode shape and the corresponding singular value at each frequency point. The clustering module is used to cluster each frequency point based on the frequency domain mode shape and the singular value using a hierarchical density clustering algorithm to obtain candidate mode clusters. The filtering module is used to fuse amplitude domain and morphological domain information based on DS evidence theory and remove false modes from the candidate mode clusters to obtain the modal frequencies and mode shapes of the true modes. The spatial filtering module is used to perform spatial filtering on the multi-channel acceleration response data with the mode shape of the real mode as weights to obtain a single-degree-of-freedom generalized coordinate response. The damping ratio extraction module is used to resample the single-degree-of-freedom generalized coordinate response based on the modal frequency of the true mode, extract a local frequency band centered on the modal frequency, construct a frequency domain optimization objective function for the local frequency band, perform parameter optimization, and obtain the damping ratio of the true mode.

[0023] Using this technique, the data acquisition module acquires multi-channel acceleration response data of the structure under random excitation. The data preprocessing module processes the acquired multi-channel acceleration response data to obtain the optimal resolution and analysis frequency band. The frequency domain decomposition module performs frequency domain decomposition on the multi-channel acceleration response data to obtain the frequency domain mode shapes and singular values ​​at each frequency point. The clustering module uses a hierarchical density clustering algorithm based on the frequency domain mode shapes and singular values ​​to cluster each frequency point, obtaining candidate mode clusters. The screening module uses DS evidence theory to fuse amplitude domain and morphological domain information to remove false modes from the candidate mode clusters, obtaining the modal frequencies and mode shapes of the true modes. The spatial filtering module uses the mode shapes of the true modes as weights to perform weighted summation on the multi-channel acceleration response data to obtain the single-degree-of-freedom generalized coordinate response. The damping ratio extraction module resamples the single-degree-of-freedom generalized coordinate response based on the modal frequencies of the true modes and constructs a frequency domain optimization objective function to optimize parameters, obtaining the damping ratio of the true modes.

[0024] On the other hand, an electronic device is provided, comprising: a memory having a computer program stored thereon; and a processor for executing the computer program in the memory to implement the steps of the method as described above.

[0025] This technique stores the aforementioned method steps as computer programs in the memory of an electronic device, which are then executed by the processor. This programmed implementation enables the automatic execution of algorithmic steps such as adaptive parameter determination, frequency domain decomposition, improved density clustering, DS evidence fusion screening, and frequency domain optimization fitting within the computing device. This eliminates the need for operators to perform peak picking or mode screening, thereby transforming the methodological effects into deployable automated computing capabilities, facilitating integration into the hardware platform of a structural health monitoring system.

[0026] On the other hand, a computer-readable storage medium is provided that stores a computer program thereon, which, when executed by a processor, implements the steps of the method as described above.

[0027] This technique allows the computer program for the aforementioned method to be stored in a readable form on a non-volatile storage medium. When the program is loaded and executed by a processor, the complete technical process from data acquisition to high-precision damping ratio extraction can be reproduced. The provision of the storage medium facilitates the distribution, portability, and version management of the method's code, providing a unified software foundation for implementation on different hardware platforms.

[0028] In summary, the beneficial effects of this application are as follows: 1. A hierarchical density clustering algorithm is used to cluster the mode shapes and singular values ​​of each frequency point after frequency domain decomposition. Frequency points belonging to the same physical mode are automatically aggregated into candidate mode clusters. Based on DS evidence theory, amplitude domain and morphological domain information are fused to screen for false modes in the candidate mode clusters, thereby obtaining the modal frequencies and mode shapes of the true modes. Simultaneously, the mode shapes of the true modes are used as weights to perform spatial filtering on the multi-channel acceleration response data to obtain the single-degree-of-freedom generalized coordinate response. Resampling and frequency domain optimization objective function fitting are performed based on the true modal frequencies to obtain the damping ratio. Therefore, in frequency domain working modal analysis, the identification process of modal frequencies, mode shapes, and damping ratios does not rely on manual peak picking and mode screening, and the damping ratio identification accuracy is improved compared to traditional half-power bandwidth methods or enhanced frequency domain decomposition methods.

[0029] 2. By combining frequency similarity, mode shape confidence, and spectral amplitude weights into pairwise distances, the mutual reachability distance is calculated based on these pairwise distances, and a minimum spanning tree is constructed. Then, the minimum spanning tree is subjected to hierarchical splitting and noise point removal. This allows frequency points with similar modes and close frequencies to be automatically aggregated into candidate mode clusters, while noise frequencies are removed. Thus, applying the density clustering algorithm to frequency domain mode shape clustering of frequency domain FDD singular value spectra enables automatic identification of modal frequencies and mode shapes, reducing reliance on manual peak picking experience.

[0030] 3. An amplitude-domain evidence source is established by calculating the global noise floor based on power spectral density, and a morphological-domain evidence source is established based on the attenuation and prominence on both sides of the candidate peak point. The two types of evidence sources are then orthogonalized and fused to obtain a joint confidence score, which is used to filter candidate peak points. Thus, candidate modes are comprehensively judged from two dimensions: global amplitude level and local peak shape, improving the accuracy of false mode removal and reducing the risk of misjudgment caused by noise interference and spectral leakage.

