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

Abstract

The invention discloses a PPP-RTK-based bridge multi-modal frequency identification method and system. The method comprises the steps of obtaining a file including a fast satellite orbit, a clock and an observation station product; carrying out non-differential and non-combined PPP-AR model processing on the local reference station network data in sequence, and carrying out ambiguity calculation to obtain fixed inclined ionosphere delay and fixed troposphere delay; calculating single-difference ionosphere and troposphere products based on ionosphere and troposphere interpolation, and realizing ambiguity solution by using a PPP-RTK model to obtain an instantaneous centimeter-level high-precision positioning result; decomposing the PPP-RTK monitoring displacement time sequence into a series of frequency band signals corresponding to different modes; performing empirical mode decomposition processing on the frequency band signals of different modes to obtain a stable intrinsic mode function; extracting a free attenuation signal from the selected intrinsic mode function by using a random decline technology; and constructing a Hilbert analytic function based on the free attenuation signal, and determining a multi-modal frequency.

Description

Technical Field

[0001] The present invention relates to a method and system for identifying multi-modal frequencies of bridges based on PPP-RTK. Background Art

[0002] As an important part of the urban traffic network, the safety and stability of long-span bridges need to be highly emphasized throughout their entire service life. Therefore, it is crucial to monitor the displacement and multi-modal frequencies of bridges in real time and effectively, as these data are the core basis for structural damage detection, condition assessment, and safety management. Traditional structural health monitoring sensors mainly include accelerometers, strain gauges, and displacement gauges, but there are still some limitations in the application of these technologies that need to be further addressed.

[0003] Due to its automation, high reliability, continuity, and versatility, combined with high-precision positioning capabilities, the Global Navigation Satellite System (GNSS) has been widely used in the structural health monitoring of long-span bridges. Compared with traditional sensors, GNSS has significant advantages in obtaining continuous long-term displacement time series, and these data can be processed through specific algorithms to extract multi-modal frequencies, thereby realizing real-time monitoring of the operating state of bridges and ensuring their safety and stability during operation. Currently, Real-Time Kinematic (RTK) is a widely used GNSS positioning technology that can obtain high-precision relative displacement time series through the double-difference model between short-distance base stations and operates in real time. This model can solve the problem of fixed integer ambiguity, thus achieving centimeter-level high-precision positioning. However, the effectiveness of RTK depends on the deployment of a reference station in an open environment near the rover station, which requires a stable geographical environment and good communication conditions. In complex urban environments, these conditions are often difficult to meet. In addition, the displacement of the reference station (including thermal expansion and environmental loads, etc.) will contaminate the positioning results of the rover station and reduce its reliability. Precise Point Positioning (PPP), as an independent GNSS positioning technology, can achieve high-precision positioning without a reference station. By using products such as precise satellite orbits, precise satellite clock offsets, satellite phase and pseudorange observations, specific signal biases (OSB), and satellite attitudes generated by the International GNSS Service (IGS) analysis center, PPP can achieve integer ambiguity resolution (PPP-AR) without differential processing of a nearby reference station, thereby providing dynamic centimeter-level positioning capabilities for a single GNSS receiver. However, correctly resolving the floating-point ambiguity requires a long convergence time, which greatly limits the practical application of this technology.

[0004] Precise Point Positioning Real-Time Kinematic (PPP-RTK) combines the characteristics of traditional RTK and PPP, and can achieve instantaneous centimeter-level positioning without the need for nearby reference stations, which has become the research focus in the field of high-precision GNSS positioning algorithms and applications. This model not only does not require nearby reference stations but also overcomes the defect of long convergence time. PPP-RTK is mainly divided into two parts: the network side and the user side. The network side includes multiple sparsely distributed GNSS reference stations with known coordinates, and the maximum distance between stations can exceed 100 kilometers. The network side calculates precise local ionospheric and tropospheric delay corrections, precise satellite orbits and clock biases, and satellite phase and pseudorange OSB, and transmits them to users in real time. By integrating these correction information, the user side can achieve positioning performance comparable to RTK using the PPP model. So far, the PPP-RTK method has been discussed in many studies. Teunissen et al. proposed the principle of PPP-RTK and further compared the estimable parameters of different methods. Odijk et al. introduced the S-system theory to enable PPP-RTK to operate on multiple signal frequencies. Geng et al. found that the full-frequency combined PPP-RTK has better robustness than traditional PPP-RTK in complex urban environments. Gao et al. tried to use PPP-RTK technology to monitor the displacement of the Hong Kong-Zhuhai-Macao Bridge, but their research focus was on the multipath error suppression method. Currently, there are many ionospheric and tropospheric modeling methods, such as Inverse Distance Weighting (IDW), Second-Order Linear Fitting (SLF), Kriging interpolation, Radial Basis Function (RBF), Least Squares Collocation (LSC), etc. Each atmospheric interpolation model has its advantages, but its actual performance still needs further research. The performance verification of PPP-RTK positioning technology for the structural health monitoring of long-span bridges in complex urban environments is not comprehensive, and there is a lack of research on extracting structural health monitoring information from PPP-RTK monitoring time series. In summary, the PPP-RTK positioning technology has potential in the structural health monitoring of long-span bridges.

