Bridge multi-modal frequency identification method and system based on PPP-RTK

Abstract

The application discloses a bridge multi-mode frequency identification method and system based on PPP-RTK, which comprises the following steps: obtaining a file containing fast satellite orbit, clock and observation station product; sequentially performing non-difference and non-combination PPP-AR model processing on local reference station network data, and obtaining fixed tilt ionospheric delay and fixed tropospheric delay through ambiguity resolution; calculating single-difference ionospheric and tropospheric products based on ionospheric and tropospheric interpolation, and realizing ambiguity resolution by using a PPP-RTK model to obtain an instantaneous centimeter-level high-precision positioning result; decomposing a PPP-RTK monitoring displacement time sequence into a series of frequency band signals corresponding to different modes; processing the frequency band signals of different modes into stationary intrinsic mode functions through empirical mode decomposition; extracting free attenuation signals from selected intrinsic mode functions by using a random decrement technique; and constructing a Hilbert analytic function based on the free attenuation signals to determine multi-mode frequencies.

Description

Technical Field

[0001] This invention relates to a method and system for bridge multimodal frequency identification based on PPP-RTK. Background Technology

[0002] As a crucial component of urban transportation networks, the safety and stability of long-span bridges require paramount attention throughout their operational lifespan. Therefore, real-time and effective monitoring of bridge displacement and multimodal frequencies is essential, as this data forms the core foundation for structural damage detection, condition assessment, and safety management. Traditional structural health monitoring sensors primarily include accelerometers, strain gauges, and displacement gauges; however, the application of these technologies still has some limitations that require further resolution.

[0003] Global Navigation Satellite Systems (GNSS), due to their automation, high reliability, continuity, and multifunctionality, combined with high-precision positioning capabilities, have been widely used for structural health monitoring of long-span bridges. Compared with traditional sensors, GNSS has significant advantages in acquiring continuous long-term displacement time series. This data can be processed by specific algorithms to extract multimodal frequencies, thereby enabling real-time monitoring of the bridge's operational status and ensuring its safety and stability during operation. Currently, Real-Time Kinematics (RTK) is a widely used GNSS positioning technology that can acquire high-precision relative displacement time series through a double-difference model between short-range base stations, operating in real-time. This model can resolve fixed-integer ambiguity issues, thus achieving centimeter-level high-precision positioning. However, the effectiveness of RTK depends on deploying a reference station in an open environment near the rover, which requires a stable geographical environment and good communication conditions. In complex urban environments, these conditions are often difficult to meet. Furthermore, the displacement of the reference station (including thermal expansion and environmental loads) can contaminate the rover's positioning results, reducing its reliability. Precise Point Positioning (PPP), as an independent GNSS positioning technology, can achieve high-precision positioning without a reference station. By utilizing products such as precise satellite orbits, precise satellite clock biases, satellite phase and pseudorange observation-specific signal biases (OSBs), and satellite attitude generated by the International GNSS Service (IGS) Analysis Centre, PPP can achieve integer ambiguity resolution (PPP-AR) without the need for differential processing at nearby reference stations, thus providing dynamic centimeter-level positioning capabilities for a single GNSS receiver. However, the long convergence time required for accurate floating-point ambiguity resolution significantly limits the practical application of this technology.

[0004] Precise Point Positioning Real-Time Dynamic (PPP-RTK) combines the features of traditional RTK and PPP, enabling instantaneous centimeter-level positioning without the need for nearby reference stations. It has become a key research focus in high-precision GNSS positioning algorithms and applications. This model not only eliminates the need for nearby reference stations but also overcomes the drawback of long convergence times. PPP-RTK mainly consists of two parts: the network end and the user end. The network end includes multiple sparsely distributed GNSS reference stations with known coordinates, with a maximum distance between stations exceeding 100 kilometers. The network end calculates accurate local ionospheric and tropospheric delay corrections, precise satellite orbits and clock errors, as well as satellite phase and pseudorange (OSB), and transmits this information to the user in real time. By integrating this correction information, the user end using the PPP model can achieve positioning performance comparable to RTK. To date, the PPP-RTK method has been discussed in numerous studies. Teunissen et al. proposed the principle of PPP-RTK and further compared the estimable parameters of different methods. Odijk et al. introduced S-system theory, enabling PPP-RTK to operate on multiple signal frequencies. Geng et al. found that full-frequency combined PPP-RTK exhibits better robustness than traditional PPP-RTK in complex urban environments. Gao et al. attempted to use PPP-RTK technology to monitor the displacement of the Hong Kong-Zhuhai-Macau Bridge, but their research focused on multipath error suppression methods. Currently, numerous ionospheric and tropospheric modeling methods exist, such as inverse distance weighted (IDW), second-order linear fitting (SLF), Kriging, radial basis function (RBF), and least squares configuration (LSC). Each atmospheric interpolation model has its advantages, but their actual performance still requires further investigation. The performance verification of PPP-RTK positioning technology for monitoring the structural health of long-span bridges in complex urban environments is incomplete, and research on extracting structural health monitoring information from PPP-RTK monitoring time series is lacking. In conclusion, PPP-RTK positioning technology shows potential in the structural health monitoring of long-span bridges.

[0005] GNSS monitoring data contains bridge displacement and its multimodal frequency information, which can be used for structural health monitoring of long-span bridges. However, GNSS-monitored displacement time series are usually non-stationary and contain significant noise, mainly from environmental loads such as wind and temperature, low-frequency displacements caused by pedestrian and vehicle loads, and multipath errors caused by various refracted signals. This makes many multimodal frequency identification methods inaccurate and unsuitable. Empirical Mode Decomposition (EMD) and its enhanced versions, such as Ensemble Empirical Mode Decomposition (EEMD), Complete Ensemble Empirical Mode Decomposition (CEEMD), and CEEMD with Adaptive Noise (CEEMDAN), are currently effective methods for analyzing the time and frequency characteristics of signals in non-stationary systems. In addition, peak picking (PP), empirical wavelet transform (EWT), convolutional neural networks (CNN), random subspace identification (SSI), and natural excitation techniques (NET) are also widely used for modal frequency identification. However, these methods are generally applicable to low-order modes and may not be effective in identifying obscured high-order modal frequencies affected by noise. Unfortunately, noise in GNSS monitoring data often masks these high-order modal frequencies. He et al. proposed using the autoregressive power spectrum method to identify multimode frequencies from GNSS monitoring data, but this method is cumbersome and prone to subjective errors. Therefore, there is an urgent need to design a method that can accurately identify multimode frequencies from PPP-RTK monitoring data with non-stationary characteristics and noise pollution. Summary of the Invention

[0006] To overcome the shortcomings of the prior art, this invention provides a method and system for identifying bridge multimodal frequencies based on PPP-RTK. By combining Empirical Mode Decomposition (EMD), Random Attenuation Technique (RDT), and Empirical Band Decomposition Method of Hilbert Transform (EERH), it can effectively identify multimodal frequencies, especially higher-order modes, in PPP-RTK monitoring data with non-stationary characteristics and noise pollution.