[0031] 4. By resampling the single-degree-of-freedom generalized coordinate response to improve frequency resolution, and by extracting a local frequency band centered on the modal frequency to construct a frequency domain optimization objective function, the deviation between the theoretical power spectral density and the actual power spectral density is minimized, thereby obtaining the damping ratio. Thus, by replacing the traditional half-power bandwidth method or enhanced frequency domain decomposition method with an optimization fitting approach, the impact of spectral leakage and frequency resolution limitations on the damping ratio identification results is reduced. Attached Figure Description

[0032] The accompanying drawings, which form part of this application, are used to provide a further understanding of this application. The illustrative embodiments and descriptions of this application are used to explain this application and do not constitute an undue limitation of this application. In the drawings: Figure 1This is a schematic diagram of the first process of a method for identifying structural working modal parameters and calculating damping ratios, which is an optional embodiment of this application. Figure 2 This is a second flowchart illustrating the optional structural operating mode parameter identification and damping ratio calculation method in an embodiment of this application. Figure 3 This is a schematic diagram of the third process of the optional structural working mode parameter identification and damping ratio calculation method in the embodiments of this application; Figure 4 This is a schematic diagram of the fourth process of the optional structural working mode parameter identification and damping ratio calculation method in the embodiments of this application; Figure 5 This is a schematic diagram of the fifth process of the optional structural working mode parameter identification and damping ratio calculation method in the embodiments of this application; Figure 6 A schematic diagram of a five-degree-of-freedom system provided for one embodiment of this application; Figure 7 A first singular value spectrum is provided for one embodiment of this application; Figure 8 The diagram shows the modal shape and damping ratio analysis results provided for one embodiment of this application. Detailed Implementation

[0033] To enable those skilled in the art to better understand the technical solutions of this application, the technical solutions of this application will be further described below in conjunction with the accompanying drawings and embodiments.

[0034] The structural modal parameter identification and damping ratio calculation method provided in this application can be applied to structural health monitoring systems in engineering fields such as bridges, high-rise buildings, major equipment, and aerospace structures. In this application scenario, multiple acceleration sensors are arranged on the structure under test. Each sensor synchronously collects the vibration acceleration signal of the structure under random environmental excitation according to a predetermined sampling frequency, and transmits the multi-channel acceleration response data to a data processing terminal. The data processing terminal executes the method of this application embodiment to analyze and process the multi-channel acceleration response data, and automatically identifies the structural modal parameters, including modal frequencies, mode shapes, and damping ratios.

[0035] Reference Figure 1 and Figure 2 It provides methods for identifying structural operating modal parameters and calculating damping ratios, including: S101: Acquire multi-channel acceleration response data of the structure under random excitation; S102: Perform frequency domain decomposition on the multi-channel acceleration response data to obtain the frequency domain mode shape and corresponding singular value at each frequency point; S103: Based on the frequency domain mode shape and the singular value, a hierarchical density clustering algorithm is used to cluster each frequency point to obtain candidate mode clusters; S104: Based on the DS evidence theory, the amplitude domain and morphological domain information are fused and false modes are eliminated from the candidate mode clusters to obtain the modal frequencies and mode shapes of the true modes; S105: Using the mode shape of the real mode as the weight, perform spatial filtering on the multi-channel acceleration response data to obtain the single-degree-of-freedom generalized coordinate response; S106: Using the modal frequency as a reference, the single-degree-of-freedom generalized coordinate response is resampled, and a frequency domain optimization objective function is constructed to optimize the parameters and obtain the damping ratio of the true mode.

[0036] It achieves fully automated identification of the entire process from multi-channel acceleration response data to modal frequencies, mode shapes, and damping ratios, eliminating the need for manual peak picking and mode selection, thus improving the level of automation. At the same time, it improves the accuracy of damping ratio identification by replacing the traditional half-power bandwidth method or enhanced frequency domain decomposition method with frequency domain optimization objective function fitting.

[0037] like Figure 3 As shown, in one embodiment, step S102 includes: S201: Based on the physical characteristics of the multi-channel acceleration response data, the optimal parameters for frequency domain decomposition are determined by Welch self-power spectrum estimation and normalized bias error requirements; S202: Solve the logarithmic power spectrum of the multi-channel acceleration response data, extract the noise floor baseline and identify resonance peaks based on the logarithmic power spectrum, and determine the analysis frequency band; S203: Based on the optimal parameters, perform frequency domain decomposition on the multi-channel acceleration response data to obtain the singular value spectrum of each frequency point; S204: Extract the frequency domain mode shapes and corresponding singular values ​​of each frequency point within the analysis frequency band.

[0038] Specifically, to achieve optimal resolution calculation for different structures, this application employs a resolution algorithm based on data physical characteristics. First, a relatively low initial frequency resolution target is set. Based on the system's sampling frequency Calculate the initial Points : (1) in, This indicates rounding up to the nearest integer.

