Method for modal decoupling and multi-strategy collaborative modal parameter identification of towering stay wire mast
By employing the AMD method and multi-strategy collaborative identification technology in tall guyed mast structures, the tower body and fiber rope modes were successfully separated, solving the problem of dense mode separation and improving the accuracy and applicability of mode parameter identification. This method is suitable for wind-resistant design and health monitoring of tall structures.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- SOUTH CHINA UNIV OF TECH
- Filing Date
- 2026-01-12
- Publication Date
- 2026-05-08
AI Technical Summary
Existing technologies struggle to effectively separate dense modes in tall mast structures, especially under strong winds. Traditional methods suffer from mode aliasing, endpoint effects, and signal reconstruction distortion, and they also fail to meet the requirements of recognition accuracy, computational efficiency, and data quality in different engineering scenarios.
A modal decoupling and multi-strategy collaborative modal parameter identification method for tall guyed masts is adopted. By deploying acceleration sensors at different heights of the tall guyed mast structure, the signal is decomposed using the AMD method. Combined with Hilbert transform and power spectrum analysis, fiber rope modal interference is eliminated. Subsequently, an adaptive strategy is used to select algorithms such as SSI-COV, FBFFT, RDT and FDD for modal parameter identification, and spurious modes are eliminated through multi-dimensional verification indicators.
It achieves clear separation of tower body and fiber rope modes, reduces signal reconstruction error, improves the accuracy and engineering applicability of mode recognition, is applicable to different engineering scenarios, provides accurate parameter basis for wind-resistant design, and reduces the risk of structural failure.
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Figure CN121996955A_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of structural engineering technology, specifically relating to a method for modal decoupling and multi-strategy collaborative modal parameter identification of tall guyed masts. Background Technology
[0002] Tall mast structures are widely used in communications, meteorological observation, and power transmission due to their advantages such as small wind-exposed area, low cost, and convenient installation. However, these structures typically exhibit high flexibility, low damping ratio, and significant nonlinear dynamic characteristics. Under strong winds such as typhoons and downbursts, the structures display complex dynamic response characteristics with significant multimodal participation. They easily excite both the overall bending mode of the tower and the local vibration mode of the fiber optic cables, resulting in dense and overlapping modal components in the spectrum. Traditional modal decomposition methods, such as EMD and VMD, generally suffer from modal aliasing, endpoint effects, and signal reconstruction distortion when dealing with such dense modes, making it difficult to effectively separate the tower and fiber optic cable modes and increasing the error of subsequent modal identification results. In addition, strong wind measured data are often accompanied by high noise and non-stationary characteristics, further exacerbating the difficulty of modal identification. Existing modal parameter identification methods mostly adopt a single algorithm framework, which is difficult to take into account the differentiated requirements of different engineering scenarios for identification accuracy, computational efficiency, number of measurement points, and data quality.
[0003] Therefore, there is an urgent need for a technical solution that can accurately and efficiently separate dense modes, flexibly adapt the recognition algorithm according to the actual engineering scenario, and accurately identify the modal parameters under strong wind conditions, so as to improve the accuracy, reliability and engineering applicability of modal parameter identification of tall mast structures under strong wind conditions. Summary of the Invention
[0004] The main objective of this invention is to overcome the shortcomings and deficiencies of the prior art and to propose a method for modal decoupling and multi-strategy collaborative modal parameter identification for tall guyed masts.
[0005] To achieve the above objectives, the present invention adopts the following technical solution:
[0006] A method for modal decoupling and multi-strategy collaborative modal parameter identification of tall guyed masts includes the following steps:
[0007] S1. Accelerometers are installed at different heights of the tall guyed mast structure to collect the acceleration response signals of the structure under environmental excitation, and the response signals are preprocessed.
[0008] S2. Perform analytical mode decomposition (AMD) on the preprocessed response signal, including extracting dominant frequencies based on power spectrum analysis, determining the bisection circle frequency based on the trough between adjacent dominant frequencies, constructing an analytical signal using Hilbert transform, decomposing the original signal into several sub-band components based on the bisection circle frequency, removing the corresponding fiber rope mode interference, and obtaining the tower vibration mode.
[0009] S3. Based on the decoupled tower vibration components, according to the number of monitoring points, sample size and recognition accuracy requirements, an adaptive strategy is adopted to select a suitable modal parameter recognition method from the preset algorithm library for calculation, so as to obtain the modal frequency, damping ratio and vibration mode.
