Modal parameter automatic identification method based on multi-scale space

Abstract

The invention belongs to the field of structural modal identification, and particularly relates to an automatic modal parameter identification method based on a multi-scale space, which comprises the following steps: collecting a vibration data sample from a target structure, the vibration data sample comprising an acceleration signal of the structure; selecting power spectrum calculation parameters including a window function and a fast Fourier transform (FFT) length; performing frequency spectrum estimation on the acceleration signal by using interpolation power spectrum estimation to obtain frequency spectrum data; analyzing the spectrum data by using a multi-scale space algorithm, and detecting a peak value in the spectrum data to obtain a peak value frequency; through a frequency domain decomposition method, according to the peak frequency, modal parameters of the structure are calculated, the modal parameters comprise the modal frequency and the damping ratio, interpolation power spectrum estimation and a multi-scale space algorithm are innovatively combined, automatic and accurate identification of the modal parameters is achieved, and the identification precision and efficiency are remarkably improved.

Description

TECHNICAL FIELD

[0001] The present application belongs to the field of structural modal identification, and particularly relates to a modal parameter automatic identification method based on multi-scale space. BACKGROUND

[0002] The research background of automated structural modal information identification is very important because in the engineering field, the vibration characteristics of structures play a crucial role in safety, stability, and performance evaluation. The vibration modal parameters of structures, such as natural frequencies and damping ratios, provide important information about the basic characteristics of the structure and the response behavior of the structure under different loads. These parameters play a crucial role in the fields of structural health monitoring, earthquake engineering, wind engineering, bridge and building structures, etc.

[0003] In the field of structural health monitoring, automated identification of structural modal parameters is critical. Monitoring the modal parameters of a structure can be used to assess its health condition. Any damage or deterioration of a structure will have an impact on its vibration response, so through the monitoring of modal parameters, problems with the structure can be detected early, and maintenance or repair measures can be taken. This is crucial for ensuring the safety and reliability of the structure.

[0004] The field of earthquake engineering is also a key application area, where the vibration characteristics of structures determine their seismic performance. By identifying the modal parameters of a structure, it is possible to better understand its response under seismic loading, thus enabling seismic design and improvement. This helps to reduce the impact of earthquakes on structures and improve their seismic resistance.

[0005] In new construction projects, designers need to know the natural frequencies and vibration characteristics of the structure to ensure that the structure does not have problems in use. Accurate identification of modal parameters helps to design safer and more reliable structures. Similarly, in the field of wind engineering, it is necessary to have a deep understanding of the vibration characteristics of structures to ensure their stability under wind loads. Identification of modal parameters can help engineers better understand the vibration characteristics of structures under wind loads, thus enabling appropriate structural design and improvement.

[0006] In addition, the vibration modal parameters of structures can also be used to evaluate the performance of the structure. By analyzing these parameters, it is possible to determine the stiffness, mass, and dissipation capacity of the structure, thus providing key information for the performance of the structure. This is important for determining the service life of the structure and for performance improvement.

[0007] However, automated identification of structural modal parameters is not a simple task and faces many challenges. Traditionally, manual measurement of the modal parameters of a structure requires the use of specialized vibration instruments and a large amount of manpower, which is both time-consuming and labor-intensive. Automated methods require the processing of large amounts of vibration data, including acquisition, storage, and analysis, which means that powerful data processing capabilities are required.

[0008] In addition, vibration data is often disturbed by noise and other environmental factors, which can affect the accuracy of modal parameters. Automatic methods need to have the ability to filter noise and handle disturbances. At the same time, it is also crucial to choose appropriate algorithms to extract modal parameters from vibration data. Different structures and vibration conditions may require different algorithms.

[0009] Finally, some applications require real-time acquisition of modal parameters and quick decision-making. Therefore, the efficiency of the algorithm is also an important consideration. Research on automated identification of structural modal parameters is continuously evolving to meet these challenges, improve data processing and analysis capabilities, develop real-time monitoring systems, and explore new algorithms and methods to better understand and utilize the vibration characteristics of structures, improve engineering design and structural performance evaluation. Interdisciplinary collaboration will play a more important role in future research to promote the development of this field. SUMMARY

[0010] The main purpose of the present application is to provide a multi-scale space-based modal parameter automatic identification method, which aims to solve the problems of noise sensitivity, limited analysis accuracy in low frequency band and low automation degree in the prior art.

[0011] The present application discloses a multi-scale space-based modal parameter automatic identification method, comprising:

[0012] Collecting vibration data samples from the target structure, the vibration data samples including acceleration signals of the structure;

[0013] Selecting power spectrum calculation parameters, including window function and fast Fourier transform (FFT) length;

[0014] Using interpolation power spectrum estimation to perform frequency spectrum estimation on the acceleration signals and obtaining frequency spectrum data;

[0015] Applying a multi-scale space algorithm to analyze the frequency spectrum data and detect peak values in the frequency spectrum data to obtain peak frequencies;

[0016] Calculating modal parameters of the structure according to the peak frequencies through frequency domain decomposition method, the modal parameters including modal frequencies and damping ratios.