[0039] Based on this, the multi-channel acceleration response... Welch self-power spectrum estimation was performed separately, and the energies of each channel spectrum were linearly superimposed to obtain the global logarithmic power spectrum. Subsequently, a nonlinear peak-finding algorithm was applied to the global logarithmic power spectrum to identify the peaks. Identify the dominant resonance peaks and calculate their half-power bandwidths, then take the minimum value. As the narrowest physical bandwidth of the system.

[0040] In practical engineering, because a limited measurement time and resolution bandwidth are used to approximate the true spectrum, a normalized bias error will occur at the resonance peak of the actual spectrum. It can be approximated as: (2) in, This refers to the system's resolution bandwidth.

[0041] In order to To reach a negligible level, generally requires The value is around -0.02. Substituting into equation (2), we obtain Therefore, in practical engineering, it is generally required that... .make Calculate the system's resolution bandwidth With the corresponding Points: (3) The number of sampling points for the Welch averaging method is thus obtained. .

[0042] To further reduce computational load and avoid interference from high-frequency boundary spurious peaks, after determining... Subsequently, the first singular value logarithmic spectrum of the entire frequency band is analyzed. Since actual environmental excitation is usually not ideal white noise, the spectral lines will exhibit obvious energy trends. Directly using absolute threshold peak finding can easily lead to misjudgment of low-frequency false peaks or missed detection of high-frequency weak modes. Therefore, this application introduces a moving median filter to extract frequency points. The corresponding logarithmic spectrum value of the background noise : (4) In the formula, Take the logarithm of the sum of the power spectra of all channels across the entire frequency band; For a wideband window, 60Hz is used in this application; and This refers to the physical frequency, measured in Hz.

[0043] Will and The difference is used to obtain the prominence of a frequency point relative to the background noise. : (5) exist Peak search is performed, and frequency points whose absolute and relative salience both exceed the thresholds are retained as candidate peaks. Meanwhile, to avoid spurious peaks caused by spectral leakage near the Nyquist boundary and to ensure the complete preservation of the modal attenuation region, safety margins are introduced at both ends of the candidate peaks. This ensures that the resonance peak attenuation band is not truncated. Ultimately, the upper and lower limits of the structural analysis band are obtained: (6) In the formula, This is the lower frequency boundary; This represents the upper frequency boundary. For safety margin; The peak frequency with the lowest frequency. The peak frequency is the highest frequency.

[0044] Furthermore, such as Figure 4 As shown, in one embodiment, step S103 includes: S301: Calculate frequency similarity and mode confidence based on the frequency domain mode shape, calculate spectral line amplitude weight based on the singular value, and construct a pairwise distance by combining the frequency similarity, the mode confidence, and the spectral line amplitude weight; S302: Calculate the mutual reachability distance based on the pairwise distance, and construct the minimum spanning tree based on the mutual reachability distance; S303: Perform hierarchical splitting and noise point stripping on the minimum spanning tree, and extract stable clusters as candidate modal clusters.

[0045] Specifically, the mutual reachability distance between discrete frequency points is first calculated. After obtaining the first-order singular vectors of each discrete frequency point, HDBSCAN (Hierarchical Density Clustering Algorithm) is used to cluster the frequency domain mode shapes to achieve automatic identification of modal frequencies. The core of HDBSCAN is the mutual reachability distance. For any two points i and j, the following is defined: (7) in, Let i be the distance from point i to its k-th nearest neighbor. For paired distances.

[0046] When clustering mode shapes using the HDBSCAN algorithm, a pairwise distance formula needs to be constructed. The pairwise distance formula transforms structural dynamic characteristics such as mode shape similarity and frequency similarity into quantifiable similarity metrics that can be analyzed by clustering algorithms, serving as a bridge between structural features and clustering algorithms. Therefore, setting a reasonable pairwise distance formula can significantly improve the accuracy of clustering. This application constructs a pairwise distance formula by simultaneously introducing frequency similarity, mode shape confidence, and singular value penalty terms, and couples these quantifiable metrics through a product. The final pairwise distance formula is shown below: (8) in: (9) (10) (11) (12) in, Frequency point Normalized singular value weights that include noise floor; Frequency point The corresponding first singular value; It represents the median of the normalized singular values ​​across the entire frequency band.

[0047] Based on the mutual reachability distance, Prim's algorithm is used to construct a minimum spanning tree, where each side of the minimum spanning tree represents the mutual reachability distance between corresponding points. The process of sorting the edges of the minimum spanning tree in descending order of weight, disconnecting them sequentially, and recording this process constructs a hierarchical clustering structure. To avoid an overly complex hierarchical clustering structure, the HDBSCAN algorithm introduces a minimum cluster size. In each split of the minimum spanning tree, if the number of nodes in the resulting sub-cluster is less than the limit, it is considered a noise point and removed; if it is greater than the limit, it is considered a true cluster split.