[0010] S4. Establish multi-dimensional verification indicators for frequency stability, damping stability, and mode shape similarity. Perform collaborative cross-validation on modal parameters identified by different algorithms, eliminate false modes, and output the final modal parameter identification results.
[0011] Compared with the prior art, the present invention has the following advantages and beneficial effects:
[0012] 1. This invention utilizes the AMD method to separate the dense modes of the tower body and fiber ropes, fundamentally overcoming the mode mixing and endpoint effects problems of traditional methods such as EMD and VMD. The reconstructed signal after decomposition has extremely low error and completely preserves the dynamic characteristics of the original signal. This invention innovatively integrates multiple algorithms such as SSI-COV, FBFFT, RDT, and FDD, and forms a complementary recognition mechanism through multi-strategy adaptive selection and collaborative cross-validation, breaking the limitations of a single algorithm and significantly improving the engineering applicability of the method. Differentiated recognition paths are designed for different engineering scenarios, balancing recognition accuracy and engineering practicality. It provides accurate modal parameter basis for the wind-resistant design of mast structures in strong wind areas, and can support the whole life cycle health monitoring of the structure, reducing the risk of structural failure under extreme wind disasters. Attached Figure Description
[0013] Figure 1 This is an overall flowchart of the method of the present invention.
[0014] Figure 2 This is a time history diagram of sample acceleration in the embodiment.
[0015] Figure 3 This is a schematic diagram of the AMD mode decomposition results in the embodiment.
[0016] Figure 4 This is a comparison diagram of the AMD signal reconstruction diagram and the original signal in the embodiment.
[0017] Figure 5 This is a comparison diagram of the modal frequencies identified by the four methods in the embodiment.
[0018] Figure 6 This is a comparison diagram of modal damping identified by the four methods in the embodiment.
[0019] Figure 7 This is a comparison diagram of the identified vibration modes and the finite element vibration modes in the embodiment. Detailed Implementation
[0020] The present invention will be further described in detail below with reference to the embodiments and accompanying drawings, but the embodiments of the present invention are not limited thereto.
[0021] like Figure 1 As shown, the present invention provides a method for modal decoupling and multi-strategy collaborative modal parameter identification of tall guyed masts, comprising the following steps:
[0022] S1. Accelerometers are installed at different heights on the tall guyed mast structure to collect the acceleration response signals of the structure under environmental excitation, and the response signals are preprocessed; the preprocessing is as follows:
[0023] The acquired response signal was preprocessed by frequency domain filtering using a Kaiser window FIR bandpass filter to retain the low-frequency dominant vibration frequency band signal of 0~2.5Hz.
[0024] S2. Perform analytical mode decomposition (AMD) on the preprocessed response signal, including extracting dominant frequencies based on power spectrum analysis, determining the bisection circle frequency based on the troughs between adjacent dominant frequencies, constructing an analytical signal using Hilbert transform, decomposing the original signal into several sub-band components based on the bisection circle frequency, removing corresponding fiber rope mode interference, and obtaining the tower vibration modes; specifically:
[0025] Power spectrum analysis of the acceleration response signal was performed using the Welch power spectrum estimation method to extract dominant frequencies in the low-frequency range and determine the frequency range of dense modes.
[0026] Based on the distribution of dominant frequencies, the frequency corresponding to the trough between adjacent dominant frequencies is calculated as the bisection circle frequency, and the frequency boundaries of the tower body mode and the fiber rope mode are divided.
[0027] Constructing a sub-signal separation function using Hilbert transform:
[0028] ;
[0029] Where i = 1, 2, ..., n-1; This corresponds to the i-th sub-signal; Let H[·] be the i-th bisection circle frequency; H[·] represents the Hilbert transform, expressed as:
[0030] ;
[0031] The original signal is decomposed based on i-1 bisection circle frequencies, thereby eliminating fiber rope mode interference.
[0032] S3. Based on the decoupled tower vibration components, and according to the number of monitoring points, sample size, and recognition accuracy requirements, an adaptive strategy is adopted to select a suitable modal parameter recognition method from a pre-set algorithm library for calculation, obtaining the modal frequency, damping ratio, and mode shape; wherein, the pre-set algorithm library includes:
[0033] Covariance-driven random subspace method SSI-COV, fast Bayesian FFT method FBFFT, random decrement method RDT, and frequency domain decomposition method FDD;
[0034] In step S3, the adaptive strategy is specifically as follows:
[0035] When there are multiple monitoring points and high requirements are placed on identification accuracy and mode shape identification, the method of combining SSI-COV with stability diagrams is adopted.