[0007] According to one aspect of the present invention, a bridge multimodal frequency identification method based on PPP-RTK is provided, comprising:

[0008] Obtain files containing fast satellite orbit, clock, and observatory products;

[0009] Based on the acquired files, the local reference station network data were sequentially processed using undifferentiated and uncombined PPP-AR models, and the fixed oblique ionospheric delay and fixed tropospheric delay were obtained through ambiguity resolution.

[0010] Based on the interpolation of the ionosphere and troposphere, single-difference ionospheric and tropospheric products are calculated, and based on the calculated single-difference ionospheric and tropospheric products, ambiguity resolution is achieved using the PPP-RTK model to obtain instantaneous centimeter-level high-precision positioning results;

[0011] The PPP-RTK monitoring displacement time series, formed by instantaneous centimeter-level high-precision positioning results, is decomposed into a series of frequency band signals corresponding to different modes;

[0012] The frequency band signals of the different modes are processed into stationary intrinsic mode functions through empirical mode decomposition;

[0013] The free decay signal is extracted from the selected intrinsic mode function using a random decrease technique.

[0014] Based on the free decay signal, a Hilbert analytical function is constructed to determine the multimodal frequency.

[0015] As a further technical solution, the PPP-RTK monitoring displacement time series formed by instantaneous centimeter-level high-precision positioning results is decomposed into a series of frequency band signals corresponding to different modes, including:

[0016] Based on the theoretical modal frequencies or other prior values ​​obtained through the finite element method, the frequency bands of different modes are divided.

[0017] A bandpass filter is used to decompose the PPP-RTK monitored displacement time series into signals corresponding to different modes within a specified frequency band.

[0018] As a further technical solution, the frequency band signals of the different modes are processed into stationary intrinsic mode functions through empirical mode decomposition, including:

[0019] Identify local peaks and valleys in the input signal;

[0020] The upper and lower envelopes are obtained using cubic spline interpolation.

[0021] When the difference between the number of extreme points and zero-crossing points is no greater than one, and the average value of the envelope formed by the local maximum and minimum points is always zero, a stationary intrinsic mode function is obtained.

[0022] As a further technical solution, the method also includes:

[0023] Select an effective intrinsic mode function based on the threshold of the correlation coefficient of the intrinsic mode function.

[0024] As a further technical solution, the method also includes:

[0025] A partial fuzziness resolution strategy is adopted for fuzziness resolution.

[0026] According to one aspect of the present invention, a bridge multimodal frequency identification system based on PPP-RTK is provided, comprising:

[0027] The first main module is used to acquire files containing fast satellite orbits, clocks, and observatory products;

[0028] The second main module is used to process the local reference station network data in a PPP-AR model without differentiation and without combination based on the acquired files, and obtain the fixed oblique ionospheric delay and fixed tropospheric delay through ambiguity resolution.

[0029] The third main module is used to calculate single-difference ionospheric and tropospheric products based on ionospheric and tropospheric interpolation, and to perform ambiguity resolution based on the calculated single-difference ionospheric and tropospheric products using the PPP-RTK model to obtain instantaneous centimeter-level high-precision positioning results.

[0030] The fourth main module is used to decompose the PPP-RTK monitoring displacement time series formed by instantaneous centimeter-level high-precision positioning results into a series of frequency band signals corresponding to different modes;

[0031] The fifth main module is used to process the frequency band signals of the different modes into stable intrinsic mode functions through empirical mode decomposition;

[0032] The sixth main module is used to extract the free decay signal from the selected intrinsic mode function using a random decrease technique;

[0033] The seventh main module is used to construct a Hilbert analytical function based on the free decay signal to determine the multimodal frequency.

[0034] According to one aspect of the present invention, an execution device is provided, including a memory and a processor, the memory storing program instructions to be executed by the processor, the processor invoking the program instructions to perform the steps of the PPP-RTK-based bridge multimodal frequency identification method.

[0035] According to one aspect of the present invention, a non-transitory computer-readable storage medium is provided, the non-transitory computer-readable storage medium storing computer instructions that cause the computer to perform the steps of the bridge multimodal frequency identification method based on PPP-RTK.

[0036] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0037] 1. This invention designs a new method—Empirical Frequency Band Decomposition (EERH) combining EMD, RDT, and Hilbert transform—to effectively identify multimodal frequencies, especially higher-order modes, in PPP-RTK monitoring data with non-stationary characteristics and noise pollution, thereby evaluating the performance of PPP-RTK in monitoring the structural health of long-span bridges in urban environments.

[0038] 2. This invention successfully verified the effectiveness of the proposed multimodal frequency identification method using multiple sets of PPP-RTK monitoring data from the Wuhan Yingwuzhou Yangtze River Bridge. The power spectral density (PSD) analysis results of PPP-AR, RTK, and PPP-RTK clearly showed the first-order modal frequency of 0.103 Hz and the third-order modal frequency of 0.164 Hz, respectively. The EERH method of this invention can effectively identify the first six modes of the Wuhan Yingwuzhou Yangtze River Bridge in the PPP-RTK monitoring data. Only the error of the fourth-order modal frequency was 12.96%, and the remaining results were consistent with the theoretical values. Attached Figure Description

[0039] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the accompanying drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the accompanying drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0040] Figure 1 This is a flowchart illustrating a bridge multimodal frequency identification method based on PPP-RTK provided in an embodiment of the present invention.

[0041] Figure 2 This is a schematic diagram of the distribution of monitoring stations provided in an embodiment of the present invention.

[0042] Figure 3 This is a schematic diagram illustrating the errors of three tilted ionospheric delay interpolation models provided in embodiments of the present invention.

[0043] Figure 4 This is a schematic diagram of the multipath parameters for all reference stations provided in the embodiments of the present invention.

[0044] Figure 5 This is a schematic diagram of three types of tropospheric delay interpolation errors provided in the embodiments of the present invention.

[0045] Figure 6 This is a time series diagram illustrating the use of three products in three directions of the ENU for three networks provided in an embodiment of the present invention.

[0046] Figure 7 This is a schematic diagram of the first convergence epoch of the three networks provided in an embodiment of the present invention.

[0047] Figure 8 This is a schematic diagram of the ambiguity fixation rate of the three networks and three models provided in the embodiments of the present invention.

[0048] Figure 9 This is a schematic diagram of the normal distribution fitting of the three networks provided in an embodiment of the present invention.

[0049] Figure 10 (a)-(b) are actual on-site measurement diagrams provided in the embodiments of the present invention.

[0050] Figure 11 The distribution map of experimental stations provided for embodiments of the present invention.

[0051] Figure 12 This is a schematic diagram of the X-direction positioning results of sites L076 and L075 using RTK, PPP-AR, and PPP-RTK models during DOY 207 and 208 provided in this embodiment of the invention.

[0052] Figure 13 This is a schematic diagram of the Y-direction positioning results of stations L076 and L075 using RTK, PPP-AR, and PPP-RTK models during DOY 207 and 208 provided for embodiments of the present invention.

[0053] Figure 14 This is a schematic diagram of the Z-direction positioning results of sites L076 and L075 using RTK, PPP-AR, and PPP-RTK models during DOY 207 and 208, as provided in the embodiments of the present invention.