[0005] GNSS monitoring data contains bridge displacement and its multi-modal frequency information, which can be used for structural health monitoring of long-span bridges. However, the GNSS monitoring displacement time series is usually non-stationary and has 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 refraction signals. This makes many multi-modal frequency identification methods inaccurate and inapplicable. Empirical mode decomposition (EMD) and its enhanced versions, such as ensemble empirical mode decomposition (EEMD), complete ensemble empirical mode decomposition (CEEMD), CEEMD with adaptive noise (CEEMDAN), etc., are currently effective methods for analyzing the time and frequency characteristics of signals in non-stationary systems. In addition, methods such as peak picking method (PP), empirical wavelet transform (EWT), convolutional neural network (CNN), stochastic subspace identification (SSI), natural excitation technique (NET), etc. are also widely used for modal frequency identification. However, these methods are usually applicable to low-order modes and may not work well in identifying the ambiguous high-order modal frequencies affected by noise. Unfortunately, the noise in GNSS monitoring data often masks these high-order modal frequencies. He et al. proposed using the autoregressive power spectrum method to identify multi-modal 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 multi-modal frequencies from PPP-RTK monitoring data with non-stationary characteristics and noise pollution. Summary of the Invention

[0006] To overcome the deficiencies of the above prior art, the present invention provides a method and system for identifying multi-modal frequencies of bridges based on PPP-RTK. By combining empirical mode decomposition (EMD), random decrement technique (RDT), and empirical frequency band decomposition method based on Hilbert transform (abbreviated as EERH), it can effectively identify multi-modal frequencies, especially high-order modes, in PPP-RTK monitoring data with non-stationary characteristics and noise pollution.

[0007] According to one aspect of the specification of the present invention, a method for identifying multi-modal frequencies of bridges based on PPP-RTK is provided, including:

[0008] Obtain a file containing fast satellite orbits, clocks, and observation station products;

[0009] Based on the obtained file, perform undifferenced and uncombined PPP-AR model processing on the local reference station network data in sequence, and through ambiguity resolution, obtain fixed slant ionospheric delay and fixed tropospheric delay;

[0010] Based on the ionospheric and tropospheric interpolation, calculate single-difference ionospheric and tropospheric products, and use the PPP-RTK model based on the calculated single-difference ionospheric and tropospheric products to achieve ambiguity resolution, obtaining instantaneous centimeter-level high-precision positioning results;

[0011] Decompose the PPP-RTK monitoring displacement time series formed by the instantaneous centimeter-level high-precision positioning result into a series of band signals corresponding to different modes;

[0012] Process the band signals of the different modes into stationary intrinsic mode functions through empirical mode decomposition;

[0013] Extract the free decay signal from the selected intrinsic mode functions using the stochastic decrement technique;

[0014] Construct a Hilbert analytic function based on the free decay signal to determine the multi-modal frequency.

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

[0016] Divide the frequency bands where different modes are located according to the theoretical modal frequencies obtained by the finite element method or other prior values;

[0017] Use a band-pass filter to decompose the PPP-RTK monitoring displacement time series into signals corresponding to different modes within the specified frequency bands.

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

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

[0020] Adopt the cubic spline interpolation method to obtain the upper envelope and the lower envelope;

[0021] When the difference in the number of extreme points and zero-crossing points is not greater than one, and the average value of the envelope lines formed by the local maximum and minimum points is always zero, obtain the stationary intrinsic mode function.

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

[0023] Select effective intrinsic mode functions according to the threshold of the correlation coefficient of the intrinsic mode functions.

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

[0025] Adopt a partial ambiguity resolution strategy for ambiguity resolution.

[0026] According to one aspect of the specification of the present invention, provide a bridge multi-modal frequency identification system based on PPP-RTK, including:

[0027] The first main module is used to obtain a file containing rapid satellite orbits, clocks, and observatory products;

[0028] The second main module is used to perform undifferenced and uncombined PPP-AR model processing on the local reference station network data in sequence based on the obtained file, and through ambiguity resolution, obtain fixed slant ionospheric delay and fixed tropospheric delay;

[0029] The third main module is used to calculate single-difference ionospheric and tropospheric products based on ionospheric and tropospheric interpolation, and use the PPP-RTK model based on the calculated single-difference ionospheric and tropospheric products to achieve ambiguity resolution, obtaining 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 the instantaneous centimeter-level high-precision positioning results into a series of band signals corresponding to different modes;

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

[0032] The sixth main module is used to extract free decay signals from the selected intrinsic mode functions using the random decrement technique;

[0033] The seventh main module is used to construct a Hilbert analytic function based on the free decay signals to determine multi-modal frequencies.

[0034] According to one aspect of the specification of the present invention, there is provided an execution device, including a memory and a processor, the memory stores program instructions executed by the processor, and the processor calls the program instructions to execute the steps of a method for identifying multi-modal frequencies of a bridge based on PPP-RTK.

[0035] According to one aspect of the specification of the present invention, there is provided a non-transitory computer-readable storage medium, the non-transitory computer-readable storage medium stores computer instructions, and the computer instructions cause the computer to execute the steps of a method for identifying multi-modal frequencies of a bridge based on PPP-RTK.

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

[0037] 1. The present invention designs a new method - an empirical band decomposition method combining EMD, RDT, and Hilbert transform (abbreviated as EERH) to effectively identify multi-modal frequencies, especially high-order modes, in PPP-RTK monitoring data with non-stationary characteristics and noise pollution, so as to evaluate the performance of PPP-RTK in the health monitoring of long-span bridge structures in urban environments.