[0036] When there are multiple monitoring points, a large amount of sample data, and high requirements for computational efficiency, the FBFFT method is adopted.
[0037] When the monitoring point is a single point and the sample sampling time meets the statistical requirements, the RDT method or FDD method is used.
[0038] The calculation using the SSI-COV method combined with stability plots includes:
[0039] Based on the multi-point tower vibration components, the output covariance matrix is calculated, and a Toeplitz matrix is constructed. The number of rows and blocks i in the matrix ranges from 2β to 4β, where β is the ratio of the sampling frequency to the fundamental frequency of the mast structure. The effective order of the system is determined by the stable state of the singular entropy increment. Singular value decomposition (SVD) is performed on the weighted Toeplitz matrix to remove noise components corresponding to small singular values. The system matrix of the discrete state-space model is solved, and eigenvalue decomposition is performed to obtain the initial set of modal parameters. A multidimensional criterion stability graph containing frequency, damping ratio, and modal confidence (MAC) is constructed to screen the true modal parameters that meet the stability conditions. The threshold values for the stability conditions are: frequency tolerance ≤ 5%, damping ratio tolerance ≤ 15%, and mode shape tolerance ≤ 5%.
[0040] The specific steps are as follows:
[0041] The covariance sequence is calculated based on the tower vibration components at multiple measuring points. , i is the time interval, y k Represents the system's output vector at time k; construct the Toeplitz matrix:
[0042] ;
[0043] in, Obtained from the Hankel matrix, The number of rows i in the Toeplitz matrix ranges from 2β to 4β, where β is the ratio of the sampling frequency to the fundamental frequency of the mast structure.
[0044] Singular Value Decomposition (SVD) is performed on the weighted Toeplitz matrix to obtain:
[0045] ;
[0046] in, ;
[0047] Calculate the singular entropy increment to determine the effective order of the system. The calculation formula is:
[0048] ;
[0049] in, It is the i-th discrete-time complex eigenvalue.
[0050] When the singular entropy increment tends to stabilize, the corresponding order is the effective order of the system, ensuring that there is no omission or redundancy in modal information;
[0051] Calculate the observable matrix from the singular value decomposition results of the Toeplitz matrix. and the inverted controllable matrix The system matrix A is identified based on the least squares method, and eigenvalue decomposition is performed to obtain discrete-time complex eigenvalues. The least squares identification system matrix A is represented as:
[0052] ;
[0053] in, This indicates a pseudo-inverse operation;
[0054] Perform eigenvalue decomposition on the system matrix A and calculate the structural modal parameters:
[0055] ;
[0056] in, = diag(λ i ) is a diagonal matrix of order i composed of discrete-time complex eigenvalues; It is a complex eigenvector matrix;
[0057] ;
[0058] Where Re represents the real part.
[0059] A multidimensional stability graph incorporating frequency stability, damping ratio stability, and MAC mode shape similarity is constructed to screen for true modal parameters that satisfy stability conditions. The criterion for determining a stable point is that it simultaneously satisfies the following conditions:
[0060] ;
[0061] Where j is the system order; f, , These represent the frequency, damping ratio, and mode shape corresponding to each order, respectively, while MAC is the modal confidence factor.
[0062] When the deviation between the higher-order parameter and the lower-order parameter is within the tolerance range, it is determined to be a stable mode. Divergent spurious modes are then eliminated to obtain the final mode parameters.
[0063] The calculation using the FBFFT method includes:
[0064] Fourier transform is performed on the single-mode tower vibration components after AMD decomposition to obtain the real and imaginary parts of the frequency domain data; the spectral density matrix is constructed and eigenvalue decomposition is performed, and the eigenvector corresponding to the largest eigenvalue is taken as the best estimate of the mode shape; a negative log-likelihood function is constructed, and an unconstrained optimization function is used to iteratively solve for the frequency and damping ratio that minimize the likelihood function; based on the obtained optimal solution, the Hessian matrix and posterior covariance matrix are calculated, and the posterior uncertainty of the identification parameters is quantified by the coefficient of variation;
[0065] The specific steps are as follows:
[0066] Using the signal containing single-mode information obtained in step S2, perform a Discrete Fourier Transform (FFT) to obtain the real part of the response signal. and the virtual part The calculation formula is:
[0067] ;
[0068] in, Indicates the sampling interval; and These represent the response signals y and y, respectively. j The real and imaginary parts obtained from the Fourier transform; k=1,2,……,N, but considering the endpoint effect and that the Fourier transform yields a conjugate two-sided spectrum, only the data corresponding to k=2,3,……,int[N / 2]+1 are used for subsequent analysis, corresponding to the frequency f. k =(k-1) / (N ).