[0054] Figure 15 This is a schematic diagram of the power spectral density (PSD) analysis of station L075 in the vertical direction, extracted from RTK, PPP-AR, and PPP-RTK results, provided for an embodiment of the present invention.

[0055] Figure 16 A schematic diagram of the effective IMF extracted from PPP-RTK displacement monitoring data, provided for an embodiment of the present invention.

[0056] Figure 17 This is a schematic diagram of the free decay signal extracted from the effective IMF, provided for an embodiment of the present invention. Detailed Implementation

[0057] It should be noted that:

[0058] PPP-RTK, as an extension of non-differential and non-combined (UDUC) PPP, mainly consists of two parts: the network end and the user end. The network end generates accurate satellite products, including orbit, clock, OSB, local oblique ionospheric delay, and tropospheric delay. The user end receives these products and performs instantaneous integer ambiguity resolution in real-time PPP, thereby achieving instantaneous centimeter-level high-precision positioning.

[0059] At the network end, precise satellite orbit, clock, attitude, and OSB products are calculated using globally distributed IGS reference stations. In this embodiment of the invention, all products except for the local oblique ionospheric delay product and the tropospheric delay product are sourced from the Wuhan University IGS Data Center (http: / / www.igs.gnsswhu.cn / ). Therefore, the focus is on generating the local oblique ionospheric delay and tropospheric delay products. The original observation equations for GNSS pseudorange and carrier phase can be described as:

[0060]

[0061] in and These are pseudorange and carrier phase, respectively. The superscript 's' represents the satellite, and the subscripts 'r' and 'i' represent the receiver and frequency, respectively. This represents the geometric distance between the satellite and the receiver. C represents the speed of light in a vacuum, and t represents the speed of light in a vacuum. r and t s Representing the clock bias at the receiver and satellite respectively, γ i Represents the ionospheric delay factor. T represents ionospheric delay, M represents the projection function, and T represents the projection function. i Indicates tropospheric delay, d r,i and λ represents the hardware delay of the receiver and the satellite pseudorange, respectively. i Indicates wavelength. Indicates integer ambiguity, b r,i and Let represent the phase hardware delay of the receiver and the satellite, respectively. σ and ε represent the pseudorange and phase noise, respectively. Furthermore, the observation equations are affected by various systematic errors, which must be accurately modeled and subsequently eliminated to ensure precise positioning. These errors include relativistic effects, antenna phase center offsets (PCOs) and variations (PCVs), Earth rotation parameters, solid Earth tides, etc. After considering these error sources through appropriate modeling and correction strategies, the remaining parameters to be estimated can be mathematically expressed as follows:

[0062]

[0063] Parameter X can be estimated using sequential least squares estimation or Kalman filtering. It is worth noting that due to factors such as receiver hardware delay, observation noise, and multipath error, the directly estimated ambiguity parameters are real values ​​rather than correct integers, leading to inaccuracies in other calculated parameters. Therefore, calculating correct integer ambiguities and incorporating them as virtual observation equations into the normal equations can effectively improve the estimation accuracy and robustness of the parameters. Currently, by utilizing the least squares ambiguity decorrelation adjustment (LAMBDA) algorithm and performing a ratio check, the ambiguities can be effectively fixed to correct integers. After resolving the ambiguities, high-precision tropospheric wet delay and oblique ionospheric delay can be obtained. It is important to note that some receiver pseudorange and phase hardware delays are included in the estimated parameters.

[0064] After calculating the oblique ionospheric delay and tropospheric delay for multiple reference stations at the network end, interpolation algorithms such as IDW, SLF, and Kriging interpolation can be applied to derive the corresponding delay products for the user end. The calculation of the oblique ionospheric delay product and tropospheric delay product using the IDW model can be expressed as:

[0065]

[0066] In the formula This represents the tilted ionospheric delay, which includes hardware delay at the reference station receiver. The latitude of the puncture point represents the satellite and ionospheric reference altitude of the rover. This represents the latitude of the puncture point between the satellite and the ionospheric reference altitude of the i-th reference station. The longitude of the puncture point indicates the satellite and ionospheric reference altitude of the rover. B represents the longitude of the puncture point between the satellite and the ionospheric reference altitude of the i-th reference station. r B represents the geographical latitude of the rover station. i L represents the geographical latitude of the i-th reference station. r L represents the geographical longitude of the rover station. i H represents the geographical longitude of the i-th reference station. r H represents the geodetic elevation of the rover station. i Let represent the geodetic elevation of the i-th reference station.

[0067] The formulas for calculating tropospheric delay and ionospheric delay using SLF are as follows:

[0068]

[0069] a0, a1, a2, a3, a4, and a5 are the fitting coefficients for the tilted ionospheric delay. b0, b1, b2, b3, and b4 are the fitting coefficients for the tropospheric delay. The differences in longitude, latitude, and altitude between reference stations are dB.i ,dL i ,dH i In addition, Kriging interpolation is an alternative method, which will not be discussed in detail here.

[0070] At the user end, real-time data stream products are received, including satellite orbits, satellite clocks, OSBs, etc., published by the IGS data center, as well as ionospheric and tropospheric delay products generated by local sparse reference stations. It is worth noting that because the generated ionospheric products contain receiver hardware delays from different reference stations, inter-satellite single-differential (SD) analysis is required to eliminate these delays. This can be represented as:

[0071]

[0072] In the formula, k represents the k-th satellite and s represents the reference satellite.

[0073] The user-side model can then be expressed as follows:

[0074]

[0075] In the formula and These represent the pseudorange observation value and the phase observation value minus the calculated value, respectively. Denotes the linearization coefficient, x r Represents the coordinates of the rover station, δt r This indicates the combined receiver clock bias. Indicates the ionospheric delay after combination. This indicates the phase ambiguity after combination. Indicates a tropospheric delayed product, T r,0 This represents the initial value of the tropospheric delay. This indicates an ionospheric delay product; the meanings of the other parameters are the same as described above.

[0076] The prior noise for the tropospheric wet delay and tilted ionospheric delay pseudo-observation equations can be empirically set to 2 cm and 5 cm, respectively. To accelerate convergence, the user terminal needs to use partial ambiguity fixation and set a low ratio test threshold. Using the PPP-RTK model, the user terminal can quickly resolve the ambiguity problem, thereby achieving instantaneous high-precision positioning.

[0077] In PPP-RTK displacement monitoring time series of long-span bridges, the main challenge in identifying multimodal frequencies, especially higher-order modes, is the non-stationarity of the signal. Furthermore, higher-order modes are easily overwhelmed by significant noise. To address these challenges, the EERH method proposed in this invention combines empirical bandgap signal decomposition, empirical mode decomposition (EMD), random attenuation technique (RDT), and Hilbert transform. First, the frequency bands corresponding to different modes can be divided based on theoretical modal frequencies obtained through the finite element method (FE) or other prior values. Then, a bandpass filter (such as a Chebyshev bandpass filter) can be used to decompose the PPP-RTK displacement monitoring time series into signals corresponding to different modes within the specified frequency bands, as follows:

[0078]

[0079] By using empirical frequency band signal decomposition, the mode mixing problem in EMD can be effectively solved, thereby effectively avoiding the problem of identifying modes with similar frequencies and insignificant higher-order modes, and thus reducing identification errors.