[0038] 2. The present invention has successfully verified the effectiveness of the proposed multi-modal frequency identification method through multiple groups of PPP-RTK monitoring data of the Wuhan Yangtze River Parrot Island Bridge. The power spectral density (PSD) analysis results of PPP-AR, RTK, and PPP-RTK clearly show the first-order modal frequency of 0.103 Hz and the third-order modal frequency of 0.164 Hz, respectively. The EERH method of the present invention can effectively identify the first six-order modes of the Wuhan Yangtze River Parrot Island Bridge in the PPP-RTK monitoring data. The error of only the fourth-order modal frequency is 12.96%, and the remaining results are consistent with the theoretical values. Brief Description of the Drawings

[0039] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings used in the description of the embodiments or the prior art. Obviously, the following drawings are some embodiments of the present invention. For those of ordinary skill in the art, without creative efforts, other drawings can also be obtained based on these drawings.

[0040] Figure 1 It is a schematic flow chart of a bridge multi-modal frequency identification method based on PPP-RTK provided by an embodiment of the present invention.

[0041] Figure 2 It is a schematic diagram of the distribution of survey stations provided by an embodiment of the present invention.

[0042] Figure 3 It is a schematic diagram of the errors of three inclined ionospheric delay interpolation models provided by an embodiment of the present invention.

[0043] Figure 4 It is a schematic diagram of the multipath parameters of all reference stations provided by an embodiment of the present invention.

[0044] Figure 5 It is a schematic diagram of the interpolation errors of three tropospheric delays provided by an embodiment of the present invention.

[0045] Figure 6 It is a schematic diagram of the time series of three products used in the ENU three directions of three networks provided by an embodiment of the present invention.

[0046] Figure 7 It is a schematic diagram of the first convergence epochs of three networks provided by an embodiment of the present invention.

[0047] Figure 8 It is a schematic diagram of the ambiguity fixation rates of three models of three networks provided by an embodiment of the present invention.

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

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

[0050] Figure 11 It is the experimental measurement station distribution diagram provided by the embodiments of the present invention.

[0051] Figure 12 It is a schematic diagram of the X-direction positioning results of the L076 and L075 stations using the RTK, PPP-AR, and PPP-RTK models during DOY 207 and 208 provided by the embodiments of the present invention.

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

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

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

[0055] Figure 16 It is a schematic diagram of the effective IMF extracted from the PPP-RTK displacement monitoring data provided by the embodiments of the present invention.

[0056] Figure 17 It is a schematic diagram of the free decay signal extracted from the effective IMF provided by the embodiments of the present invention. Detailed implementation manners

[0057] It should be noted that:

[0058] PPP-RTK, as an extended technology of non-differential and non-combination (UDUC) PPP, mainly consists of two parts: the network side and the user side. Precise satellite products, including orbits, clocks, OSB, local slant ionospheric delays, and tropospheric delays, are generated on the network side. The user side receives these products to achieve instantaneous integer ambiguity resolution in real-time PPP, thereby achieving instantaneous centimeter-level high-precision positioning.

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

[0060]

[0061] where and are the pseudorange and carrier phase respectively, the superscript s represents the satellite, and the subscripts r and i represent the receiver and frequency respectively. represents the geometric distance between the satellite and the receiver. C represents the speed of light in vacuum, t r and t s represent the clock biases at the receiver and satellite ends respectively, γ i represents the ionospheric delay coefficient, represents the ionospheric delay, M represents the projection function, T i represents the tropospheric delay, d r,i and represent the receiver and satellite pseudorange hardware delays respectively, λ i represents the wavelength, represents the integer ambiguity, b r,i and represent the receiver and satellite phase hardware delays respectively. σ and ε represent the pseudorange and phase noises respectively. In addition, the observation equations are affected by various systematic errors, which must be accurately modeled and then 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 by sequential least squares estimation or Kalman filtering. It should be noted that due to the influence of factors such as receiver hardware delay, observation noise, and multipath error, the directly estimated ambiguity parameter is a real value rather than the correct integer, which will lead to inaccurate calculation of the remaining parameters. Therefore, calculating the correct integer ambiguities and incorporating them into the normal equations as virtual observation equations can effectively improve the estimation accuracy and robustness of the parameters. Currently, by using the Least-Squares Ambiguity Decorrelation Adjustment (LAMBDA) algorithm and performing the ratio test method, the ambiguities can be effectively fixed as the correct integers. After resolving the ambiguities, high-precision tropospheric wet delay and slant ionospheric delay can be obtained. It should be noted that part of the receiver pseudorange and phase hardware delays are included in the estimated parameters.

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

[0065]

[0066] Where represents the slant ionospheric delay with the hardware delay at the receiver end of the attached reference station, represents the latitude of the piercing point of the satellite of the rover and the ionospheric reference height, represents the latitude of the piercing point of the satellite of the i-th reference station and the ionospheric reference height, represents the longitude of the piercing point of the satellite of the rover and the ionospheric reference height, represents the longitude of the piercing point of the satellite of the i-th reference station and the ionospheric reference height, B r represents the geodetic latitude of the rover, B i represents the geodetic latitude of the i-th reference station, L r represents the geodetic longitude of the rover, L i represents the geodetic longitude of the i-th reference station, H r represents the geodetic height of the rover, H i represents the geodetic height of the i-th reference station.

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

[0068]

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

[0070] At the user side, real-time data stream products are received, including satellite orbits, satellite clocks, OSB, etc. published by the IGS data center, as well as ionospheric delay and tropospheric delay products generated by local sparse reference stations. It should be noted that since the generated ionospheric products contain receiver hardware delays of different reference stations, inter-satellite single-differencing (SD) is required to eliminate these delays. This can be expressed as:

[0071]

[0072] where k represents the k-th satellite and s represents the reference satellite.