[0048] By calculating the stability score of each cluster, stable clusters are extracted from all clusters, thereby enabling the identification of mode shapes and modal frequencies.

[0049] Furthermore, such as Figure 5 As shown, in one embodiment, S104 includes: S401: Extract candidate peak points from the candidate mode cluster; S402: Calculate the global noise floor value based on the singular values, establish an amplitude domain evidence source based on the global noise floor value, and calculate the true modal confidence and false modal confidence of each candidate peak point based on the amplitude domain evidence source; S403: Establish a morphological domain evidence source based on the attenuation degree and prominence of the candidate peak points on both sides of the singular value, and calculate the true modal confidence and false modal confidence of each candidate peak point based on the morphological domain evidence source; S404: Calculate the conflict coefficient based on the confidence levels of the amplitude domain evidence source and the morphological domain evidence source, and perform orthogonalization and fusion to obtain the joint confidence level of each candidate peak point; S405: Based on the joint confidence level, the candidate peak points are screened, and the candidate peak points that meet the true mode decision criteria are retained. The corresponding candidate mode clusters are determined as true modes, and the modal frequencies and mode shapes of the true modes are obtained.

[0050] Specifically, although the HDBSCAN algorithm can effectively cluster stable modal frequencies, it may still generate spurious clusters caused by noise due to factors such as low signal-to-noise ratio or spectral leakage. Meanwhile, structural vibration signals are often accompanied by strong background noise and non-stationary forced interference, making it difficult to completely eliminate spurious modes caused by noise and other factors using only a single feature threshold or basic clustering algorithm. To improve the accuracy and robustness of modal recognition results, this application, after initially obtaining candidate modal clusters using the HDBSCAN method, extracts the frequency point with the largest singular value in the candidate modal cluster as the candidate peak point corresponding to that modal cluster. Based on multi-source information fusion and DS evidence theory, a multi-dimensional joint screening framework including amplitude and morphological domains is constructed, thereby realizing an automated modal screening strategy.

[0051] This embodiment constructs two independent underlying sources of evidence according to the following steps: One approach is a mode selection strategy based on the global noise floor. True structural modes typically exhibit singularity peaks in the first singularity spectrum that are significantly higher than the global noise floor. Therefore, mode selection can be performed by measuring the magnitude of the mode singularity versus the global noise singularity. This embodiment uses the absolute median difference as the metric for global noise floor. The formula for calculating the absolute median difference is as follows: (13) in, R is the absolute median difference; R is a sequence vector of singular value ratios at global frequencies, where the elements are... The calculation formula is as follows: (14) in, The first singular value corresponding to frequency point i; It represents the median of the singular values ​​across the entire frequency band.

[0052] based on Establish a lower bound for global frequency singularity evaluation. With the upper realm : (15) in, and These are the control coefficients for the lower and upper boundaries, respectively.

[0053] For a given candidate peak point, let its singular value ratio be... The confidence level assignment is calculated using a linear interpolation function. To characterize the measurement uncertainty of the system, a reservation is made... The final global confidence scores for the true modes and spurious noise are obtained. and as follows: (16) (17) Another approach is a mode selection strategy based on peak shape and salience. According to the theory of the FDD method, a system mode will always exhibit a prominent peak in the first singular value spectrum, and this peak will be accompanied by a significant decrease in singular values ​​on both sides. Based on this theory, this application introduces a peak detection mechanism into the mode selection method. Since peak salience is more suitable for measurement in decibels, the singular values ​​within this interval are converted to a decibel scale, as follows: (1) Peak shape verification. The HDBSCAN algorithm identifies possible modal peaks. Afterwards, Each side is selected as a sub-interval with a width of 3Hz, denoted as follows: and Subsequently, the singular values ​​of the minimum points within the left and right subintervals are calculated relative to... The degree of decay of singular values: (18) (19) in, and Representing the peak points respectively The degree of decay of singular values ​​on both sides; Representative candidate peak point The corresponding logarithmic singular values; The singular value corresponding to the candidate peak point; and These represent the logarithmic singular value vectors of the frequency points within the two sub-intervals, respectively.

[0054] When candidate peak points satisfy and Only when all values ​​are greater than 0.5 dB are they considered reasonable peak values ​​and further screening proceeded; otherwise, the mode is directly eliminated. , The core objective of this stage is to eliminate spurious peaks that, due to windowing or truncation, exhibit rapid decay on one side of the true peak while still showing an upward trend on the other side, dependent on the true modal peak. Simultaneously, setting a very low threshold of 0.5 dB ensures that, in actual analysis, while filtering out these spurious peaks, true modal peaks with undesirable shapes are not mistakenly filtered out.

[0055] (2) Peak prominence test. For the candidate peaks that pass (1), in order to measure the dynamic amplification effect of the candidate peak points, a peak prominence test mechanism is introduced. Take the same two sub-intervals as in (1) and merge the two sub-intervals into a 6Hz wide interval.