[0069] Calculate the process quantities and construct matrix A0:
[0070] ;
[0071] Perform eigenvalue decomposition on A0, and the eigenvector corresponding to the largest eigenvalue λ0 is the best estimate (MPV) of the mode shape vector; and calculate... and prediction spectral density error MPV value:
[0072] ;
[0073] Where, N f N represents the number of data points used for analysis. f =int[N / 2].
[0074] Construct the log-likelihood function:
[0075] ;
[0076] in, ;
[0077] In MATLAB, the modal frequencies and damping ratios are obtained using the unconstrained optimization function fminunc. The initial iteration values of the unconstrained optimization function are set as follows: the initial frequency is the corresponding dominant frequency extracted by AMD, and the initial damping ratio is 0.5%.
[0078] Assemble the Hessian matrix of the log-likelihood function using the second-order partial derivatives of the log-likelihood function:
[0079] ;
[0080] in, yes Characteristic base, These are the corresponding eigenvalues.
[0081] Calculate the covariance matrix C. The coefficient of variation (COV) is used to measure the posterior uncertainty of the identified modal parameters, providing a confidence interval reference for engineering applications.
[0082] When using the RDT method for calculation, the following are included:
[0083] The root mean square (RMS) acceleration of the modal components of the tower body is calculated and used as an adaptive trigger threshold. A cross-triggered method is adopted to extract several random sub-samples that meet the threshold requirements. All random sub-samples are time-aligned and arithmetically averaged to obtain the free decay vibration response curve after removing random noise interference. The peaks and troughs of the free decay vibration response curve are fitted with an exponential decay model to identify the modal frequencies and damping ratios. The trigger threshold is set to 0.8 to 1.5 times the root mean square (RMS) of the acceleration response. When the number of extracted sub-samples is less than the preset value (e.g., 30), the threshold is automatically lowered and the samples are extracted again until at least 30 valid sub-samples are obtained.
[0084] The specific steps are as follows:
[0085] Using the single-mode information signal obtained in step S2, a cross-triggered method is employed. A trigger threshold A is set to intercept the signal, resulting in a series of different intersection times, thus obtaining random subsamples, represented as follows:
[0086] ;
[0087] Where D(t) represents the free vibration response of the system with an initial displacement of 1 and an initial velocity of 0; V(t) represents the free vibration response of the system with an initial displacement of 0 and an initial velocity of 1. Let be the system vibration velocity; h(t) be the unit impulse response function; and f(t) be the external excitation.
[0088] By performing time alignment and arithmetic averaging on random subsamples to eliminate the influence of random excitation, the free vibration response X(t) with initial displacement A and initial velocity 0 can be obtained:
[0089] ;
[0090] Where N is the number of random subsamples.
[0091] The free vibration decay curve is extracted, and both its peaks and troughs exhibit exponential decay.
[0092] ;
[0093] Where ζ is the structural damping ratio, w n Let be the undamped circular frequency of the structure. The frequency and damping ratio of the structure are obtained by fitting the peaks and troughs of the free vibration decay curve obtained by the RDT method according to the above formula.
[0094] When using the FDD method for calculation, the following are included:
[0095] Calculate the power spectral density matrix of the acceleration response signal and perform singular value decomposition on it;
[0096] The frequencies corresponding to the peak values of the singular value curves are extracted as candidate tower body modal frequencies, and the dominant mode is determined by the modal confidence (MAC).
[0097] Frequency band data near the peak value is selected and subjected to inverse Fourier transform (IFFT) to obtain the normalized autocorrelation function; the damping ratio of the corresponding mode is identified by linear fitting of the logarithmic decay rate.