[0080] By using EMD technology, any non-stationary signal will be processed into multiple stationary intrinsic mode functions (IMFs). It is important to note that this process is crucial because a stationary signal is required as input when constructing the instantaneous frequency function using the Hilbert transform. Otherwise, negative values ​​will appear in the result, losing physical meaning. However, PPP-RTK monitoring displacement time series are typically non-stationary; therefore, the method in this embodiment introduces EMD to ensure that the input signal is stationary. First, local peaks and valleys of the input signal are initially identified. Subsequently, cubic spline interpolation can be used to obtain the upper and lower envelopes. The dominant oscillation mode is represented as:

[0081] o1(t)=z i (t)-a1(t)

[0082] Then, determine if the following two characteristics are met: First, the difference between the number of extreme points and zero-crossing points is no greater than one; second, the average value of the envelope formed by the local maxima and minima is always zero. If these two conditions are not met, treat the signal as normal and repeat the above process until they are met. Finally, the signal that meets the conditions is the first IMF. Meanwhile, the residual signal is denoted as:

[0083] r1(t)=z i (t)-IMF

[0084] RDT can separate the free decay signal from the random vibration response, helping to minimize the influence of random components in the vibration and thus improving the accuracy of modal parameter identification. The displacement response is separated into several time-sampling functions. The random decay function can be expressed as:

[0085]

[0086] z i (t j ) = a0 is the triggering condition, t j It is the trigger time, τ = tt j This indicates the exceeded trigger time, N represents the number of sampling points, and the random decreasing function is a conditional expectation estimate. The trigger condition can be defined according to different scenarios, and typically fluctuates within one to two standard deviations of the input signal.

[0087] The Hilbert transform can be used to construct analytic functions for time series. Multimodal frequencies can be estimated using the least squares method. The Hilbert transform can be expressed as:

[0088]

[0089] By z i (t) is the real part input, and the signal obtained by the Hilbert transform is... As the imaginary part, an analytic function f can be constructed. i (t):

[0090]

[0091] in Represents the instantaneous amplitude function. Let represent the instantaneous phase function, and let the instantaneous frequency function be the derivative of the instantaneous phase function, as follows:

[0092]

[0093] Multimodal frequencies can be calculated by nonlinear curve fitting techniques on instantaneous frequency functions, or simply by taking the average value.

[0094] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention. In addition, the technical features of the various embodiments or individual embodiments provided by the present invention can be arbitrarily combined to form new technical solutions. Such combinations are not bound by the order of steps and / or structural composition patterns, but must be based on the ability of those skilled in the art to implement them. When the combination of technical solutions is contradictory or cannot be implemented, it should be considered that such a combination of technical solutions does not exist and is not within the scope of protection claimed by the present invention.

[0095] The main process of the bridge multimodal frequency identification method based on PPP-RTK provided by this invention is as follows: Figure 1 As shown in the figure, the yellow boxes represent data or results, the blue boxes represent the algorithm flow, and the part within the green dashed box is the modal frequency identification process. At the beginning of the process, files containing fast satellite orbits, clocks, and OSBs (Observatory Products) are retrieved from the network. Then, the local reference station network data is processed sequentially using undifferentiated and uncombined PPP-AR models. Through ambiguity resolution, fixed oblique ionospheric delays and fixed tropospheric delays are obtained. Subsequently, single-difference ionospheric and tropospheric products are calculated through ionospheric and tropospheric interpolation. Users can use these products to achieve fast or even instantaneous ambiguity resolution using the PPP-RTK model, thereby obtaining instantaneous centimeter-level high-precision positioning results. Next, the GNSS monitoring displacement time series is decomposed into a series of frequency band signals corresponding to different modes. These non-stationary signals are processed into stationary IMFs (Intrinsic Mode Functions) through EMD (Empirical Mode Decomposition), during which effective IMFs need to be selected based on their correlation coefficients.

[0096]

[0097] Existing research results indicate that the correlation coefficient ρ i This can be considered a strong correlation. Therefore, in this embodiment of the invention, the threshold is set to 0.8. Furthermore, the free decay signal can be extracted from the selected effective IMF using RDT (Random Decrease Technique). Finally, by constructing a Hilbert analytic function based on the free decay signal, the multimodal frequencies can be determined.

[0098] To evaluate the feasibility and effectiveness of PPP-RTK, raw GNSS observation files from 11 reference stations in Wuhan and surrounding cities on day 60 of 2023 were randomly selected. The distribution of these stations is as follows: Figure 2 As shown. The JFNG station in the middle is designated as a rover station. Figure 2 (Marked with red dots in the middle), the remaining stations are divided into three networks based on distance ( Figure 2(Marked with blue triangles in the middle). Network composition, maximum inter-station distance, and average inter-station altitude difference are shown in Table 1. The sampling rate for all observation files is 30 seconds. Based on the Positioning and Navigation Data Analysis Platform (PANDA), this embodiment of the invention developed undifferentiated and uncombined PPP-AR and PPP-RTK modules, and used this platform for all GNSS data processing in this embodiment. For PPP-RTK, fast and reliable ambiguity resolution is crucial. Therefore, this embodiment of the invention adopts a partial ambiguity resolution strategy. All ambiguity parameters are used as candidate parameters. A ratio test is performed using the quadratic form of the best and second-best integer ambiguity resolution residuals to determine whether the ambiguity resolution is correct. Empirically, the threshold is set to 3. If the test fails, the ambiguity parameter with the largest variance is eliminated, and the search is repeated until the test passes. The PPP-RTK data processing strategy is shown in Table 2.

[0099] Table 1. Composition of the monitoring station network

[0100] network Station Maximum distance between stations (km) Average height difference (m) 1 WUH2,H001,H002,H003 60.1 38.1 2 H002, H004, H005, H006 86.9 29.2 3 H003, H007, H008, H009 124.4 23.8

[0101] Table 2 Calculation Strategy

[0102]

[0103]

[0104] The accuracy and reliability of oblique ionospheric delay and tropospheric delay products significantly impact the effectiveness of PPP-RTK. To optimize the accuracy of these products, this embodiment of the invention compares and analyzes widely used interpolation models, including IDW, SLF, and Kriging interpolation. First, the coordinates of all stations (including the rover) are calculated using a static PPP-AR method. Then, a fixed oblique ionospheric delay and tropospheric delay are calculated using a dynamic PPP-AR model with fixed reference station coordinates. Next, the corresponding single-difference ionospheric delay and tropospheric delay products are calculated using the three interpolation models. To evaluate the performance of local oblique ionospheric delay and tropospheric delay products, this embodiment of the invention fixes the known coordinates of the rover JFNG and calculates the true values ​​of the single-difference oblique ionospheric delay and tropospheric delay. It is worth noting that PPP-AR at the network end requires a certain convergence time. This embodiment of the invention starts interpolation calculations from 3 points to obtain fixed ionospheric and tropospheric delays. It is important to emphasize that in practical applications, the network can continuously broadcast the corresponding ionospheric and tropospheric delay products, thereby eliminating the convergence time problem.