[0073] Then the model at the user side can be expressed as follows:

[0074]

[0075] where and represent the pseudorange observation value and the phase observation value minus the calculated value respectively, represents the linearization coefficient, x r represents the rover coordinates, δt r represents the combined receiver clock offset, represents the combined ionospheric delay, represents the combined phase ambiguity, represents the tropospheric delay product, T r,0 represents the initial value of the tropospheric delay, represents the ionospheric delay product, and the meanings of the remaining parameters are the same as above.

[0076] The prior noise of the tropospheric wet delay and the slant ionospheric delay pseudo-observation equations can be empirically set to 2 cm and 5 cm. To accelerate convergence, the user side needs to use partial ambiguity fixing and set a lower ratio test threshold. Using the PPP-RTK model, the user side can quickly solve the ambiguity problem and thus achieve instantaneous high-precision positioning.

[0077] In the PPP-RTK displacement monitoring time series of long-span bridges, the main challenges in identifying multi-modal frequencies, especially high-order modes, are the non-stationarity of the signals. In addition, high-order modes are easily overwhelmed by significant noise. To address these challenges, the EERH method proposed in the embodiments of the present invention combines empirical band signal decomposition, empirical mode decomposition (EMD), random decrement technique (RDT), and Hilbert transform. First, the frequency bands where different modes are located can be divided according to the theoretical modal frequencies obtained by the finite element method (FE) or other prior values. Then, the PPP-RTK displacement monitoring time series can be decomposed into signals corresponding to different modes within the specified frequency bands using a band-pass filter (such as a Chebyshev band-pass filter), as follows:

[0078]

[0079] Through empirical band signal decomposition, the mode mixing problem in EMD can be effectively solved, thus effectively avoiding the problems of identifying modes with close frequencies and insignificant high-order modes, and further reducing the identification error.

[0080] By using the EMD technique, any signal with non-stationarity will be processed into multiple stationary intrinsic mode functions (IMFs). It should be noted that this process is crucial because when constructing the instantaneous frequency function using the Hilbert transform, a stationary signal needs to be used as the input. Otherwise, negative values will appear in the results, losing physical meaning. However, the PPP-RTK monitored displacement time series is usually non-stationary, so the method in the embodiments of the present invention introduces EMD to ensure that the input signal is stationary. First, the local peaks and valleys of the input signal are initially identified. Subsequently, the cubic spline interpolation method can be used to obtain the upper envelope and the lower envelope. The primary oscillation mode is expressed as:

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

[0082] Then, it is determined whether the following two characteristics are satisfied: First, the difference in the number of extreme points and zero-crossing points is not greater than one; second, the average value of the envelope line formed by the local maximum and minimum points is always zero. If these two conditions are not met, the signal is regarded as and the above process is repeated until it is satisfied. Finally, the signal that meets the conditions is the first IMF. At the same time, 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 the random component in the vibration, thereby improving the accuracy of modal parameter identification. The displacement response is separated into some time sampling functions. The random decrement function can be expressed as:

[0085]

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

[0087] The Hilbert transform can be used to construct the analytic function of a time series. The multimodal frequency can be estimated by the least squares method. The Hilbert transform can be expressed as:

[0088]

[0089] By taking z i (t) as the real part input, the signal obtained by the Hilbert transform is used as the imaginary part to construct an analytic function f i (t):

[0090]

[0091] where represents the instantaneous amplitude function, represents the instantaneous phase function, and the instantaneous frequency function is the derivative of the instantaneous phase function as follows:

[0092]

[0093] The multimodal frequency can be calculated by performing non - linear curve fitting techniques on the instantaneous frequency function or simply taking the average.

[0094] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are some, but not all, of the embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present invention. Additionally, the technical features in each embodiment or individual embodiment provided by the present invention can be combined with each other arbitrarily to form a new technical solution. Such combination is not restricted by the order of steps and / or the pattern of structural composition, but must be based on the fact that those of ordinary skill in the art can implement it. When the combination of technical solutions results in contradictions or cannot be implemented, it should be considered that such a combination of technical solutions does not exist and is not within the protection scope required by the present invention.

[0095] The main process of the bridge multi-modal frequency identification method based on PPP-RTK provided by the present invention is as follows Figure 1 shown. In the figure, the yellow boxes represent data or results, the blue boxes represent algorithm processes, and the part within the green dashed box is the process of modal frequency identification. At the beginning of the process, files containing fast satellite orbits, clocks, and OSB (observation station products) are retrieved from the network. Then, the undifferenced and uncombined PPP-AR model is processed for the local reference station network data in sequence. Through ambiguity resolution, fixed slant ionospheric delay and fixed tropospheric delay can be obtained. Subsequently, single-difference ionospheric and tropospheric products are calculated through ionospheric and tropospheric interpolation. Users can utilize these products to achieve fast or even instantaneous ambiguity resolution based on 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 band signals corresponding to different modes. These non-stationary signals are processed into some stationary IMFs (intrinsic mode functions) through EMD (empirical mode decomposition), and effective IMFs need to be selected according to their correlation coefficients during this process.

[0096]

[0097] Existing research results show that the correlation coefficient ρ i can be considered strongly correlated. Therefore, the threshold is set to 0.8 in the embodiments of the present invention. In addition, the free decay signal can be extracted from the selected effective IMFs using RDT (random decrement technique). Finally, the multi-modal frequency can be determined by constructing a Hilbert analytic function based on the free decay signal.