[0098] The specific steps are as follows:
[0099] Using the single-mode information signal obtained in step S2, calculate the output power spectral density matrix. Its frequency response function matrix Input power spectral density matrix satisfy:
[0100] ;
[0101] in, The structure is the frequency response function matrix; and These are the power spectral density matrices of the system input and output, respectively; This represents the complex conjugate transpose operation of a matrix;
[0102] right When performing singular value decomposition (SVD), if only the r-th mode dominates in a certain frequency range, the decomposition result is approximately:
[0103] ;
[0104] in, That is, the mode shape vector of the r-th mode; d r It is a real constant; Let be the r-th order pole; Re denotes taking the real part.
[0105] The frequency of the r-th mode can be determined by comparing the MAC values of the mode shapes near the peak of the singular value curve.
[0106] Performing an inverse Fourier transform (IFFT) on the corresponding frequency band yields the normalized autocorrelation function, which is then used to calculate the logarithmic attenuation rate. By performing a linear fit, the damping ratio of the r-th mode can be obtained. :
[0107] ;
[0108] in, and These represent the initial value of the autocorrelation function and the value after decaying through k peaks, respectively.
[0109] S4. Establish multi-dimensional verification indicators for frequency stability, damping stability, and mode shape similarity. Perform collaborative cross-validation on modal parameters identified by different algorithms, eliminate false modes, and output the final modal parameter identification results.
[0110] Example: This example uses a 356m high Shenzhen meteorological observation gradient tower (lattice-type guyed mast structure) as an example. The bottom cross-section of the meteorological tower is 5m × 5m, which gradually changes to 2.5m × 2.5m at an elevation of 15m. The guyed anchorage heights are 65m, 130m, 195m, 260m and 325m, with two guyed ropes in each direction on the 2nd and 4th floors, and a single guyed rope in each direction on the 1st, 3rd and 5th floors.
[0111] Five LAC-II accelerometers were deployed at heights of 50m, 160m, 250m, 300m, and 350m. Thirteen WMT703 cup anemometers and four CSAT3 ultrasonic anemometers were simultaneously installed on the mast structure to achieve synchronous acquisition of acceleration and wind speed for the identification of strong wind events.
[0112] This embodiment includes the following steps:
[0113] 1. Data Acquisition and Preprocessing: Strong typhoons and downburst events were identified using deployed wind speed and acceleration acquisition equipment. 29 downburst samples were collected between 2018 and 2020, and 734 1-hour measured samples were obtained before and after Typhoons Lionrock and Kompasu in October 2021.
[0114] Taking typhoon events as an example, six samples were selected for analysis during October 2021, such as... Figure 2 As shown in the figure. Samples 1 and 2 correspond to samples with weak mast response; samples 3 and 4 correspond to samples with relatively strong mast vibration; samples 5 and 6 correspond to samples with strong mast vibration under the influence of typhoon.
[0115] The acceleration signal is preprocessed using digital filter technology to remove high-frequency signals above 2.5Hz from the measured signal, while retaining the low-frequency dominant frequency band covering the first three bending modes of the tower.
[0116] 2. Tower-to-wire coupling dense mode separation: Power spectrum analysis was performed to obtain the dominant frequency and bisection circle frequency. Through AMD decomposition, the tower body mode and fiber rope mode were separated, and the first-order tower body mode frequency was successfully extracted, such as... Figure 3 The image shows a schematic diagram of the mode decomposition results. To verify the decomposition effect, the two components obtained by AMD are reconstructed and compared with the original signal, as shown below. Figure 4 As shown, the time-domain waveform and power spectral density are highly consistent, proving that there is no information loss during the decomposition process. The power spectrum of each component contains only a single peak, clearly corresponding to a physical mode, thus completely solving the problem of dense coupling.
[0117] 3. Modal identification and output of modal parameters;
[0118] Based on the tower vibration signal after modal decoupling, four modal identification methods—SSI-COV, FBFFT, RDT, and FDD—were used to identify structural modal parameters, obtaining several sets of parameters for each method. A comparative analysis was performed on the modal parameter results identified by each method, including modal frequencies and modal damping. Figure 5 and Figure 6 As shown, the mode shape is as follows Figure 7 As shown, the overall consistency of the identification results from each method is high, intuitively verifying the stability, consistency, and rationality of the multi-strategy identification method of this invention under strong wind conditions, providing a reliable foundation for subsequent parameter identification. Combined with the adaptive strategy of this invention, appropriate modal identification methods can be selected for different application scenarios of the structure in engineering, thereby improving the accuracy of modal parameter identification.