[0105] The errors of the three single-difference ionospheric delay interpolation models in the three networks are as follows: Figure 3As shown in the figure, different colors correspond to different satellite pairs, with the reference satellite identified as the one with the highest elevation angle. The figure shows that the results obtained by the three methods for the three networks are relatively similar, with small errors, most within ±5 cm. This indicates that all three models are suitable for modeling oblique ionospheric delay and can be effectively applied to PPP-RTK ionospheric products with a maximum distance of 124 km between reference stations. Furthermore, analysis of the root mean square (RMS) results shows that the Kriging interpolation method is slightly better than IDW, which in turn is better than SLF. However, it is worth noting that the Kriging interpolation method may encounter some points with errors greater than ±10 cm, while IDW does not. Therefore, IDW is more robust in all three sets of experiments.

[0106] Although the results of Networks 1 and 2 are not as ideal as those of Network 3, most errors are still within ±5cm, making them still suitable for PPP-RTK positioning. To investigate the reasons for the poor results of Networks 1 and 2 (the inter-station distances of these two networks are smaller than that of Network 3), this embodiment of the invention calculated the multipath parameters of all original observation files. MP1 and MP2 are defined as follows:

[0107]

[0108] P1 represents the pseudorange at frequency f1, L1 represents the carrier phase at frequency f1, P2 represents the pseudorange at frequency f2, and L2 represents the carrier phase at frequency f2.

[0109] The MP1 and MP2 results for all reference stations are as follows: Figure 4 As shown, the MP1 and MP2 values ​​of station H002 in Networks 1 and 2 are higher than those of other reference stations, indicating that this station is severely affected by multipath effects. Simultaneously, the multipath errors of stations in Networks 1 and 2 are significantly higher than those in Network 3. Poor data quality leads to reduced accuracy of ionospheric results, making the results of Networks 1 and 2 inferior to those of Network 3, even though the maximum inter-station distance in Network 3 is much greater than that in Networks 1 and 2. This result also indicates that even with stations exhibiting poor data quality, the generated ionospheric model can still meet accuracy requirements.

[0110] Table 3. RMS values ​​for three networks and three tropospheric delay interpolation models.

[0111] method Network 1 Network 2 Network 3 Inverse distance weighted (cm) 1.31 1.35 1.08 Second-order linear fitting (cm) 1.53 1.40 1.53 Kriging interpolation (cm) 1.47 1.46 1.19

[0112] The errors of the three tropospheric delay interpolation models are reflected in the three networks as follows: Figure 5As shown in Table 3, the tropospheric products calculated by the three methods in Networks 1 and 2 exhibit similar trends, with most errors less than 2 cm. However, in Network 3, the tropospheric products obtained using the SLF method show significant differences and larger errors compared to the other two methods. Since the observation data quality of Network 3 is slightly better than that of Networks 1 and 2, and the mean height difference between stations is relatively close, this indicates that the inter-station distance is the main reason for the poorer results. Experimental results show that the IDW and Kriging methods are more suitable for larger reference station networks than the SLF method, while in smaller networks, the results of the three methods are relatively similar. The root mean square (RMS) values ​​of the three tropospheric delay interpolation models in the three networks are shown in Table 3, where the RMS value of Network 3 is significantly better than that of Networks 1 and 2, except for the SLF method. Considering the maximum inter-station distance and the mean height difference between stations, this indicates that multipath error is the main factor affecting the accuracy of tropospheric products when using the same interpolation model. From the comparison results, the IDW method performs slightly better than the Kriging and SLF methods.

[0113] Using three single-difference oblique ionospheric delay and tropospheric delay products, the PPP-RTK positioning results for the three networks are as follows: Figure 6 As shown. The experiment started at point 3. To reduce the randomness of the experiment, the data was interrupted and reconverged every 3 hours. Furthermore, for comparison, the results of dynamic PPP-AR are represented by dark blue dots in the figure. PPP-AR also reconverged every 3 hours. To show more clearly, the time-series data using the IDW and SLF models were shifted upwards by 20cm and 10cm respectively, while the PPP-AR localization results were shifted downwards by 10cm. Observation Figure 6 It is evident that dynamic PPP-AR requires a longer convergence time, while PPP-RTK can achieve centimeter-level positioning accuracy within several epochs or even a single epoch. The displacement time-series data calculated using the IDW model product and the Kriging interpolation model product are relatively close, and slightly better than the results calculated using the SLF model product. Furthermore, the results for the three networks are roughly the same. The PPP-RTK positioning model exhibits enhanced performance, overcomes the limitations of nearby reference stations, and solves the problem of long convergence times, making it more suitable for structural health monitoring of long-span bridges in complex urban environments.

[0114] The first convergence epoch of the three networks is as follows Figure 7As shown, the time interval between epochs is 30 seconds. The first convergence epoch has many definitions; in this embodiment, the standard is a starting epoch with an error of less than 10 cm for 10 consecutive epochs. In this embodiment, the average convergence epochs of PPP-AR in the East (E), North (N), and Up (U) directions are 30.1, 21.0, and 38.8, respectively. These values ​​are significantly higher than the average convergence epochs of PPP-RTK, which are 3.7, 3.7, and 3.9 in the E, N, and U directions, respectively. Meanwhile, using the three model products, Network 1's results are slightly better than Networks 2 and 3, although Network 1's ionospheric and tropospheric products have lower accuracy. This indicates that the convergence time is mainly affected by the accuracy of the model products in the first few epochs. Despite the slightly lower accuracy of the obtained ionospheric and tropospheric product models, the PPP-RTK model still achieves fast convergence. The average convergence epochs of the three models are 3.1, 4.0, and 3.9, respectively. The IDW model is slightly better than the other two models in terms of convergence time metrics. This result demonstrates that although the Kriging interpolation method produces a lower ionospheric RMS value, the IDW method exhibits better robustness in convergence time and is more recommended. Overall, PPP-RTK performs excellently in significantly reducing convergence time, achieving rapid and even single-epoch centimeter-level localization.

[0115] The positioning feasibility of PPP-RTK is assessed by calculating the ambiguity resolution rate, which is defined as the proportion of satellites that pass the ratio test out of the total number of satellites. Figure 8 As shown, a higher resolution rate indicates more reliable results. The results show that the ambiguity resolution rates of all three models exceed 86% across the three networks. Compared to PPP-AR's 70.35%, PPP-RTK achieves a 16.1% improvement in average ambiguity fixation rate. Furthermore, the ambiguity fixation rate after convergence is approximately the same for products using each model.

[0116] To ensure that the positioning accuracy of PPP-RTK meets the requirements for structural health monitoring of long-span bridges, statistical analysis was performed on the displacement results in the N, E, and U directions, such as... Figure 9 As shown. A normal distribution fit was performed on the displacement distribution (…). Figure 9 (The red curve in the image). Statistical analysis shows that the horizontal positioning accuracy is higher, the error distribution is more concentrated, and the mean is close to 0, which is significantly better than the vertical direction. Although the vertical positioning accuracy is lower, most displacements are within ±3cm, meeting the requirements for displacement monitoring of long-span bridges. However, this increases the difficulty of modal frequency identification, requiring the use of more accurate and reliable modal frequency identification methods.