[0056] Sort the data points within the interval in ascending order of their logarithmic singular values, and extract the logarithmic singular value corresponding to the minimum value. This is used as the noise floor value for that interval. The logarithmic singular values ​​of the candidate peak points are then used. The difference between this value and the noise floor is used to determine the absolute prominence of the candidate peak point relative to the noise floor. : (20) Then, the absolute median difference of the logarithmic singular values ​​within this interval is calculated. : (twenty one) in, It is the logarithmic singular value vector of the frequency points within this interval.

[0057] based on Establish the lower and upper bounds of the peak salience of the frequency points in this local interval: (twenty two) in, and These are the lower and upper bounds for evaluating the peak prominence of this local interval, respectively. and These are the control coefficients for the lower and upper boundaries, respectively.

[0058] The confidence level assignment is also calculated using a linear interpolation function. To characterize the measurement uncertainty of the system, a reservation is made... The final global confidence scores for the true modes and spurious noise are obtained. and as follows: (twenty three) (twenty four) Based on multi-source information fusion and DS evidence theory, this embodiment constructs a multi-dimensional joint screening framework encompassing the amplitude and morphological domains, thereby realizing an automated modality screening strategy. Specifically, the discrimination framework for modality recognition is defined as follows: ,in and These represent the real physical modes and the spurious modes formed by various factors, respectively.

[0059] Define the conflict coefficient of the evidence interval as follows: (25) Subsequently, the joint confidence assignment after fusion is calculated. and : (26) The final modality selection follows the following decision criterion: only if the confidence level after fusion meets the following criteria. and Only when the condition is met will the candidate peak be considered a true mode and retained; otherwise, it will be treated as environmental noise and removed.

[0060] Furthermore, in one embodiment, a specific method for step S105 is provided: To address the issue of large errors in calculating extremely low-frequency modes and high-frequency low-damping modes using the traditional EFDD (Enhanced Frequency Domain Decomposition) method, a single-degree-of-freedom frequency domain curve fitting method based on nonlinear optimization is employed to achieve high-precision damping identification.

[0061] To eliminate interference from other modes and maximize the signal-to-noise ratio of the target mode, this embodiment utilizes the mode clusters obtained by the HDBSCAN method described above, and selects the first singular vector corresponding to the frequency point with the largest singular value as the mode shape vector corresponding to the mode cluster. Subsequently through For the multi-channel raw acceleration response matrix Perform spatial filtering to extract the first... k Generalized coordinate response of first mode : (27) in, The dimensional arrangement is time × channel.

[0062] Further, in one embodiment, step S106 includes: S601: Resample the single-degree-of-freedom generalized coordinate response based on the modal frequencies; S602: Perform frequency domain transformation on the resampled single-degree-of-freedom generalized coordinate response, extract a local frequency band centered on the modal frequency, obtain the power spectral density of the local frequency band, and construct a frequency domain optimization objective function based on the power spectral density of the local frequency band to optimize parameters and obtain the damping ratio of the true mode.

[0063] Step S601 includes: The target sampling frequency is calculated based on the modal frequency, and the resampling scale factor is determined by rational fraction approximation. The single-degree-of-freedom generalized coordinate response is then resampled based on the resampling scale factor.

[0064] Step S602 includes: Construct a theoretical single-degree-of-freedom power spectral density function, and construct a logarithmic domain residual sum of squares error function based on the deviation between the power spectral density of the local frequency band and the theoretical single-degree-of-freedom power spectral density function; The initial parameter vector is derived inversely based on the modal frequency, the minimum and peak power spectral density of the local frequency band; Based on the initial parameter vector, the minimum value of the error function is solved using the simplex method to obtain the damping ratio of the true mode.

[0065] Specifically as follows: In power spectrum estimation based on the Welch method, frequency resolution From the original sampling frequency and Fourier transform points This is jointly determined. To accurately fit the half-power bandwidth of sharp peaks, it is typically required that... Less than 0.015 Hz. If the original sampling frequency... A higher damping ratio requires a very large number of Fourier transform points, which not only leads to an exponential increase in computation time but also significantly reduces the average number of iterations of the Welch method, affecting the final identification result. To address these issues, this embodiment introduces a time series resampling method when performing refined damping ratio recalculation. This method first targets the current analysis... k Target modal frequency Calculate the target sampling frequency for safety : (28) According to Shannon's sampling theorem, the sampling frequency should be at least twice the target frequency. Here, a sampling frequency of four times the target frequency is set to provide sufficient transition band for subsequent anti-aliasing filtering and prevent spectral leakage. Since digital signal processing algorithms cannot directly perform arbitrary frequency conversions, this application extracts the simplest coprime scaling factor through rational fraction approximation. P and Q , P and Q satisfy: (29) Finally, the new sampling frequency after resampling is obtained. for: (30) Obtain the new sampling frequency Then, the algorithm reverse-engineers the solution to satisfy the target resolution. The ideal length of a Fourier window: (31) In the formula, This indicates rounding up to the nearest integer.