[0017] Preferably, the vibration data samples are sampled at a uniform sampling frequency.

[0018] Preferably, the window function is a Hanning window function, and the FFT length is set to 1024 sample points.

[0019] Preferably, the frequency spectrum estimation on the acceleration signals using interpolation power spectrum estimation specifically comprises:

[0020] determining a minimum analysis frequency and a maximum analysis frequency, wherein the minimum analysis frequency the maximum analysis frequency wherein f s is a sampling frequency, f min and f max are respectively a minimum analysis frequency and a maximum analysis frequency in the acceleration signal, and N is a number of sample points;

[0021] determining a minimum frequency resolution, wherein the minimum frequency resolution:

[0022] wherein ξ is an overlap coefficient, K min is a minimum number of segments;

[0023] dividing the frequency band into K segments, K being greater than 1, and considering an overlap between the segments;

[0024] when the frequency resolution is less than the minimum frequency resolution, setting the frequency resolution to the minimum frequency resolution.

[0025] Preferably, the application of the multi-scale spatial algorithm to the spectral data comprises specifically:

[0026] determining a power spectrum extreme point set Q by local maximum calculation, wherein Q = localmax(x), and x is the spectral data;

[0027] defining a peak point to satisfy a condition: wherein n is a data point index.

[0028] Preferably, the frequency domain decomposition method is a frequency domain decomposition method FDD, and the calculation of the modal parameters by the frequency domain decomposition method is only modal analysis on the peak frequency.

[0029] Preferably, the method further comprises:

[0030] normalizing the modal parameters and normalizing the mode shapes with mode shape extreme points as reference points.

[0031] Preferably, the method further comprises:

[0032] screening the peak frequency, removing noise peaks, and retaining true natural frequencies of the structure.

[0033] Preferably, the method further comprises:

[0034] evaluating the health state of the structure based on the modal parameters, wherein the evaluation comprises comparing changes in the modal parameters at different time points.

[0035] Preferably, the method further comprises:

[0036] The modal parameters are compared with the parameters calculated by the theoretical model to verify the accuracy of the modal parameters

[0037] The beneficial effects of the present application include:

[0038] 1. By innovatively combining the interpolation power spectrum estimation with the multi-scale spatial algorithm, the automatic accurate identification of modal parameters is realized, and the identification accuracy and efficiency are significantly improved;

[0039] 2. A specific frequency resolution optimization method is proposed for low-frequency analysis, making the low-frequency analysis more precise and enabling more accurate capture of the inherent frequency of the structure;

[0040] 3. The multi-scale spatial algorithm is used for peak detection, effectively reducing noise interference and improving the accuracy of real frequency identification;

[0041] 4. A complete automatic processing flow is established, reducing manual intervention and saving time and labor costs;

[0042] 5. Through verification experiments, the modal parameters identified by the method are highly consistent with the theoretical values, indicating the effectiveness and reliability of the method. BRIEF DESCRIPTION OF DRAWINGS

[0043] Figure 1 is a flowchart of the method of the present application, showing the complete process of automatic identification of modal parameters;

[0044] Figure 2 is an acceleration sensor layout and structural schematic diagram of a real bridge monitoring experiment in an embodiment of the present application;

[0045] Figure 3 is an interpolation power spectrum estimation and peak point identification result schematic diagram in the method of the present application;

[0046] Figure 4 is a structural mode shape and theoretical value comparison result schematic diagram (first order) of FDD identification in the method of the present application. DETAILED DESCRIPTION

[0047] The present application will be further described in detail below in conjunction with the drawings and specific embodiments. It should be understood that the specific embodiments described herein are only for illustration and explanation of the present application, and are not intended to limit the present application.

[0048] This invention provides an automatic modal parameter identification method based on multi-scale space. The method includes the following steps: collecting vibration data samples from the target structure; selecting power spectrum calculation parameters; using interpolated power spectrum estimation to perform spectrum estimation on the acceleration signal; applying a multi-scale space algorithm to perform peak detection on the spectrum data; and calculating the modal parameters of the structure through frequency domain decomposition.

[0049] Reference Figure 1 The flowchart shown illustrates the steps of the automatic modal parameter identification method based on multi-scale space provided in this embodiment:

[0050] Step 1: Sample Sampling and Signal Acquisition. First, vibration data samples are collected from the target structure, typically the structure's acceleration signals. This vibration data can be acquired using accelerometers installed at key locations on the structure to capture its vibration response. Preferably, a uniform sampling frequency is used to sample all sensor data to ensure data consistency and comparability.

[0051] In this embodiment, the sampling frequency can be selected as 100Hz, that is, 100 data points are collected per second. Of course, depending on the actual structural characteristics and analysis requirements, a higher or lower sampling frequency can be selected. For example, for structures with obvious high-frequency vibration characteristics, a higher sampling frequency (such as 200Hz or 500Hz) may be required; while for large structures with predominantly low-frequency vibration, a lower sampling frequency (such as 50Hz) may be sufficient.