[0117] Table 4 shows the RMS values ​​of the three networks after convergence using the three products. The coordinate reference was obtained through 24-hour static PPP-AR calculation. The larger the RMS value of the single-difference oblique ionospheric delay product, the larger the RMS value of PPP-RTK positioning. The average RMS values ​​in the E, N, and U directions after convergence in multiple PPP-RTK experiments were 0.82 cm, 0.73 cm, and 1.90 cm, respectively, which are improvements of 67.5%, 57.6%, and 41.2% compared to PPP-AR. The accuracy in each direction is significantly improved, especially in the E direction. However, it should be noted that the accuracy of the oblique ionospheric delay and tropospheric delay products will affect the positioning reliability after convergence. The average RMS values ​​after convergence for the IDW, SLF, and Kriging methods were 1.15 cm, 1.15 cm, and 1.15 cm, respectively. Although the three methods are roughly the same in terms of average RMS value, considering factors such as convergence time, robustness, and computational complexity, the IDW method is more recommended for practical applications. Despite lower data quality at some sites, the three interpolation models described above can still achieve superior positioning performance over longer inter-site distances. Therefore, PPP-RTK has significant potential and outperforms traditional RTK and PPP.

[0118] Table 4. RMS of three networks using three products, ENU, in three directions.

[0119]

[0120]

[0121] To evaluate the practical application effect of PPP-RTK in the structural health monitoring of large bridges, a field experiment was conducted on the Wuhan Yingwuzhou Yangtze River Bridge from 18:30 to 20:30 on DOY 207 and 208 in 2021. The temperature at that time was approximately 28 degrees Celsius. Figure 10 As shown in (a)-(b), two rover stations, L075 and L076, were located on the steel frame in the middle of the road, at one-quarter and three-quarters distance from the bridgehead, respectively, from west to east. The bridge was closed during the experiment, allowing only a small number of vehicles and personnel to pass through for load testing. The two monitoring stations used in the experiment were equipped with Leica GM30 receivers and AR10 choke coil antennas. The surrounding environment was relatively open, with only the steel frame of the bridge and road surface reflecting some multipath signals. Two IGS stations, WUH2 and JFNG, and a station named L074 located on a rooftop near the bridge were used to establish a reference station network. This network was used to generate local single-difference oblique ionospheric delay products and tropospheric delay products. The distribution of the reference stations and monitoring stations is as follows: Figure 11 As shown, the maximum distance between stations is 21.6 kilometers. GPS observation signals were used in the experiment, with a sampling rate of 1 Hz.

[0122] During DOY 207 and 208 in 2021, results for sites L075 and L076 were calculated using PPP-RTK, employing the calculation strategies outlined in Table 2. Based on the above analysis, this embodiment of the invention selected the IDW model to calculate the oblique ionospheric delay and tropospheric delay products because this model has better robustness and lower complexity. Meanwhile, for comparison, the displacements of sites L075 and L076 were calculated using both RTK and PPP-AR models. Station L074 was used as a reference station, forming a short baseline with the monitoring station in the RTK model.

[0123] It is worth noting that the calculation results are in a Cartesian coordinate system (E, N, U). Therefore, this embodiment of the invention defines a bridge coordinate system (X, Y, Z) (e.g., Figure 11 As shown), this is used to analyze the lateral, longitudinal, and vertical displacement states of the bridge. The transformation between the local Cartesian coordinate system and the bridge coordinate system is expressed as follows:

[0124]

[0125] During DOY 207 and 208 in 2021, the localization results of sites L076 and L075 using RTK, PPP-AR, and PPP-RTK models are as follows: Figure 12 , Figure 13 and Figure 14 As shown. Since the bridge was closed and there was almost no wind during the experiment, there was no significant lateral or longitudinal displacement of the bridge, which verifies... Figure 12 and Figure 13 The reliability of RTK and PPP-RTK positioning. Furthermore, the PPP-RTK model can achieve fast convergence, reaching accuracy similar to RTK, while PPP-AR cannot.

[0126] from Figure 14It can be seen that short-baseline RTK can achieve instantaneous convergence in a single epoch, achieving the highest positioning accuracy. Therefore, RTK remains the most commonly used GNSS positioning technology. However, in complex urban environments, suitable locations for deploying reference stations are often unavailable, and reference stations may contaminate the monitoring station's results, reducing the reliability of the positioning results. Furthermore, the positioning performance of long-baseline RTK is significantly reduced. PPP-AR requires 40 minutes or even longer to achieve centimeter-level positioning accuracy, and the convergence results also show multiple significant bridge displacements, with performance roughly the same as RTK. Its advantage lies in its ability to operate without a reference station, but the significantly extended convergence time severely limits its practicality. However, PPP-RTK can achieve centimeter-level accuracy within minutes. In this experiment, the longest convergence time among the four data sets was only 128 seconds. Its positioning performance is comparable to, and even superior to, RTK. This technology effectively addresses the shortcomings of RTK and PPP-AR positioning models, making it highly suitable for practical applications.

[0127] During DOY 207 from 19:00 to 20:00, the PPP-RTK monitoring results from station L075 in the vertical direction were selected as the raw signals for multimodal frequency identification. Several vehicle dynamic load experiments were also conducted during this period to excite the bridge's third mode. Furthermore, the GNSS positioning accuracy was high throughout the period, thus the signals were able to reflect the bridge's vibration characteristics. Power spectral density (PSD) analysis was performed on the raw signals extracted from RTK, PPP-AR, and PPP-RTK. The identification results are as follows: Figure 15 As shown, the first-order mode frequency (0.103 Hz, indicated by the purple arrow) and the third-order mode frequency (0.164 Hz, indicated by the green arrow) are clearly visible across the entire spectrum. It is worth noting that under normal circumstances, low-frequency displacement can affect the results of PSD analysis, leading to inaccurate modal frequency identification. However, during the selected experimental period, the low-frequency displacement was primarily caused by vehicle dynamic load testing, which enhanced the strength of the third-order mode frequency signal. Therefore, in Figure 15 The peaks are clearly observable. However, other less obvious modes are drowned out by noise and cannot be easily identified by peak detection.

[0128] The EERH method proposed in this invention is used to identify multimodal frequencies in PPP-RTK monitoring time series. First, frequency ranges are defined based on prior values ​​obtained from the finite element model, as shown in Table 5. This invention focuses on identifying the first six modes to meet the requirements of structural health monitoring. Then, a bandpass filter can decompose the original signal into different frequency bands corresponding to different modes. In this invention, a Type I Chebyshev bandpass filter is specifically designed to decompose the PPP-RTK monitoring results.