[0066] Through the aforementioned resampling mechanism, the algorithm significantly improves the frequency resolution without losing effective information about the target resonance peak, laying a data foundation for subsequent robust and high-precision damped fitting. Subsequently, to reduce potential interference from dense modes and focus on analyzing the physical morphology of the currently dominant mode, the algorithm extracts a frequency band centered on the resonance peak, with a width equal to the modal frequency. f k of Local frequency band This serves as the optimization domain for subsequent damping ratio identification.

[0067] High-precision damping identification based on frequency domain SDOF (single degree of freedom) objective function fitting: Assuming the environmental excitation on the target structure can be regarded as wide-stable Gaussian white noise, then according to the random vibration theory, the first degree of vibration is extracted through spatial filtering. k The theoretical distribution of the power spectral density (PSD) of the acceleration response of a generalized single-degree-of-freedom system can be expressed by the following equation: (32) In the formula, This represents the theoretical single-degree-of-freedom power spectral density. The parameter vector to be identified; The undamped natural frequency of the system; is the damping ratio of the target mode; A is the generalized amplitude factor; B is a constant term used to characterize the frequency-independent broadband random noise floor.

[0068] To ensure that the theoretical single-degree-of-freedom power spectral density function closely matches the actual power spectral density function, this application solves the problem by constructing an error function and finding its minimum. In practical analysis, the singular values ​​at the resonance peak are usually much larger than the local noise floor. If linear absolute error is directly used for fitting, the numerical optimization process will be dominated by the singular values ​​with huge peaks, thus neglecting the peak shape, which plays a decisive role in the damping ratio calculation. To balance the distribution of singular values ​​of different orders of magnitude, this application ultimately chooses to construct a residual sum of squares error function in the logarithmic domain: (33) In the formula, This represents the total error value. For summation operators; This refers to a selected local frequency band. For at frequency point The actual power spectral density at that location.

[0069] Because the objective function contains high-order powers, the computational cost of using traditional gradient algorithms for optimization is extremely high. Therefore, solving this highly nonlinear objective function requires... The algorithm employs a simplex search method without derivative requirements for parameter optimization. To ensure rapid convergence of the iterative process and prevent it from getting trapped in local minima, the parameter initialization vector... The establishment of the initial value is particularly crucial. The initial value establishment strategy adopted in this embodiment is as follows: the system's initial natural frequency... The initial value of the damping ratio is given directly from the discrete frequency points corresponding to the local peak values. The initial damping ratio is set to 1% based on common empirical experience; the initial value of the base noise is... Take the minimum actual power spectrum within the cutoff frequency band; initial value of the amplitude factor. Then, by forcing the amplitude of the theoretical model at the resonance peak to be equal to the actual peak value, the following can be derived in reverse: (34) In the formula, This represents the highest peak value of the actual power spectrum curve within the cutoff frequency band.

[0070] After multiple rounds of optimization and iterative solving using the simplex method, the algorithm extracts the core physical quantities. This refers to the high-precision extraction of the actual damping ratio of the system.

[0071] In summary, the method of this application can achieve highly automated target modal identification and high-precision damping ratio calculation, and has high adaptability to different target working scenarios.

[0072] Furthermore, in one embodiment, taking a five-degree-of-freedom spring-damped system simulation model as an example, referring to... Figure 6 .

[0073] Given that the mass of the mass block in this five-degree-of-freedom system is 50 kg and the spring stiffness is... The first two damping ratios are set to 0.01 using Rayleigh damping.

[0074] Theoretical analysis reveals that the first five modal frequencies of this five-degree-of-freedom system are 14.325Hz, 41.815Hz, 65.917Hz, 84.679Hz, and 96.581Hz.

[0075] The specific steps of step S101 in this embodiment are as follows: By establishing the mass matrix and stiffness matrix, and solving for the eigenvalues, the natural frequency of the system can be obtained.

[0076] Calculation using the first two modes and Construct the Rayleigh damping matrix.

[0077] A five-degree-of-freedom system simulation model was established using the state-space method, and white noise excitation with an amplitude of 500N along the X direction was added to each mass block.

[0078] The sampling frequency was set to 2000 Hz and the sampling time to 300 s. Acceleration data along the X direction for each degree of freedom of the five-degree-of-freedom system were collected.

[0079] In this embodiment, the specific steps of step S102 are as follows: The collected acceleration data was input into the program for analysis. First, the narrowest bandwidth of the system was found to be 5.163Hz. Then, by solving equation (35): (35) Finally, the average value obtained for subsequent Welch methods is obtained. The pixel count is 2048, which corresponds to a resolution of 0.977 Hz.

[0080] The peak frequency with the lowest frequency on the frequency axis of the structure band is obtained through peak search. The highest peak frequency is 14.648 Hz. The frequency band is 96.680 Hz. The final cut-off frequency band range is 0.5 Hz to 116.680 Hz obtained by equation (36).

[0081] (36) In the formula, Set the frequency to 0.5Hz; Pick Hz; Select 20 Hz.