[0052] The acquired data should cover a sufficiently long time period to fully reflect the dynamic characteristics of the structure. Typically, the data acquisition time should cover at least several tens of times the period of the structure's lowest-order modal. For example, if the structure's lowest-order natural frequency is approximately 1 Hz, the acquisition time should be no less than 100 seconds.

[0053] Step 2: Select power spectrum calculation parameters. Choosing appropriate power spectrum calculation parameters includes selecting the window function and setting the FFT length. The selection of these parameters will directly affect the accuracy and efficiency of spectrum estimation.

[0054] In this embodiment, the Hanning window function is uniformly used as the window function for power spectrum estimation. The Hanning window function has good frequency resolution and sidelobe suppression characteristics, making it suitable for the analysis of structural vibration signals. The mathematical expression of the Hanning window function is:

[0055]

[0056] Where N is the window function length and n is the sample index.

[0057] At the same time, the FFT length is set to 1024 sample points. The choice of FFT length needs to balance the calculation efficiency and frequency resolution: the larger the FFT length, the higher the frequency resolution, but the calculation amount also increases. The 1024-point FFT length can provide sufficient frequency resolution while maintaining reasonable calculation efficiency in most applications.

[0058] In addition, in some cases, data segmentation and averaging can be considered to reduce the influence of random noise. For example, a long time series can be divided into several 50% overlapping segments, and the FFT calculation is performed on each segment of data, and then the average value is taken, which is called the Welch method, which helps to improve the stability of power spectrum estimation.

[0059] Step 3: Perform spectral analysis using interpolated power spectrum estimation, and perform spectral estimation on the obtained acceleration information using interpolated power spectrum estimation to obtain more accurate spectral data. Interpolated power spectrum estimation can improve the limitations of traditional power spectrum estimation in frequency resolution, especially in the analysis of low frequency bands.

[0060] In order to realize the fine spectrum analysis of low frequency band, it is necessary to optimize the frequency resolution. For each Fourier analysis frequency, the frequency resolution needs to be optimized and adjusted. Specifically, the minimum analysis frequency f min and the maximum analysis frequency f max can be determined by the following formula:

[0061]

[0062] where f s is the sampling frequency and N is the number of sample points. The minimum frequency resolution R min can be expressed as

[0063]

[0064] where ξ is the overlap coefficient, usually taking a value between 0.5 and 0.75, K min is the minimum segment number, which is set according to actual needs, generally taking a value of 4 to 8. In specific implementation, the frequency band is divided into K segments (K>1), and the overlapping part of each Fourier transform segment is considered. When the frequency resolution is less than the minimum frequency resolution R min , the frequency resolution takes the minimum value R min , which can ensure that the peak point will not be filtered out in the filtering process.

[0065] In this way, the interpolated power spectrum estimation can better capture the frequency domain characteristics of the structure, especially the fine structure of the low frequency part, and provide more accurate spectral data for subsequent peak detection.

[0066] Step 4: Peak detection using multi-scale space algorithm. The multi-scale space algorithm is applied to analyze the spectral information in order to detect the peaks in the spectrum. These peaks correspond to the natural frequencies of the structure, so peak detection is a crucial step to obtain the true frequencies of the structure.

[0067] The multi-scale space peak detection method can effectively distinguish between true peaks and noise peaks by analyzing the signal at different scales. The mathematical description is as follows:

[0068] First, define the set of power spectrum extreme points Q:

[0069] Q = localmax(x),

[0070] where x is the input spectral data.

[0071] Define the conditions that the peak points must satisfy:

[0072]

[0073] where n is the data point index. This means that point n is a local maximum point whose value is greater than or equal to the values of its neighboring points. In practical applications, different scales of smoothing can be performed on the original signal using a Gaussian smoothing kernel, and then the extreme points are detected at each scale. As the smoothing scale increases, noise peaks will gradually disappear, while true structural peaks will remain stable. By comparing the extreme point distribution at different scales, the true natural frequencies of the structure can be effectively identified.

[0074] In addition, threshold conditions can also be set to further filter the peak points, for example, the amplitude of the peak point must be greater than a certain multiple (such as 3 times) of the average amplitude of the spectrum to be considered as a valid peak point.

[0075] Step 5: Calculate modal parameters through frequency domain decomposition. Finally, through the frequency domain decomposition (FDD), the modal parameters of the structure, including modal frequencies and damping ratios, are calculated based on the detected peak frequencies.

[0076] Frequency domain decomposition is a modal parameter identification method based on singular value decomposition of the power spectrum matrix. Specifically, for each frequency point, the power spectral density matrix between measurement points is calculated, and then singular value decomposition is performed on the matrix:

[0077] G yy (f) = U(f)S(f)U H (f),

[0078] where G yy (f) is the power spectral density matrix, U(f) is the unitary matrix whose column vectors are singular vectors, S(f) is the diagonal matrix whose diagonal elements are singular values, and U H(f) is the conjugate transpose of U(f).