[0119] This embodiment only demonstrates the application of the present invention to a typical tall guyed mast structure. However, those skilled in the art should understand that the present invention is also applicable to other types of flexible tall structures (such as transmission towers, wind turbine towers, broadcast masts, etc.), requiring only adjustment of the filter frequency band and AMD delimitation criteria according to their dynamic characteristics. Furthermore, the Kaiser window FIR filter, AMD decomposition process, multiple algorithm libraries, and verification mechanism can all be implemented through programming, facilitating integration into a structural health monitoring platform to achieve automated and intelligent identification of modal parameters. All equivalent substitutions or improvements made using the core idea of this invention, namely "AMD-based tower-wire modal decoupling plus scene-adaptive multi-strategy identification plus multi-dimensional cross-validation," should be considered to fall within the protection scope of this invention. The specific protection scope of this invention is defined by the appended claims.
[0120] It should also be noted that, in this specification, terms such as "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitation, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.
[0121] The above description of the disclosed embodiments enables those skilled in the art to make or use the invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the invention. Therefore, the invention is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.
Claims
1. A method for modal decoupling and multi-strategy collaborative modal parameter identification of tall guyed masts, characterized in that, Includes the following steps: S1. Accelerometers are installed at different heights of the tall guyed mast structure to collect the acceleration response signals of the structure under environmental excitation, and the response signals are preprocessed. S2. Perform analytical mode decomposition (AMD) on the preprocessed response signal, including extracting dominant frequencies based on power spectrum analysis, determining the bisection circle frequency based on the trough between adjacent dominant frequencies, constructing an analytical signal using Hilbert transform, decomposing the original signal into several sub-band components based on the bisection circle frequency, removing the corresponding fiber rope mode interference, and obtaining the tower vibration mode. S3. Based on the decoupled tower vibration components, according to the number of monitoring points, sample size and recognition accuracy requirements, an adaptive strategy is adopted to select a suitable modal parameter recognition method from the preset algorithm library for calculation, so as to obtain the modal frequency, damping ratio and vibration mode. S4. Establish multi-dimensional verification indicators for frequency stability, damping stability, and mode shape similarity. Perform collaborative cross-validation on modal parameters identified by different algorithms, eliminate false modes, and output the final modal parameter identification results.
2. The method for modal decoupling and multi-strategy collaborative modal parameter identification of a tall guyed mast according to claim 1, characterized in that, In step S1, the preprocessing specifically includes: The acquired response signal was preprocessed by frequency domain filtering using a Kaiser window FIR bandpass filter to retain the low-frequency dominant vibration frequency band signal of 0~2.5Hz.
3. The method for modal decoupling and multi-strategy collaborative modal parameter identification of a tall guyed mast according to claim 1, characterized in that, Step S2 is as follows: Power spectrum analysis of the acceleration response signal was performed using the Welch power spectrum estimation method to extract dominant frequencies in the low-frequency range and determine the frequency range of dense modes. Based on the distribution of dominant frequencies, the frequency corresponding to the trough between adjacent dominant frequencies is calculated as the bisection circle frequency, and the frequency boundaries of the tower body mode and the fiber rope mode are divided. Constructing a sub-signal separation function using Hilbert transform: ; Where i = 1, 2, ..., n-1; This corresponds to the i-th sub-signal; Let H[·] be the i-th bisection circle frequency; H[·] represents the Hilbert transform, expressed as: ; The original signal is decomposed based on i-1 bisection circle frequencies, thereby eliminating fiber rope mode interference.
4. The method for modal decoupling and multi-strategy collaborative modal parameter identification of a tall guyed mast according to claim 1, characterized in that, In step S3, the preset algorithm library includes: Covariance-driven random subspace method SSI-COV, fast Bayesian FFT method FBFFT, random decrement method RDT, and frequency domain decomposition method FDD; In step S3, the adaptive strategy is specifically as follows: When there are multiple monitoring points and high requirements are placed on identification accuracy and mode shape identification, the method of combining SSI-COV with stability diagrams is adopted. When there are multiple monitoring points, a large amount of sample data, and high requirements for computational efficiency, the FBFFT method is adopted. When the monitoring point is a single point and the sample sampling time meets the statistical requirements, the RDT method or FDD method is used.