[0098] To evaluate the feasibility and effectiveness of PPP-RTK, GNSS raw observation files of 11 reference stations in Wuhan and its surrounding cities on the 60th day of 2023 were randomly selected. The distribution of these stations is as follows Figure 2 shown. The middle JFNG station is set as the rover station ( Figure 2 marked with a red dot in Figure 2(marked in blue triangles). The network composition, maximum distance between stations, and average height difference between stations are shown in Table 1. The sampling rate of all observation files is 30 seconds. Based on the Positioning and Navigation Data Analysis Platform (PANDA), the embodiments of the present invention developed undifferenced and uncombined PPP-AR and PPP-RTK modules, and used this platform to process all GNSS data in the embodiments of the present invention. For PPP-RTK, fast and reliable ambiguity resolution is very important. Therefore, the embodiments of the present invention adopt a partial ambiguity resolution strategy. All ambiguity parameters are used as candidate parameters. The 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. According to experience, the threshold is set to 3. If the test fails, the ambiguity parameter with the largest variance is eliminated, and then the search is repeated until the test passes. The data processing strategy of PPP-RTK is shown in Table 2.

[0099] Table 1 Station Network Composition

[0100] Network Station Maximum inter-station distance (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 the slant ionospheric delay and tropospheric delay products have an important impact on the effectiveness of PPP-RTK. To optimize the accuracy of these products, the embodiments of the present invention conducted a comparative analysis of widely used interpolation models, including IDW, SLF, and Kriging interpolation. First, the coordinates of all stations (including rovers) were calculated using the static PPP-AR method. Then, the fixed slant ionospheric delay and tropospheric delay were calculated using the dynamic PPP-AR model with fixed reference station coordinates. Next, the corresponding single-difference ionospheric delay and tropospheric delay products were calculated using the three interpolation models. To evaluate the performance of the local slant ionospheric delay and tropospheric delay products, the embodiments of the present invention fixed the known coordinates of the rover JFNG and calculated the true values of the single-difference slant ionospheric delay and tropospheric delay. It should be noted that a certain convergence time is required when performing PPP-AR at the network side. The embodiments of the present invention started the interpolation calculation at 3 o'clock to obtain the fixed ionospheric and tropospheric delays. It should be emphasized that in practical applications, the network side can continuously broadcast the corresponding ionospheric and tropospheric delay products, thus eliminating the convergence time problem.

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

[0106] Although the results of Network 1 and Network 2 are not as ideal as those of Network 3, most of the errors are still within ±5 cm, which makes them still applicable to PPP-RTK positioning. To explore the reasons for the poor results of Network 1 and Network 2 (the inter-station distances of these two networks are smaller than that of Network 3), the embodiments of the present invention calculate the multipath parameters of all original observation files. MP1 and MP2 are defined as:

[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 of all reference stations are as Figure 4 shown, from which it can be observed that the MP1 and MP2 values of Station H002 in Network 1 and Network 2 are higher than those of other reference stations, indicating that this station is affected by severe multipath effects. At the same time, the multipath errors of each station in Network 1 and Network 2 are significantly higher than those of each station in Network 3. The poor data quality leads to a reduction in the accuracy of the ionospheric results, making the results of Network 1 and Network 2 inferior to those of Network 3, although the maximum inter-station distance in Network 3 is much larger than that in Network 1 and Network 2. This result also shows that even if there are stations with poor data quality, the generated ionospheric model can still meet the accuracy requirements.

[0110] Table 3 RMS of the three tropospheric delay interpolation models for the three networks

[0111] Method Network 1 Network 2 Network 3 Inverse distance weighting (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 performance of the errors of the three tropospheric delay interpolation models in the three networks is as Figure 5As shown. It is worth noting that in Network 1 and Network 2, the tropospheric products calculated by the three methods show similar trends, and most of the errors are less than 2 cm. However, in Network 3, the tropospheric products obtained using the SLF method show significant differences and larger errors compared with the other two methods. Since the quality of the observed data in Network 3 is slightly better than that in Network 1 and Network 2, and the average height difference between stations is relatively close, this indicates that the inter-station distance is the main reason for the poorer results. The 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 Network 1 and Network 2, except for the SLF method. Considering the maximum inter-station distance and the average 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 performance of the IDW method is slightly better than that of the Kriging and SLF methods.

[0113] Using the three single-difference oblique ionospheric delay and tropospheric delay products, the PPP-RTK positioning results of the three networks are as Figure 6 shown. The experiment starts at 3 o'clock. To reduce the randomness of the experiment, the data is interrupted every 3 hours and re-converged. In addition, for comparison, the results of dynamic PPP-AR are represented by dark blue dots in the figure. PPP-AR also re-converges every 3 hours. For clearer display, the time series data using the IDW and SLF model products are shifted upward by 20 cm and 10 cm respectively, while the positioning results of PPP-AR are shifted downward by 10 cm. Observing Figure 6 , it can be clearly seen 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. In addition, the results of the three networks are roughly the same. The PPP-RTK positioning model shows enhanced performance, overcomes the limitations of nearby reference stations, and solves the problem of long-term convergence, making it more suitable for the structural health monitoring of long-span bridges in complex urban environments.

[0114] The first convergence epochs of the three networks are as Figure 7As shown, the time interval between epochs is 30 seconds. There are many definitions for the first convergence epoch. In the embodiments of the present invention, the standard is the starting epoch with the error of 10 consecutive epochs less than 10 cm. In the embodiments of the present invention, 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. At the same time, using three model products, the results of Network 1 are slightly better than those of Network 2 and Network 3, although the accuracy of the ionospheric and tropospheric products of Network 1 is lower. This indicates that the convergence time is mainly affected by the accuracy of the product models in the first few epochs. Despite the slightly lower accuracy of the obtained ionospheric and tropospheric product models, the PPP-RTK model can still achieve rapid 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 the convergence time index. This result shows that although the IDW method has a lower ionospheric RMS value generated by the Kriging interpolation method, the IDW method shows better robustness in terms of convergence time and is more recommended. Generally speaking, PPP-RTK performs excellently in significantly reducing the convergence time and achieves fast even single-epoch centimeter-level positioning.