[0129] Table 5 Frequency Band Division of the Original Signal

[0130] mode f(Hz) 1st 0.09～0.12 2nd 0.12～0.15 3rd 0.15～0.21 4th 0.21～0.27 5th 0.27～0.33 6th 0.33～0.39

[0131] Next, EMD technology is used to extract the IMF from the signal in each frequency band. For example... Figure 16 As shown, an effective IMF can be selected based on the correlation coefficient (16). Subsequently, the free decay signal can be separated using the RDT technique. The results are as follows... Figure 17 As shown. Finally, the multimode frequency is calculated by averaging the derivatives of the instantaneous phase function over time. Since a certain convergence time is required, the signal obtained from the instantaneous frequency function may have significant jumps at the beginning and end; these jumps should be discarded. The PP, CEEMDAN, and EWT methods were also used for method validation.

[0132] Table 6 shows the results of multimodal frequency identification using different methods compared to theoretical values, where E(%) represents the relative error rate, and "-" indicates that a valid value could not be obtained or the error is too large. The theoretical modal frequencies calculated using finite element analysis were used as reference values, and these theoretical reference values ​​were calibrated multiple times using experimental results obtained from accelerometers and other sensors. The relative error rate is defined as:

[0133]

[0134] In the formula for calculating the relative error rate, F c (Hz) represents the calculated value, F t (Hz) represents the theoretical value. It should be noted that there may be some small differences between the theoretical and actual values. The results show that the EERH method can effectively identify the first six modes. Only the identification error for the fourth mode frequency is 12.96%. The errors in the identification results can be attributed to various reasons, such as bridge structural damage, unforeseen errors in the identification method, and the influence of observation noise. However, other methods cannot reliably calculate the first six modes, only the obvious first and third mode frequencies. The experimental results strongly demonstrate the feasibility of the EERH method in structural health monitoring applications based on PPP-RTK monitoring data (which has significant noise influence and non-stationary characteristics).

[0135] Table 6 shows the results of multimodal frequency identification obtained using different methods.

[0136]

[0137] Table 7. Results of Multi-Data Source Multimodal Frequency Identification

[0138]

[0139]

[0140] To demonstrate the versatility of this method and to investigate the causes of errors in modal frequency identification, this embodiment of the invention applies the same method to extract multimodal frequencies from the remaining three sets of data and calculates the average value of the four experiments. The results of multiple identifications are shown in Table 7. The results of the four experiments are largely the same, with the third mode showing the largest difference in identification, reaching 5.49%, fully demonstrating the versatility of the method. By calculating the average value, random errors can be effectively avoided, resulting in more robust results. In this embodiment, the maximum error of the average value is reduced by 2.43% compared to the first experiment, and the average error is reduced by 0.33%. However, the identification result of the fourth mode shows an error of about 10% relative to the reference value in each experiment, proving that this frequency component does indeed exist in these signals. Therefore, random errors and data influence can be ruled out. The true cause of this phenomenon still needs further investigation. Abnormal modal frequencies may indicate changes in the bridge structure; therefore, these identification results will serve as an important basis for judging whether the bridge has suffered structural damage.

[0141] This invention primarily explores the feasibility and performance of PPP-RTK in the structural health monitoring of long-span bridges, and further proposes a multimodal frequency identification method based on PPP-RTK displacement monitoring time series. PPP-RTK positioning technology was applied in the displacement monitoring of the Wuhan Yingwuzhou Yangtze River Bridge, while the EERH method proposed in this invention is used to extract multimodal frequencies. The summary is as follows:

[0142] Several sets of experiments verified the feasibility and effectiveness of PPP-RTK based on raw GNSS observation data from 11 reference stations in Wuhan and surrounding cities. Evaluation results of the IDW, SLF, and Kriging interpolation methods show that when the inter-station distance is less than 120 km, they can calculate single-difference oblique ionospheric delay products and tropospheric delay products with similar accuracy, making them very suitable for enhancing PPP-RTK applications. The average epochs of convergence for the three models are 3.1, 4.0, and 3.9, respectively. Meanwhile, the average epochs of convergence for PPP-RTK positioning corrected using various model products are 3.7, 3.7, and 3.9 in the east, north, and up directions, respectively. Furthermore, the ambiguity fixation rate exceeded 86% in each experiment. The average RMS values ​​after convergence for the IDW, SLF, and Kriging methods are 1.15 cm, 1.15 cm, and 1.15 cm, respectively. Considering factors such as convergence time, robustness, and computational complexity, the IDW method is more recommended for practical applications. PPP-RTK has significant potential and outperforms typical RTK and PPP-AR.

[0143] The results of on-site monitoring experiments on the Wuhan Parrot Island Yangtze River Bridge verified the applicability of PPP-RTK in displacement monitoring of long-span bridges. Using PPP-RTK, the longest convergence time was only 2 minutes, achieving positioning accuracy comparable to RTK. PPP-RTK has become a more practical and efficient solution for structural health monitoring of long-span bridges in complex urban environments.

[0144] The effectiveness of the multimodal frequency identification method was successfully verified using multiple sets of PPP-RTK monitoring data from the Wuhan Yingwuzhou Yangtze River Bridge. Power spectral density (PSD) analyses of PPP-AR, RTK, and PPP-RTK clearly revealed the first-order mode frequency of 0.103 Hz and the third-order mode frequency of 0.164 Hz, respectively. The EERH method effectively identified the first six modes of the Wuhan Yingwuzhou Yangtze River Bridge in the PPP-RTK monitoring data. Only the error for the fourth-order mode frequency was 12.96%, with the remaining results consistent with theoretical values. However, other methods could only identify obvious low-order modes. Analysis of the modal identification results across all four sets of monitoring data showed consistency between the results from different datasets. The maximum difference between the results of each experiment was only 5.49%. By calculating the average of multiple sets of results, the maximum error of the average was reduced by 2.43%, and the average error was reduced by 0.33%, highlighting the robustness and reliability of the proposed method.

[0145] The implementation of the various embodiments of the present invention is based on programmed processing by a device with processor functionality. Therefore, in practical engineering, the technical solutions and functions of the various embodiments of the present invention are encapsulated into various modules. Based on this reality, and building upon the above embodiments, the embodiments of the present invention provide a PPP-RTK-based bridge multimodal frequency identification system, which is used to execute a PPP-RTK-based bridge multimodal frequency identification method from the above method embodiments.

[0146] The system comprises: a first main module for acquiring files containing fast satellite orbits, clocks, and observatory products; a second main module for processing local reference station network data sequentially using undifferentiated and uncombined PPP-AR models based on the acquired files, and obtaining fixed oblique ionospheric delay and fixed tropospheric delay through ambiguity resolution; a third main module for calculating single-difference ionospheric and tropospheric products based on ionospheric and tropospheric interpolation, and using a PPP-RTK model to perform ambiguity resolution based on the calculated single-difference ionospheric and tropospheric products to obtain instantaneous centimeter-level high-precision positioning results; a fourth main module for decomposing the PPP-RTK monitoring displacement time series formed by the instantaneous centimeter-level high-precision positioning results into a series of frequency band signals corresponding to different modes; a fifth main module for processing the frequency band signals of the different modes into stationary intrinsic mode functions through empirical mode decomposition; a sixth main module for extracting free decay signals from the selected intrinsic mode functions using random decay techniques; and a seventh main module for constructing a Hilbert analytic function based on the free decay signals to determine multimodal frequencies.