[0079] Near the modal frequency, the first singular value is significantly larger than the others, and the corresponding singular vector is the mode shape of that mode. By analyzing the variation of singular values ​​with frequency, the modal frequencies and mode shapes of the structure can be accurately identified. For estimating the damping ratio, the half-power bandwidth method can be used. Specifically, for each modal frequency f... r Determine the corresponding half-power frequency points f1 and f2 (i.e., the frequency points where the power drops to half of the peak value), and then calculate the damping ratio ζ. r :

[0080]

[0081] In this embodiment, the frequency domain decomposition method only performs modal analysis on the peak frequencies identified by the multi-scale spatial algorithm, rather than analyzing the entire frequency range. This greatly improves computational efficiency while ensuring the accuracy of the analysis results.

[0082] Reference Figure 2 As shown, the bridge is a simply supported steel truss bridge with a main span of 59.2m and a width of 3.6m.

[0083] like Figure 2 As shown, eight accelerometers (labeled S1 to S8) are arranged on the bridge deck to monitor the bridge's vibration response. Sensors S1 to S5 are evenly distributed along the longitudinal direction of the bridge to capture the main vibration modes of the bridge; while sensors S6 to S8 are arranged in the transverse direction of the bridge to capture possible torsional modes.

[0084] The sampling frequency was set to 100Hz, and vibration data was continuously collected for 300 seconds. A 24-bit A / D converter was used to ensure data accuracy. To minimize the impact of environmental noise, data collection was conducted at night when traffic was lighter.

[0085] In power spectrum estimation, the Hanning window function was selected, and the FFT length was set to 1024 points. The data was divided into multiple 50% overlapping segments, each with a length of 1024 points, and then the average value was taken to improve the stability of power spectrum estimation.

[0086] In power spectrum estimation, the Hanning window function was selected, and the FFT length was set to 1024 points. The data was divided into multiple 50% overlapping segments, each with a length of 1024 points, and then the average was taken to improve the stability of the power spectrum estimation. For interpolated power spectrum estimation, a minimum analysis frequency f was set. min =0.1Hz, maximum analysis frequency f max =50Hz, overlap coefficient ξ=0.67, minimum number of segments K min =6. Based on these parameters, the minimum frequency resolution R is calculated.min = 0.05 Hz.

[0087] In the multi-scale spatial algorithm, three different scale Gaussian smoothing kernels (standard deviations of 0.5, 1.0 and 2.0) are used to smooth the spectral data, and then the extreme points are detected at each scale. Only the extreme points detected at least at two scales are considered as valid peak points.

[0088] Figure 3 The spectral curve obtained by interpolating the power spectrum estimate and the peak points identified by the multi-scale spatial algorithm are shown. It can be clearly seen from the figure that this method can effectively identify the significant peaks in the spectrum, which correspond to the inherent frequencies of the structure.

[0089] Table 1 lists the identification results of the first two modes of the structure, including the comparison of the identification results of the present method and the theoretical calculation values.

[0090] Table 1 Identification results of the first two modes of the structure

[0091]

[0092] Figure 4 The identification results of the first mode shape of the structure are shown compared with the theoretical values. It can be seen from the figure that the mode shape identified by the present method is highly consistent with the theoretical values, verifying the effectiveness and accuracy of the method.

[0093] By monitoring the bridge in different health states (including normal state and four different damage states), the present method can effectively identify the changes in the state of the structure. The natural frequency in the damage state is usually lower than that in the normal state, and the mode shape also changes accordingly, especially the mode shape near the damage location changes more obviously.

[0094] In order to facilitate the comparison and analysis of data from different sensors, the collected vibration data can be normalized. A simple and effective method is to subtract the mean value of each sensor's data and then divide by its standard deviation:

[0095]

[0096] where x(t) is the original vibration data, μ x is the mean value of the data, σ x is the standard deviation of the data, and x norm (t) is the normalized data.

[0097] This normalization can reduce the amplitude difference between different sensors, making the subsequent spectral analysis more accurate.

[0098] After the peak points are detected by the multi-scale spatial algorithm, some noise peaks may still be included. To further improve the accuracy of identification, the following strategies can be used to screen out the true inherent frequencies of the structure:

[0099] 1. Modal confidence criterion: For each peak frequency, calculate its modal confidence index, which is based on the proportion of singular values near the peak. Specifically, the modal confidence MC can be represented as:

[0100]

[0101] where s1(f) is the first singular value, s i (f) is the other singular value, and n is the total number of singular values. The closer the MC value is to 1, the more likely it is that the frequency point is a true modal frequency. Generally, a threshold (such as MC>0.8) can be set to screen out the true modal frequencies.