[0082] Singular value decomposition is performed on the power spectral density matrix of each frequency point within the intercepted frequency band to obtain the first singular value (characterizing the energy contribution of that frequency point) and the first singular vector (i.e., the frequency domain mode shape of that frequency point) corresponding to each frequency point.

[0083] In this embodiment, the specific steps of step S103 are as follows: Frequency points within the intercepted frequency band are constructed into pairs of distances, and clustering is performed using the HDBSCAN algorithm (Hierarchical Density-Based Spatial Clustering of Applications with Noise).

[0084] (37) in: (38) (39) (40) (41) (42) In equation (42), l Take 0.1.

[0085] The clustering algorithm yielded the modal frequencies of five candidate modes, which are 14.648 Hz, 41.992 Hz, 65.430 Hz, 84.961 Hz, and 96.680 Hz.

[0086] Step S104 is as follows: The confidence of the candidate modality cluster based on the modality screening strategy of global noise floor value is calculated using equations (43), (44), and (45).

[0087] (43) (44) (45) In equation (43), Take 2; Take 6; The confidence level of the candidate modality cluster based on the modality screening strategy of peak morphology and salience is calculated using equations (46), (47), and (48).

[0088] (46) (47) (48) In equation (46), Take 2; Take 5.

[0089] Based on equations (49) and (50), the fusion confidence of candidate modality clusters based on orthogonal sum DS information fusion and joint judgment is calculated.

[0090] (49) (50) Finally, five candidate mode clusters were obtained. and As shown in Table 1: Table 1. Modal confidence distribution of candidate modes

[0091] After screening, the modal frequencies of the five candidate modal clusters were all true modal frequencies.

[0092] In this embodiment, the specific steps of steps S105 and S106 are as follows: Spatial filtering is performed on the selected modal clusters using equation (51).

[0093] (51) The filtered modal clusters are resampled using equations (52), (53), (54), and (55).

[0094] (52) (53) (54) (55) Constructing the error function The error function is minimized using the simplex method, and the modal damping ratio of the selected modal clusters is finally obtained.

[0095] (56) The modal frequencies, modal damping ratios, and mode shapes of the fifth-order modes are finally obtained, as shown in Table 2. Figure 7 and Figure 8 As shown: Table 2. Final obtained modal frequencies, modal damping ratios, and mode shapes.

[0096] Table 3 shows a comparison between the modal frequencies obtained by the algorithm and the theoretical modal frequencies.

[0097] Table 3 Modal Frequency Comparison

[0098] The modal damping ratios obtained using the frequency domain nonlinear fitting algorithm are compared with the theoretical modal damping ratios and the modal damping ratios obtained using the traditional EFDD method, as shown in Table 4. Since the theoretical model adopts the Rayleigh damping assumption, the modal damping ratios of the first two modes are mainly compared.

[0099] Table 4 Comparison of Damping Ratio Errors

[0100] The comparison shows that the damping ratio calculation method used in this application significantly reduces the error in damping ratio calculation compared to the traditional EFDD method.

[0101] The foregoing has shown and described the basic principles, main features, and advantages of this application. Those skilled in the art should understand that this application is not limited to the above embodiments. The embodiments and descriptions in the specification are merely illustrative of the principles of this application. Various changes and modifications can be made to this application without departing from the spirit and scope thereof, and all such changes and modifications fall within the scope of this application as claimed. The scope of protection of this application is defined by the appended claims and their equivalents.

Claims

1. A method for identifying structural operating modal parameters and calculating damping ratio, characterized in that, include: Acquire multi-channel acceleration response data of the structure under random excitation; The multi-channel acceleration response data is decomposed in the frequency domain to obtain the frequency domain mode shape and the corresponding singular value at each frequency point; Based on the frequency domain mode shape and the singular value, a hierarchical density clustering algorithm is used to cluster each frequency point to obtain candidate mode clusters; Based on the DS evidence theory, the amplitude domain and morphological domain information are fused and false modes are eliminated from the candidate mode clusters to obtain the modal frequencies and mode shapes of the true modes; Using the mode shapes of the actual modes as weights, spatial filtering is performed on the multi-channel acceleration response data to obtain the single-degree-of-freedom generalized coordinate response; Using the modal frequency of the true mode as a reference, the single-degree-of-freedom generalized coordinate response is resampled, a local frequency band centered on the modal frequency is extracted, and the parameters of the frequency domain optimization objective function are optimized to obtain the damping ratio of the true mode.

2. The method according to claim 1, characterized in that, The step of performing frequency domain decomposition on the multi-channel acceleration response data to obtain the frequency domain mode shape and corresponding singular value at each frequency point includes: Based on the physical characteristics of the multi-channel acceleration response data, the optimal parameters for frequency domain decomposition are determined by Welch self-power spectrum estimation and normalized bias error requirements. Solve the logarithmic power spectrum of the multi-channel acceleration response data, extract the noise floor baseline and identify resonance peaks based on the logarithmic power spectrum, and determine the analysis frequency band; Based on the optimal parameters, the multi-channel acceleration response data is decomposed in the frequency domain to obtain the singular value spectrum of each frequency point. Extract the frequency domain mode shapes and corresponding singular values ​​of each frequency point within the analysis frequency band.