[0147] This invention provides a PPP-RTK-based bridge multimodal frequency identification system, addressing the problem of identifying multimodal frequencies from GNSS monitoring data. It employs several modules and combines Empirical Mode Decomposition (EMD), Random Attenuation Technique (RDT), and Empirical Band Decomposition Method of Hilbert Transform (EERH) to effectively identify multimodal frequencies, especially higher-order modes, in PPP-RTK monitoring data with non-stationary characteristics and noise pollution.

[0148] It should be noted that the system embodiments provided by the present invention are used not only to implement the methods in the above method embodiments, but also to implement the methods in other method embodiments provided by the present invention. The only difference is that corresponding functional modules are set. The principle is basically the same as that of the above system embodiments provided by the present invention. As long as those skilled in the art can improve the modules in the above system embodiments by referring to the specific technical solutions in other method embodiments and combining technical features to obtain corresponding technical means and technical solutions composed of these technical means, on the basis of the above system embodiments, and on the premise of ensuring the practicality of the technical solutions, they can obtain corresponding system-like embodiments for implementing the methods in other method-like embodiments.

[0149] Based on the same inventive concept as the foregoing embodiments, this embodiment of the invention also provides an execution device, including a memory and a processor. The memory stores program instructions that are executed by the processor, and the processor calls the program instructions to execute the steps of the PPP-RTK-based bridge multimodal frequency identification method.

[0150] Based on the same inventive concept as the foregoing embodiments, this embodiment of the invention also provides a non-transitory computer-readable storage medium storing computer instructions that cause the computer to execute the steps of the PPP-RTK-based bridge multimodal frequency identification method.

[0151] In summary, this invention explores the feasibility and effectiveness of PPP-RTK in the structural health monitoring of long-span bridges in complex urban environments, and further proposes a method for reliably identifying multimodal frequencies based on displacement monitoring time series acquired by PPP-RTK. By validating the PPP-RTK capabilities of three networks consisting of 11 stations in Wuhan and its surrounding areas, three typical models for generating local single-difference oblique ionospheric delay and tropospheric delay products were evaluated. Subsequently, PPP-RTK and the proposed multimodal frequency identification method were applied to the structural health monitoring of the Wuhan Yingwuzhou Yangtze River Bridge. The results show that the positioning capability and multimodal frequency identification performance of PPP-RTK are comparable to those of RTK. The multimodal frequency identification method proposed in this invention demonstrates excellent ability to identify the first six modal frequencies, showing excellent consistency with reference values ​​obtained through finite element method calculations and experimental calibration, far exceeding typical methods. Therefore, PPP-RTK has the potential to serve as an alternative technology for the structural health monitoring of long-span bridges.

[0152] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features therein; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the technical solutions of the embodiments of the present invention.

Claims

1. A bridge multimodal frequency identification method based on PPP-RTK, characterized in that, The method for accurately identifying multimodal frequencies from PPP-RTK monitoring data with non-stationary characteristics and noise pollution, the multimodal frequencies including the first six modal frequencies, comprises: Obtain files containing fast satellite orbit, clock, and observatory products; Based on the acquired files, the local reference station network data were processed sequentially using a non-differential and non-combined PPP-AR model, and the fixed tilted ionospheric delay and fixed tropospheric delay were obtained through ambiguity resolution. Based on the interpolation of the ionosphere and troposphere, single-difference ionospheric and tropospheric products are calculated, and based on the calculated single-difference ionospheric and tropospheric products, ambiguity resolution is achieved using the PPP-RTK model to obtain instantaneous centimeter-level high-precision positioning results; The PPP-RTK monitoring displacement time series, formed by instantaneous centimeter-level high-precision positioning results, is decomposed into a series of frequency band signals corresponding to different modes; The frequency band signals of the different modes are processed into stationary intrinsic mode functions through empirical mode decomposition; The free decay signal is extracted from the selected intrinsic mode function using a random decrease technique. Based on the free decay signal, a Hilbert analytical function is constructed to determine the multimodal frequency.

2. The bridge multimodal frequency identification method based on PPP-RTK according to claim 1, characterized in that, The PPP-RTK monitoring displacement time series, formed from instantaneous centimeter-level high-precision positioning results, is decomposed into a series of frequency band signals corresponding to different modes, including: Based on the theoretical modal frequencies or other prior values ​​obtained through the finite element method, the frequency bands of different modes are divided. A bandpass filter is used to decompose the PPP-RTK monitored displacement time series into signals corresponding to different modes within a specified frequency band.

3. The bridge multimodal frequency identification method based on PPP-RTK according to claim 1, characterized in that, The frequency band signals of the different modes are processed into stationary intrinsic mode functions through empirical mode decomposition, including: Identify local peaks and valleys in the input signal; The upper and lower envelopes are obtained using cubic spline interpolation. When the difference between the number of extreme points and zero-crossing points is no greater than one, and the average value of the envelope formed by the local maximum and minimum points is always zero, a stationary intrinsic mode function is obtained.

4. The bridge multimodal frequency identification method based on PPP-RTK according to claim 3, characterized in that, The method further includes: Select an effective intrinsic mode function based on the threshold of the correlation coefficient of the intrinsic mode function.

5. The bridge multimodal frequency identification method based on PPP-RTK according to claim 1, characterized in that, The method further includes: A partial fuzziness resolution strategy is adopted for fuzziness resolution.

6. A bridge multimodal frequency identification system based on PPP-RTK, characterized in that, For accurately identifying multimodal frequencies from PPP-RTK monitoring data with non-stationary characteristics and noise pollution, the multimodal frequencies including the first six modal frequencies, the system comprises: The first main module is used to acquire files containing fast satellite orbits, clocks, and observatory products; The second main module is used to perform non-differential and non-combined PPP-AR model processing on the local reference station network data based on the acquired files, and obtain fixed oblique ionospheric delay and fixed tropospheric delay through ambiguity resolution. The third main module is used to calculate single-difference ionospheric and tropospheric products based on ionospheric and tropospheric interpolation, and to perform ambiguity resolution based on the calculated single-difference ionospheric and tropospheric products using the PPP-RTK model to obtain instantaneous centimeter-level high-precision positioning results. The fourth main module is used to decompose the PPP-RTK monitoring displacement time series formed by instantaneous centimeter-level high-precision positioning results into a series of frequency band signals corresponding to different modes; The fifth main module is used to process the frequency band signals of the different modes into stable intrinsic mode functions through empirical mode decomposition; The sixth main module is used to extract the free decay signal from the selected intrinsic mode function using a random decrease technique; The seventh main module is used to construct a Hilbert analytical function based on the free decay signal to determine the multimodal frequency.

7. An execution device, characterized in that, The method includes a memory and a processor, wherein the memory stores program instructions that are executed by the processor, and the processor invokes the program instructions to perform the steps of the PPP-RTK-based bridge multimodal frequency identification method as described in any one of claims 1 to 5.

8. A non-transitory computer-readable storage medium, characterized in that, The non-transitory computer-readable storage medium stores computer instructions that cause the computer to perform the steps of the PPP-RTK-based bridge multimodal frequency identification method as described in any one of claims 1 to 5.

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