[0102] 2. Modal consistency check: For modal parameters obtained under different data segments or different test conditions, calculate their consistency index. For example, for modal frequencies, the coefficient of variation (standard deviation divided by mean) can be calculated; for modal shapes, the Modal Assurance Criterion (MAC) value can be calculated. Only those modes that show high consistency under different conditions are considered as the true modes of the structure.

[0103] 3. Physical constraint condition: Use the basic principles of structural dynamics to set physical constraint conditions to exclude peaks that do not meet physical laws. For example, for simply supported structures, the inherent frequencies should satisfy certain proportional relationships; the modal shapes should have specific node distribution characteristics.

[0104] By combining the above strategies, the true inherent frequencies of the structure can be effectively screened out, improving the accuracy and reliability of modal parameter identification.

[0105] Different modal parameters have different sensitivities to structural state changes. Generally, low-order modal frequencies are more sensitive to changes in overall structural stiffness, while high-order modal frequencies and local modal frequencies are more sensitive to local damage. Modal shape changes are usually more indicative of damage location information than frequency changes.

[0106] Therefore, in structural health monitoring, appropriate monitoring indicators can be selected according to specific needs. For example, for monitoring of overall structural performance, focus on changes in low-order modal frequencies; for detection of local damage, high-order modal frequencies and modal shape changes should be combined for analysis.

[0107] The evaluation of the health status of a structure based on modal parameters usually includes the following steps:

[0108] 1. Establish baseline modal parameters: In the normal state of the structure, use the method of the invention to identify the modal parameters of the structure as the baseline for subsequent evaluation.

[0109] 2. Regular monitoring: Repeat the modal parameter identification at predetermined time intervals (such as daily, weekly or monthly) and compare with the baseline parameters.

[0110] 3. Deviation analysis: Calculate the deviation between the monitoring parameters and the baseline parameters. For modal frequencies, the relative frequency change can be calculated:

[0111]

[0112] where f r is the rth order modal frequency currently monitored, f r,0 is the corresponding baseline frequency. For modal shapes, the Modal Assurance Criterion (MAC) value can be calculated:

[0113]

[0114] where φ r is the rth order modal shape currently monitored, φ r,0 is the corresponding baseline shape. The closer the MAC value is to 1, the more similar the two shapes are; if the MAC value is significantly less than 1, it indicates that the structure may have changed.

[0115] 4. Health assessment: Based on the results of the deviation analysis, evaluate the health status of the structure. Generally, a warning threshold can be set, such as a relative frequency change of more than 3% or a MAC value of less than 0.95, which triggers further inspection or maintenance decisions.

[0116] In practical applications, environmental factors (such as temperature, humidity) should also be considered to affect the modal parameters, and necessary corrections and compensations should be made.

[0117] Theoretical models are usually based on the finite element method (FEM) and calculate the modal parameters of the structure according to its geometric characteristics, material properties and boundary conditions. However, due to simplifying assumptions, parameter uncertainties and other factors, the predicted results of the theoretical model may differ from the actual situation.

[0118] By comparing the modal parameters identified by the method of the invention with the theoretical calculation results, the accuracy of the theoretical model can be evaluated and possible model defects can be found. Specifically, the following indicators can be calculated:

[0119] 1. Frequency error:

[0120]

[0121] where f FEMis the frequency calculated by the theoretical model, f exp is the frequency identified by the method of the present application.

[0122] 2. Mode shape correlation (MAC value):

[0123]

[0124] where φ FEM is the mode shape calculated by the theoretical model, φ exp is the mode shape identified by the method of the present application.

[0125] Based on the comparison results, the theoretical model can be optimized through model updating techniques to more accurately reflect the actual characteristics of the structure. Model updating usually involves adjusting model parameters (such as material elastic modulus, mass density, boundary conditions, etc.) to make the theoretical predictions more consistent with the measured results.

[0126] A commonly used model updating method is the sensitivity method, which basically involves establishing a relationship between the objective function (such as the weighted sum of frequency errors and MAC values) and the model parameters, and then solving the optimal parameter values through optimization algorithms (such as least squares method, genetic algorithm, etc.).

[0127] In this way, the method of the present application not only accurately identifies the modal parameters of the structure, but also provides reliable measured basis for the optimization and improvement of the theoretical model, further improving the accuracy of structural analysis and design.

[0128] In large and complex structures, there may be multiple modes with similar frequencies, which may appear as overlapping peaks in the frequency spectrum, posing challenges to modal parameter identification.

[0129] To address this issue, the enhanced frequency domain decomposition method (EFDD) can be used. The EFDD method can more accurately distinguish between dense modes by analyzing the frequency correlation of the singular value decomposition results. Specifically, for each peak frequency point, the effective frequency range of the singular vector is determined (i.e., the frequency range where the MAC value of the singular vector and the singular vector of the peak frequency point is greater than a predetermined threshold), and then the singular value curve in this range is converted back to the time domain, obtaining the impulse response function of a single degree of freedom system. By analyzing this function, the frequency and damping ratio of the dense modes can be more accurately identified.