[0115] The positioning feasibility of PPP-RTK is evaluated by calculating the ambiguity resolution rate, which is defined as the ratio of the number of satellites passing the ratio test to the total number of satellites, as Figure 8 shown. A higher resolution rate indicates more reliable results. The results show that the ambiguity resolution rates of the three models in the three networks all exceed 86%. Compared with 70.35% of PPP-AR, the average ambiguity fixing rate of PPP-RTK has increased by 16.1%. In addition, the ambiguity fixing rate after convergence is roughly the same for the products using each model.

[0116] To ensure that the positioning accuracy of PPP-RTK meets the requirements of long-span bridge structural health monitoring, statistical analysis is carried out on the displacement results in the N, E, and U directions, as Figure 9 shown. And a normal distribution fitting is performed on the displacement distribution ( Figure 9 the red curve in). The statistical analysis shows that the positioning accuracy in the horizontal direction is higher, the error distribution is more concentrated, and the mean value is close to 0, which is significantly better than that in the vertical direction. Although the positioning accuracy in the vertical direction is lower, most displacements are within ±3 cm, meeting the requirements of long-span bridge displacement monitoring. However, this will increase the difficulty of modal frequency identification and more accurate and reliable modal frequency identification methods need to be used.

[0117] Table 4 shows the RMS values of three products used by three networks after convergence. 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 for multiple PPP-RTK experiments were 0.82 cm, 0.73 cm, and 1.90 cm respectively, which were 67.5%, 57.6%, and 41.2% higher than those of PPP-AR respectively. The accuracy in each direction was significantly improved, especially in the E direction. However, it should be noted that the accuracy of the oblique ionospheric delay and tropospheric delay products affects the positioning reliability after convergence. The average RMS values of the IDW, SLF, and Kriging methods after convergence were 1.15 cm, 1.15 cm, and 1.15 cm respectively. Although the three methods were 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 the low data quality at some stations, superior positioning performance can still be achieved at long inter-station distances using the above three interpolation models. Therefore, PPP-RTK has significant potential and is superior to traditional RTK and PPP.

[0118] Table 4 RMS of ENU three directions of three products used by three networks

[0119]

[0120]

[0121] To evaluate the practical application effect of PPP-RTK in the health monitoring of large bridge structures, a field experiment was conducted on the Wuhan Yangtze River Parrot Island Bridge from 18:30 to 20:30 on DOY 207 and 208 in 2021, when the temperature was about 28 degrees Celsius, as Figure 10 (a)-(b) shown. Two rovers, L075 and L076, were respectively located on the steel frames in the middle of the road, at one-quarter and three-quarters of the distance from the bridgehead from west to east. The bridge was closed during the experiment, and only a small number of vehicles and personnel for load testing passed. The two monitoring stations used in the experiment were equipped with Leica GM30 receivers and AR10 choke antennas. The surrounding environment was relatively open, and only the steel frames of the bridge and the road surface reflected some multipath signals. The experiment used two IGS stations, WUH2 and JFNG, and a station named L074 located on the roof near the bridge 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 Figure 11 shown, and the maximum inter-station distance is 21.6 km. GPS observation signals with a sampling rate of 1 Hz were used in the experiment.

[0122] During DOY 207 and 208 in 2021, the results at stations L075 and L076 were calculated using PPP-RTK, adopting the calculation strategy outlined in Table 2. Based on the above analysis, the embodiments of the present 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 stations L075 and L076 were calculated using the RTK and PPP-AR models. Station L074 was used as a reference station to form a short baseline with the monitoring stations in the RTK model.

[0123] It should be noted that the calculation results are in the Cartesian coordinate system (E, N, U). Therefore, the embodiments of the present invention defined a bridge coordinate system (X, Y, Z) (as Figure 11 shown) 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

[0124]

[0125] During DOY 207 and 208 in 2021, the positioning results of stations L076 and L075 using the RTK, PPP-AR, and PPP-RTK models are respectively as Figure 12 、 Figure 13 and Figure 14 shown. Since the bridge was closed and there was almost no wind during the experiment, the bridge had no significant lateral or longitudinal displacement, which verified the Figure 12 and Figure 13 reliability of RTK and PPP-RTK positioning. In addition, the PPP-RTK model can achieve fast convergence and reach an accuracy similar to that of RTK, while PPP-AR cannot.

[0126] From Figure 14It can be seen that short-baseline RTK can achieve single-epoch instantaneous convergence and has the highest positioning accuracy. Therefore, RTK remains the most commonly used GNSS positioning technology at present. However, in complex urban environments, there is usually no suitable location to deploy reference stations, and reference stations may contaminate the results of monitoring stations, reducing the reliability of positioning results. In addition, the positioning performance of long baselines will be significantly reduced. PPP-AR takes 40 minutes or even longer to achieve centimeter-level positioning accuracy, and the results after convergence also show significant bridge displacements multiple times, with performance roughly the same as RTK. Its advantage is that it can operate without reference stations, but the significantly extended convergence time severely limits its practicality. However, PPP-RTK can achieve centimeter-level accuracy within a few minutes. In this experiment, the longest convergence time in the four groups of data was only 128 seconds. Then, its positioning performance can be comparable to RTK, and even better than PPP-AR. This technology effectively solves the deficiencies of the RTK and PPP-AR positioning models and is very suitable for practical applications.