5. The method for modal decoupling and multi-strategy collaborative modal parameter identification of a tall guyed mast according to claim 4, characterized in that, When performing calculations using the SSI-COV method combined with stability plots, the following are included: The covariance matrix is calculated based on the vibration components of the tower body at multiple measurement points, and a Toeplitz matrix is constructed. The effective order of the system is determined by the stable state of the singular entropy increment. The weighted Toeplitz matrix is subjected to SVD singular value decomposition to remove noise components corresponding to small singular values. The system matrix of the discrete state-space model is solved, and its eigenvalues are decomposed to obtain the initial set of modal parameters. A multidimensional criterion stability graph containing frequency, damping ratio, and modal confidence (MAC) is constructed to screen the true modal parameters that meet the stability conditions. The threshold values for the stability conditions are: frequency tolerance ≤ 5%, damping ratio tolerance ≤ 15%, and mode shape tolerance ≤ 5%. The specific steps are as follows: The covariance sequence is calculated based on the tower vibration components at multiple measuring points. , i is the time interval, y k Represents the system's output vector at time k; construct the Toeplitz matrix: ; in, Obtained from the Hankel matrix, The number of rows i in the Toeplitz matrix ranges from 2β to 4β, where β is the ratio of the sampling frequency to the fundamental frequency of the mast structure. Performing SVD singular value decomposition on the weighted Toeplitz matrix yields: ; in, ; Calculate the singular entropy increment to determine the effective order of the system. The calculation formula is: ; in, It is the i-th discrete-time complex eigenvalue; When the singular entropy increment tends to stabilize, the corresponding order is the effective order of the system, ensuring that there is no omission or redundancy in modal information; Calculate the observable matrix from the singular value decomposition results of the Toeplitz matrix. and the inverted controllable matrix The system matrix A is identified based on the least squares method, and eigenvalue decomposition is performed to obtain discrete-time complex eigenvalues. The system matrix A, identified using the linear least squares method, is represented as: ; in, This indicates a pseudo-inverse operation; Perform eigenvalue decomposition on the system matrix A and calculate the structural modal parameters: ; in, = diag(λ i ) is a diagonal matrix of order i composed of discrete-time complex eigenvalues; It is a complex eigenvector matrix; ; Where Re represents the real part; A multidimensional stability graph incorporating frequency stability, damping ratio stability, and MAC mode shape similarity is constructed to screen for true modal parameters that satisfy stability conditions. The criterion for determining a stable point is that it simultaneously satisfies the following conditions: ; Where j is the system order; f, , These represent the frequency, damping ratio, and mode shape corresponding to each order, respectively, while MAC is the modal confidence factor. When the deviation between the higher-order parameter and the lower-order parameter is within the tolerance range, it is determined to be a stable mode. Divergent spurious modes are then eliminated to obtain the final mode parameters.
6. The method for modal decoupling and multi-strategy collaborative modal parameter identification of a tall guyed mast according to claim 4, characterized in that, When performing calculations using the FBFFT method, the following are included: Fourier transform is performed on the single-mode tower vibration components after AMD decomposition to obtain the real and imaginary parts of the frequency domain data; the spectral density matrix is constructed and eigenvalue decomposition is performed, and the eigenvector corresponding to the largest eigenvalue is taken as the best estimate of the mode shape; a negative log-likelihood function is constructed, and an unconstrained optimization function is used to iteratively solve for the frequency and damping ratio that minimize the likelihood function; based on the obtained optimal solution, the Hessian matrix and posterior covariance matrix are calculated, and the posterior uncertainty of the identification parameters is quantified by the coefficient of variation; The specific steps are as follows: Using the signal containing single-mode information obtained in step S2, perform a Discrete Fourier Transform (FFT) to obtain the real part of the response signal. and the virtual part The calculation formula is: ; in, Indicates the sampling interval; and These represent the response signals y and y, respectively. j The real and imaginary parts obtained from the Fourier transform; k=1,2,……,N, but considering the endpoint effect and that the Fourier transform yields a conjugate two-sided spectrum, only the data corresponding to k=2,3,……,int[N / 2]+1 are used for subsequent analysis, corresponding to the frequency f. k =(k-1) / (N ); Calculate the process quantities and construct matrix A0: ; Perform eigenvalue decomposition on A0, and the eigenvector corresponding to the largest eigenvalue λ0 is the best estimate of the mode shape vector. ; and calculate and prediction spectral density error MPV value: ; Where, N f N represents the number of data points used for analysis. f =int[N / 2]; Construct the log-likelihood function and solve for the frequency f and damping ratio. : ; in, ; In MATLAB, the modal frequencies and damping ratios are obtained using the unconstrained optimization function fminunc. Assemble the Hessian matrix of the log-likelihood function using the second-order partial derivatives of the log-likelihood function: ; in, yes Characteristic base, These are the corresponding eigenvalues; Calculate the covariance matrix C. The coefficient of variation is used to measure the posterior uncertainty of the identified modal parameters, providing a confidence interval reference for engineering applications.