[0130] In actual engineering environments, vibration signals are often disturbed by various noises, including instrument noise, environmental noise, and external excitation. To reduce the impact of noise on modal parameter identification, the following strategies can be adopted:

[0131] 1. Data preprocessing: Preprocess the original vibration data, such as detrending, filtering, and outlier detection, to remove obvious noise and interference.

[0132] 2. Advanced spectrum estimation methods: In addition to the interpolated power spectrum estimation, other high-resolution spectrum estimation methods can be considered, such as adaptive polynomial power spectrum estimation, maximum entropy spectrum estimation, etc. These methods have better performance in low signal-to-noise ratio conditions.

[0133] 3. Robust peak detection algorithms: Based on the multi-scale space algorithm, robust statistical methods such as M-estimation or LTS estimation are introduced to reduce the influence of outliers on peak detection.

[0134] 4. Multiple measurements and statistical analysis: Perform multiple independent measurements, then perform statistical analysis on the identification results, such as calculating the mean, variance and confidence interval, etc. to improve the reliability of identification.

[0135] The actual structure may have various nonlinear effects, such as material nonlinearity, geometric nonlinearity and contact nonlinearity, etc. These effects will cause the modal parameters to change with the vibration amplitude, bringing challenges to traditional linear modal analysis.

[0136] For nonlinear effects, the following methods can be used:

[0137] 1. Piecewise linear analysis: Divide the vibration data into several segments according to the amplitude, identify the modal parameters respectively, and then analyze the variation law of the modal parameters with the amplitude.

[0138] 2. High-order spectrum analysis: In addition to the traditional self-power spectrum and cross-power spectrum, high-order spectrum (such as bispectrum and trispectrum) can be calculated, which can capture the nonlinear characteristics of the signal.

[0139] 3. Nonlinear modal theory: Introduce nonlinear modal theory, such as normal mode, nonlinear normal mode, etc., to establish a more realistic structure dynamics model.

[0140] Through these extensions and improvements, the method of the present invention can adapt to more extensive engineering practical needs, providing a powerful tool for modal parameter identification of large and complex structures.

[0141] The structure health monitoring system based on the method of the present invention generally includes the following components:

[0142] 1. Sensor network: including acceleration sensors, displacement sensors, strain sensors, etc. for collecting the vibration response of the structure. The sensors should be arranged at key positions of the structure to capture the main vibration modes.

[0143] 2. Data acquisition system: responsible for converting sensor signals into digital form and performing preliminary processing such as filtering, sampling and formatting, etc. The acquisition system should have sufficient precision, sampling rate and channel number to meet the monitoring requirements.

[0144] 3. Data Transmission Network: Transmits the collected data to the central processing unit. Depending on the actual requirements, a wired network (such as Ethernet) or a wireless network (such as Wi-Fi, ZigBee, or LoRa) can be chosen.

[0145] 4. Central Processing Unit: Runs the modal parameter automatic identification algorithm of the invention to analyze the dynamic characteristics of the structure. Depending on the monitoring scale and complexity, an industrial computer, a server, or a cloud computing platform can be chosen.

[0146] 5. Storage System: Used to save monitoring data, identification results, and historical records, supporting long-term trend analysis and comparison.

[0147] 6. User Interface: Provides data visualization, result query, and alarm management functions, making it easy for users to understand the structure's state and make decisions.

[0148] In an actual monitoring system, the data flow usually includes the following steps:

[0149] 1. Data Collection: Collects vibration data of the structure according to the predetermined sampling plan (such as once every hour, 300 seconds each time).

[0150] 2. Data Preprocessing: Performs preprocessing on the original data, such as detrending, filtering, and anomaly detection, to improve data quality.

[0151] 3. Modal Parameter Identification: Automatically identifies the modal parameters of the structure using the method of the invention, including modal frequency, mode shape, and damping ratio.

[0152] 4. Health Assessment: Compares the identified modal parameters with the baseline parameters or threshold values to assess the health status of the structure.

[0153] 5. Data Storage: Saves the original data, processing results, and assessment conclusions to the database for subsequent analysis and query.

[0154] 6. Result Presentation: Presents the monitoring results and assessment conclusions in the form of charts, reports, or alarms through the user interface.

[0155] Based on the modal parameters identified by the method of the invention, support can be provided for structure management and maintenance decisions, including:

[0156] 1. State Assessment: Based on the changes in modal parameters, assess the overall state and local damage of the structure.

[0157] 2. Early Warning Mechanism: Set the early warning threshold for the change in modal parameters, and automatically trigger an alarm or notify relevant personnel when the threshold is exceeded.

[0158] 3. Maintenance Planning: Based on the results of state assessment, develop targeted inspection and maintenance plans to optimize resource allocation.

[0159] 4. Life prediction: By combining modal parameter variation trends and structural aging models, predict the remaining service life of the structure to assist long-term planning decisions.