[0127] During the period from 19:00 to 20:00 on DOY 207, the PPP-RTK monitoring results in the vertical direction of Station L075 were selected as the original signal for multimodal frequency identification. During this time period, several vehicle dynamic load experiments were conducted simultaneously to excite the third mode of the bridge. In addition, the GNSS positioning accuracy was very high throughout the period, so the signal could reflect the vibration characteristics of the bridge. Power spectral density (PSD) analysis was performed on the original signals extracted from RTK, PPP-AR, and PPP-RTK. The identification results are as Figure 15 shown, where in all spectra, the first-order modal frequency of 0.103 Hz (indicated by the purple arrow) and the third-order modal frequency of 0.164 Hz (indicated by the green arrow) are clearly visible. It should be noted that under normal circumstances, low-frequency displacements may affect the results of PSD analysis, leading to inaccurate identification of modal frequencies. However, during the period selected for the experiment, the low-frequency displacements were mainly caused by vehicle dynamic load tests, which enhanced the intensity of the third-order modal frequency signal. Therefore, it can be clearly observed in Figure 15 . However, other less obvious modes are submerged by noise and cannot be easily identified through peak detection.

[0128] The EERH method proposed in the embodiment of the present invention is used to identify multimodal frequencies in the PPP-RTK monitoring time series. First, a frequency interval is defined according to the prior values obtained from the finite element model, as shown in Table 5. The embodiment of the present invention focuses on identifying the first six modes to meet the requirements of structural health monitoring. Then, a band-pass filter can decompose the original signal into different band signals corresponding to different modes. In the embodiment of the present invention, a type-I Chebyshev band-pass filter is specifically designed for decomposing the PPP-RTK monitoring results.

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

[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, the IMF is extracted from each band signal using the EMD technique. As Figure 16 shown, the 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 Figure 17 shown. Finally, the multimodal frequency is calculated by taking the average of the derivative of the instantaneous phase function with respect to 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, and these jumps should be discarded. At the same time, the PP, CEEMDAN, and EWT methods are also used for method verification.

[0132] The results of the multimodal frequencies identified using different methods and the theoretical values are shown in Table 6, where E(%) represents the relative error rate, and "-" indicates that a valid value cannot be obtained or the error is too large. The theoretical modal frequencies calculated using finite element analysis are used as reference values, and the theoretical reference values have been calibrated with experimental results obtained from accelerometers and other sensors multiple times. 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, and F t (Hz) represents the theoretical value. It should be noted that there may be some small differences between the theoretical value and the actual value. From the results, it can be seen that the EERH method can effectively identify the first six-order modes. Only the identification error of the fourth-order modal frequency is 12.96%. The errors in the identification results may be attributed to various reasons, such as bridge structure damage, unforeseen errors in the identification method, the influence of observation noise, etc. However, other methods cannot reliably calculate the first six-order modes, and only the obvious first-order and third-order modal frequencies can be calculated. The experimental results strongly prove the feasibility of the EERH method in structural health monitoring applications based on PPP-RTK monitoring data (with significant noise influence and non-stationary characteristics).

[0135] Table 6 Identification Results of Multimodal Frequencies Obtained Using Different Methods

[0136]

[0137] Table 7 Identification Results of Multimodal Frequencies from Multiple Data Sources

[0138]

[0139]

[0140] To demonstrate the generality of the method and study the reasons for errors in the process of identifying modal frequencies, the embodiments of the present invention applied the same method to extract multi-modal frequencies from the remaining three groups of data and calculated the average values of the four groups of experiments. The results of multiple identifications are shown in Table 7. The results of the four groups of experiments are roughly the same, and the identification difference of the third mode is the largest, reaching 5.49%, fully demonstrating the generality of the method. By calculating the average value, the occurrence of accidental errors can be effectively avoided and more robust results can be obtained. In the embodiments of the present invention, the maximum error of the average value is reduced by 2.43% compared with the results of the first experiment, and the average error is reduced by 0.33%. However, the identification results of the fourth-order mode have an error of about 10% relative to the reference value in each experiment, which proves that there is indeed such a frequency component in these signals. Therefore, the reasons of accidental errors and data influence can be excluded. The real reason for this phenomenon still needs further study. Abnormal modal frequencies may indicate changes in the bridge structure, so these identification results will be used as an important basis for judging whether the bridge has suffered structural damage.

[0141] The present invention mainly explores the feasibility and performance of PPP-RTK in the health monitoring of long-span bridge structures, and further proposes a multi-modal frequency identification method based on the displacement monitoring time series of PPP-RTK. The PPP-RTK positioning technology is applied in the displacement monitoring of the Wuhan Yangtze River Parrot Island Bridge, and the EERH method proposed in the embodiments of the present invention is used to extract multi-modal frequencies. The summary is as follows:

[0142] The feasibility and effectiveness of PPP-RTK based on the GNSS raw observation data of 11 reference stations in Wuhan and its surrounding cities are verified through several groups of experiments. The 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 the single-difference oblique ionospheric delay product and tropospheric delay product with similar accuracy, which makes them very suitable for enhancing PPP-RTK applications. The average convergence epochs of the three models are 3.1, 4.0 and 3.9 respectively. At the same time, the average convergence epochs of PPP-RTK positioning corrected by various model products are 3.7, 3.7 and 3.9 in the east, north and up directions respectively. In addition, the ambiguity fixation rate in each experiment exceeds 86%. The average RMS values after convergence of 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 in practical applications. PPP-RTK has significant potential and is superior to typical RTK and PPP-AR.