7. The method for modal decoupling and multi-strategy collaborative modal parameter identification of a tall guyed mast according to claim 4, characterized in that, When using the RDT method for calculation, it includes: The root mean square (RMS) acceleration of the tower body modal components is calculated and used as an adaptive trigger threshold. A cross-triggering method is adopted to extract several random sub-samples that meet the threshold requirements. All random sub-samples are time-aligned and arithmetically averaged to obtain the free decay vibration response curve after removing random noise interference. The peaks and troughs of the free decay vibration response curve are fitted with an exponential decay model to identify the modal frequencies and damping ratios. The specific steps are as follows: Using the single-mode information signal obtained in step S2, a cross-triggered method is employed. A trigger threshold A is set to intercept the signal, resulting in a series of different intersection times, thus obtaining random subsamples, represented as follows: ; Where D(t) represents the free vibration response of the system with an initial displacement of 1 and an initial velocity of 0; V(t) represents the free vibration response of the system with an initial displacement of 0 and an initial velocity of 1. Let be the system vibration velocity; h(t) be the unit impulse response function; and f(t) be the external excitation. For random subsamples By performing time alignment and arithmetic averaging to eliminate the influence of random excitation, the free vibration response X(t) with initial displacement A and initial velocity 0 can be obtained: ; Where N is the number of random subsamples; The free vibration decay curve is extracted, and both its peaks and troughs exhibit exponential decay. ; Where ζ is the structural damping ratio, w n Let be the undamped circular frequency of the structure; the frequency and damping ratio of the structure are obtained by fitting the peaks and troughs of the free vibration decay curve obtained by the RDT method according to the above formula.
8. The method for modal decoupling and multi-strategy collaborative modal parameter identification of a tall guyed mast according to claim 4, characterized in that, When performing calculations using the FDD method, the following are included: Calculate the power spectral density matrix of the acceleration response signal and perform singular value decomposition on it; The frequencies corresponding to the peak values of the singular value curves are extracted as candidate tower body mode frequencies, and the dominant mode is determined by the modal confidence (MAC). Frequency band data near the peak value is selected and subjected to inverse Fourier transform (IFFT) to obtain the normalized autocorrelation function; the damping ratio of the corresponding mode is identified by linear fitting of the logarithmic attenuation rate. The specific steps are as follows: Using the single-mode information obtained in step S2, the input and output power spectral density matrices of the system satisfy the following relationship: ; in, The structure is the frequency response function matrix; and These are the power spectral density matrices of the system input and output, respectively; This represents the complex conjugate transpose operation of a matrix; right When performing singular value decomposition, if only the r-th mode dominates in a certain frequency range, the decomposition result is approximately: ; in, That is, the mode shape vector of the r-th mode; d r It is a real constant; Let R be the r-th pole; Re denotes taking the real part; The frequency of the r-th mode is determined by comparing the MAC values of the mode shapes near the peak of the singular value curve. Performing an inverse Fourier transform (IFFT) on the corresponding frequency band yields the normalized autocorrelation function, which is then used to calculate the logarithmic attenuation rate. The damping ratio of the r-th mode was obtained by performing linear fitting. : ; in, and These represent the initial value of the autocorrelation function and the value after decaying through k peaks, respectively.
9. The method for modal decoupling and multi-strategy collaborative modal parameter identification of a tall guyed mast according to claim 6, characterized in that, The initial iteration values of the unconstrained optimization function are set as follows: The initial frequency is the corresponding optimal frequency extracted by AMD, and the initial damping ratio is 0.5%.
10. The method for modal decoupling and multi-strategy collaborative modal parameter identification of a tall guyed mast according to claim 7, characterized in that, The trigger threshold is set to 0.8 to 1.5 times the root mean square (RMS) of the acceleration response. When the number of subsamples is less than the preset value, the threshold is automatically lowered and the subsamples are retried until a number of valid subsamples of no less than the preset value are obtained.