[0160] 5. Effect verification: By comparing modal parameters before and after maintenance, verify the maintenance effect to ensure that the structure performance is effectively restored.

[0161] In practical applications, the system design and processing flow should be flexibly adjusted according to the specific structure type, monitoring purpose and resource conditions to maximize the monitoring benefit and decision value.

[0162] For high-rise buildings or large-span buildings, the method can accurately identify their low-frequency vibration modes, providing a basis for seismic performance evaluation and wind-induced vibration control of buildings. For example, in the monitoring of a 30-story high-rise building, the method successfully identified the first five modes of the building, including two bending modes, two torsional modes and one longitudinal mode. These modal information helps to evaluate the dynamic performance of the building, verify the design assumptions, and guide the implementation of vibration reduction measures.

[0163] In particular, the method performs well in processing building environmental vibration responses, and can extract the natural frequency and mode shape of the building from low-amplitude background vibrations without additional excitation equipment, greatly reducing the complexity and cost of monitoring.

[0164] For various types of bridge structures, including beam bridges, arch bridges, suspension bridges and cable-stayed bridges, the method shows good adaptability and accuracy. Taking a cable-stayed bridge with a span of 820 meters as an example, the method successfully identified more than 20 vibration modes of the bridge under vehicle load, including vertical bending modes, lateral bending modes, torsional modes and local vibration modes.

[0165] It is particularly worth mentioning that the method can effectively distinguish modes with similar frequencies, such as two nearly identical modes (one vertical bending mode and one lateral bending mode) near 0.5Hz. Through precise peak detection of the multi-scale space algorithm and modal separation of the enhanced frequency domain decomposition method, the method successfully identifies the two modes accurately.

[0166] Wind turbine generators are typical rotating machinery, and their vibration characteristics are significantly affected by rotational frequency and operating conditions. By analyzing the vibration response of the tower and nacelle of the wind turbine, the method can identify the bending modes of the tower, the translational modes of the nacelle, and the flap and edgewise modes of the blades.

[0167] In a study involving a 5MW wind turbine, this method identified the modal parameters of the turbine under different wind speeds and operating conditions, and analyzed the variation of these parameters with operating conditions. The results show that the increase in wind speed will lead to the decrease of some modal frequencies, which is mainly due to the influence of aerodynamic damping. These findings provide important reference for the optimization design and fault diagnosis of wind turbines.

[0168] Aerospace structures usually have complex geometry, lightweight and high-strength material properties, and strict performance requirements, which pose higher challenges to the accuracy of modal parameter identification.

[0169] In a ground test of a satellite antenna, this method successfully identified multiple vibration modes of the antenna, including out-of-plane bending modes, in-plane stretching modes, and local chatter modes, by analyzing the response data of the knock test. These modal information is of great value for evaluating the dynamic performance of the antenna, predicting the on-orbit working state and optimizing the control strategy.

[0170] In addition, this method has also achieved good results in the modal parameter identification of aerospace structures such as aircraft wings, rocket shells and space station modules, proving its reliability and applicability in high-precision and large-dynamic-range applications.

[0171] Overall, the method of the present invention has excellent performance in the modal parameter identification of various engineering structures, and can adapt to different structural characteristics, operating conditions and monitoring requirements, providing strong technical support for the design, evaluation, maintenance and management of structures.

[0172] In order to further improve the accuracy and robustness of modal parameter identification, the core algorithm of the present invention can be optimized:

[0173] 1. Adaptive window function selection: According to the characteristics of the signal (such as length, bandwidth and signal-to-noise ratio), the most suitable window function is automatically selected, such as rectangular window, Hanning window, Hamming window, Blackman window or Kaiser window, etc. The optimization selection of window function can be carried out by information entropy criterion or minimum variance criterion, etc.

[0174] 2. Intelligent frequency resolution adjustment: In the interpolation power spectrum estimation, an adaptive algorithm is used to dynamically adjust the frequency resolution, increase the resolution in the key frequency range (such as near the expected modal frequency), and appropriately reduce the resolution in other ranges, so as to improve the accuracy of key information while maintaining the calculation efficiency.

[0175] 3. Deep learning enhanced peak detection: Combined with deep learning techniques such as convolutional neural network (CNN) or recurrent neural network (RNN), a peak detection model is constructed to learn the features of real modal peaks in the spectrum, improve the accuracy of peak detection, especially in low signal-to-noise ratio or dense modal conditions.

[0176] In large-scale monitoring systems or real-time analysis scenarios, computational efficiency is a key consideration.

[0177] The following techniques can be used to improve the computational efficiency of the proposed method:

[0178] 1. Parallel computing framework: Utilize multi-core CPUs, GPUs, or distributed computing resources to perform parallel processing on computationally intensive steps such as power spectrum estimation, multi-scale spatial analysis, and frequency domain decomposition. For example, different frequency band power spectrum calculations can be assigned to different processing units, or data from multiple measurement points can be processed simultaneously.