3. The method according to claim 1, characterized in that, The step of clustering each frequency point using a hierarchical density clustering algorithm based on the frequency domain mode shape and the singular values ​​includes: Based on the frequency domain mode shape, calculate the frequency similarity and mode shape confidence; based on the singular values, calculate the spectral line amplitude weights; and construct the frequency similarity, the mode shape confidence, and the spectral line amplitude weights into a pairwise distance. The mutual reachability distance is calculated based on the pairwise distance, and a minimum spanning tree is constructed based on the mutual reachability distance; The minimum spanning tree is hierarchically split and noise points are removed to extract stable clusters as candidate mode clusters.

4. The method according to claim 1, characterized in that, The step of fusing amplitude domain and morphological domain information and removing false modes from the candidate mode cluster based on DS evidence theory includes: Extract candidate peak points from the candidate mode cluster; The global noise floor is calculated based on the singular values. An amplitude domain evidence source is established based on the global noise floor. The true modal confidence and false modal confidence of each candidate peak point are calculated based on the amplitude domain evidence source. Based on the attenuation degree and prominence of the candidate peak points on both sides of the singular value, a morphological domain evidence source is established, and the true modal confidence and false modal confidence of each candidate peak point are calculated based on the morphological domain evidence source. The conflict coefficient is calculated based on the confidence levels of the amplitude domain evidence sources and the morphological domain evidence sources, and orthogonalization and fusion are performed to obtain the joint confidence level of each candidate peak point; The candidate peak points are screened based on the joint confidence level, and the candidate peak points that meet the true mode decision criteria are retained. The corresponding candidate mode clusters are determined as true modes, and the modal frequencies and mode shapes of the true modes are obtained.

5. The method according to claim 1, characterized in that, The steps of resampling the single-degree-of-freedom generalized coordinate response based on the modal frequency of the true mode, constructing a frequency domain optimization objective function for parameter optimization, and obtaining the damping ratio of the true mode include: The single-degree-of-freedom generalized coordinate response is resampled based on the modal frequencies; The resampled single-degree-of-freedom generalized coordinate response is subjected to frequency domain transformation, and a local frequency band centered on the modal frequency is extracted to obtain the power spectral density of the local frequency band. Based on the power spectral density of the local frequency band, a frequency domain optimization objective function is constructed to optimize the parameters and obtain the damping ratio of the true mode.

6. The method according to claim 5, characterized in that, The step of resampling the single-degree-of-freedom generalized coordinate response based on the modal frequency includes: The target sampling frequency is calculated based on the modal frequency, and the resampling scale factor is determined by rational fraction approximation. The single-degree-of-freedom generalized coordinate response is then resampled based on the resampling scale factor.

7. The method according to claim 5, characterized in that, The steps of performing frequency domain transformation on the resampled single-degree-of-freedom generalized coordinate response, extracting a local frequency band centered on the modal frequency to obtain the power spectral density of the local frequency band, and constructing a frequency domain optimization objective function based on the power spectral density of the local frequency band to optimize parameters and obtain the damping ratio of the true mode include: Construct a theoretical single-degree-of-freedom power spectral density function, and construct a logarithmic domain residual sum of squares error function based on the deviation between the power spectral density of the local frequency band and the theoretical single-degree-of-freedom power spectral density function; The initial parameter vector is derived inversely based on the modal frequency, the minimum and peak power spectral density of the local frequency band; Based on the initial parameter vector, the minimum value of the error function is solved using the simplex method to obtain the damping ratio of the true mode.

8. A system for identifying structural operating mode parameters and calculating damping ratio, characterized in that, include: The data acquisition module is used to acquire multi-channel acceleration response data of the structure under random excitation; The frequency domain decomposition module is used to perform frequency domain decomposition on the multi-channel acceleration response data to obtain the frequency domain mode shape and the corresponding singular value at each frequency point. The clustering module is used to cluster each frequency point based on the frequency domain mode shape and the singular value using a hierarchical density clustering algorithm to obtain candidate mode clusters. The filtering module is used to fuse amplitude domain and morphological domain information based on DS evidence theory and remove false modes from the candidate mode clusters to obtain the modal frequencies and mode shapes of the true modes. The spatial filtering module is used to perform spatial filtering on the multi-channel acceleration response data with the mode shape of the real mode as weights to obtain a single-degree-of-freedom generalized coordinate response. The damping ratio extraction module is used to resample the single-degree-of-freedom generalized coordinate response based on the modal frequency of the true mode, extract a local frequency band centered on the modal frequency, construct a frequency domain optimization objective function for the local frequency band, perform parameter optimization, and obtain the damping ratio of the true mode.

9. An electronic device, characterized in that, include: A memory on which computer programs are stored; A processor for executing the computer program in the memory to implement the steps of the method according to any one of claims 1-7.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by a processor, it implements the steps of the method according to any one of claims 1-7.

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