[0179] 2. Incremental computation strategy: For continuous monitoring data, use an incremental computation strategy that only processes new data, reusing previous computation results to avoid repeated calculations. This method is particularly suitable for sliding time window analysis and can significantly reduce computational load.

[0180] 3. Approximation algorithms: Introduce approximation algorithms in certain computational bottleneck steps to trade off time for precision. For example, use random projection or sub-gigantization techniques in singular value decomposition to reduce computational complexity while preserving main features.

[0181] 4. Hardware acceleration: Optimize algorithm implementation for specific hardware platforms (such as FPGA or ASIC) to fully utilize hardware acceleration features such as vector operation units, hardware FFT modules, etc., to improve computational efficiency.

[0182] Applying the proposed method to real-time structural health monitoring requires addressing data stream processing, real-time analysis, and timely response. The following are some key technologies for real-time monitoring:

[0183] 1. Streaming data processing: Use a sliding time window method to process continuous input vibration data, processing a certain length of data segment each time and updating the results when new data arrives. The window length and overlap degree should be optimized according to the structure characteristics and monitoring requirements.

[0184] 2. Incremental modal parameter update: Incrementally update modal parameters when new data arrives instead of computing from scratch. For example, use online singular value decomposition algorithms or recursive least squares methods to quickly update power spectrum matrices and modal parameters.

[0185] 3. Multi-level warning mechanism: Establish a multi-level warning mechanism based on modal parameter changes, such as attention, warning, and emergency levels corresponding to different degrees of modal parameter deviation. The system can automatically adjust the monitoring frequency and response strategy according to the warning level.

[0186] 4. Abnormality detection algorithm: Develop an abnormality detection algorithm combining statistical pattern recognition and machine learning techniques to automatically identify abnormal changes in modal parameters and analyze possible causes and impacts.

[0187] Through these extensions and improvements, the method of the present application can better adapt to various complex engineering practical needs, providing more powerful and flexible technical support for structural health monitoring and safety management.

[0188] The embodiments described herein are only a part of the embodiments of the present application, rather than all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative labor shall belong to the protection scope of the present application.

Claims

1. An automatic modal parameter identification method based on multi-scale space, characterized in that, include: Vibration data samples are collected from the target structure, including the structure's acceleration signals; Select the power spectrum calculation parameters, including the window function and the Fast Fourier Transform (FFT) length; The acceleration signal is subjected to spectrum estimation using interpolated power spectrum estimation to obtain spectrum data; The spectrum data is analyzed using a multi-scale spatial algorithm to detect peak values ​​and obtain peak frequencies. The modal parameters of the structure are calculated based on the peak frequency using the frequency domain decomposition method. The modal parameters include the modal frequency and the damping ratio.

2. The method according to claim 1, characterized in that, The vibration data samples are sampled using a uniform sampling frequency.

3. The method according to claim 1, characterized in that, The window function is the Hanning window function, and the FFT length is set to 1024 sample points.

4. The method according to claim 1, characterized in that, The step of using interpolated power spectrum estimation to perform spectrum estimation on the acceleration signal specifically includes: Determine the minimum analysis frequency and the maximum analysis frequency, wherein the minimum analysis frequency... The maximum analysis frequency Where f s f is the sampling frequency. min and f max The minimum and maximum analysis frequencies in the acceleration signal are respectively defined, where N is the number of sample points; Determine the minimum frequency resolution, wherein the minimum frequency resolution is: Where ξ is the overlap coefficient, K min Minimum number of segments; Divide the frequency band into K segments, where K is greater than 1, and consider the overlap between the segments; When the frequency resolution is less than the minimum frequency resolution, the frequency resolution is set to the minimum frequency resolution.

5. The method according to claim 1, characterized in that, The application of a multi-scale spatial algorithm to analyze the spectral data specifically includes: The set of extreme points Q of the power spectrum is determined by calculating local maxima, where Q = localmax(x), and x is the spectrum data; Define the peak point to satisfy the following conditions: Where n is the index of the data point.

6. The method according to claim 1, characterized in that, The frequency domain decomposition method is the frequency domain decomposition method (FDD), and the modal parameters of the structure calculated by the frequency domain decomposition method are only modally analyzed at the peak frequency.

7. The method according to any one of claims 1 to 6, characterized in that, The method further includes: The modal parameters are normalized, and mode shape normalization is performed with the mode shape extreme points as reference points.

8. The method according to claim 7, characterized in that, The method further includes: The peak frequencies are filtered to remove noise peaks and retain the true inherent frequencies of the structure.

9. The method according to claim 8, characterized in that, The method further includes: The health status of the structure is evaluated based on the modal parameters, wherein the evaluation includes comparing the changes in modal parameters at different time points.

10. The method according to claim 9, characterized in that, The method further includes: The modal parameters are compared with the parameters calculated by the theoretical model to verify the accuracy of the modal parameters.

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