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

[0144] The effectiveness of the multi-modal frequency identification method was successfully verified through multiple groups of PPP-RTK monitoring data of the Wuhan Yangtze River Parrot Island 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 can effectively identify the first six-order modes in the PPP-RTK monitoring data of the Wuhan Yangtze River Parrot Island Bridge. The error of only the fourth-order modal frequency is 12.96%, and the remaining results are consistent with the theoretical values. However, other methods can only identify obvious low-order modes. Analyzing the modal identification results of all four groups of monitoring data shows that the results of different data sets are consistent. The maximum difference in the results of each experiment is only 5.49%. By calculating the average value of multiple groups of results, the maximum error of the average value is reduced by 2.43%, and the average error is reduced by 0.33%, highlighting the robustness and reliability of the proposed method.

[0145] The implementation basis of each embodiment of the present invention is achieved through programmed processing by a device with a processor function. Therefore, in engineering practice, the technical solutions and functions of each embodiment of the present invention are encapsulated into various modules. Based on this actual situation, on the basis of the above embodiments, an embodiment of the present invention provides a bridge multi-modal frequency identification system based on PPP-RTK, which is used to execute a bridge multi-modal frequency identification method based on PPP-RTK in the above method embodiments.

[0146] The system includes: a first main module for obtaining a file containing rapid satellite orbits, clocks, and observatory products; a second main module for performing undifferenced and uncombined PPP-AR model processing on local reference station network data in sequence based on the obtained file, and obtaining fixed slant 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 performing ambiguity resolution using the PPP-RTK model 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 band signals corresponding to different modes; a fifth main module for processing the 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 the stochastic decrement technique; a seventh main module for constructing a Hilbert analytic function based on the free decay signals to determine multimodal frequencies.

[0147] A bridge multimodal frequency identification system based on PPP-RTK provided by an embodiment of the present invention aims at the problem of identifying multimodal frequencies from GNSS monitoring data. By adopting the foregoing several modules and combining the empirical mode decomposition (EMD), stochastic decrement technique (RDT), and empirical band decomposition method of Hilbert transform (abbreviated as EERH), it can effectively identify multimodal frequencies, especially high-order modes, in PPP-RTK monitoring data with non-stationary characteristics and noise pollution.

[0148] It should be noted that the system embodiment provided by the present invention, in addition to being used to implement the method in the above method embodiment, is also used to implement the methods in other method embodiments provided by the present invention. The difference is only in setting corresponding functional modules. Its principle is basically the same as that of the above system embodiment provided by the present invention. As long as those skilled in the art, based on the above system embodiment, refer to the specific technical solutions in other method embodiments, obtain corresponding technical means by combining technical features, and the technical solutions constituted by these technical means, and on the premise of ensuring the practicability of the technical solutions, improve the modules in the above system embodiment to obtain corresponding system-like embodiments for implementing the methods in other method-like embodiments.

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

[0150] Based on the same inventive concept as the foregoing embodiments, an embodiment of the present invention further provides a non-transitory computer-readable storage medium storing computer instructions that cause a computer to execute the steps of the method for identifying multi-modal frequencies of a bridge based on PPP-RTK as described above.

[0151] In summary of the above embodiments, the present 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 multi-modal frequencies based on the displacement monitoring time series obtained by PPP-RTK. By verifying the PPP-RTK capabilities of three networks composed of 11 stations in Wuhan and its surrounding areas, three typical models for generating local single-difference slant ionospheric delay and tropospheric delay products are evaluated. Subsequently, PPP-RTK and the proposed multi-modal frequency identification method are applied to the structural health monitoring of the Wuhan Yangtze River Parrot Island Bridge. The results show that the positioning ability and multi-modal frequency identification effect of PPP-RTK are comparable to those of RTK. The multi-modal frequency identification method proposed by the present invention demonstrates excellent ability to identify the first six modal frequencies, showing excellent consistency with the reference values obtained by finite element method calculation and experimental calibration, far exceeding typical methods. Therefore, PPP-RTK has the potential to be 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 are not intended to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that they can still modify the technical solutions described in the foregoing embodiments, or perform equivalent replacements for some or all of the technical features; and these modifications or replacements 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 multi-modal frequency identification method based on PPP-RTK, characterized in that: include: Get files containing rapid satellite orbits, clocks, and observatory products; Based on the acquired files, the local reference station network data are processed by non-differential and non-combined PPP-AR models in turn, and the fixed slant ionospheric delay and fixed tropospheric delay are obtained through ambiguity resolution; The single-difference ionospheric and tropospheric products are calculated based on the interpolation of the ionosphere and troposphere, and the ambiguity resolution is realized based on the calculated single-difference ionospheric and tropospheric products using the PPP-RTK model to obtain the instantaneous centimeter-level high-precision positioning results; Decompose 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; Processing the frequency band signals of the different modes into stable intrinsic mode functions through empirical mode decomposition; The free decay signal is extracted from the selected intrinsic mode function using random decay technique; A Hilbert analytical function is constructed based on the free decay signal to determine the multi-modal frequency.

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

3. According to the PPP-RTK-based bridge multi-modal frequency identification method of claim 1, it is characterized in that: Processing the frequency band signals of different modes into stable intrinsic mode functions through empirical mode decomposition, comprising: Identify local peaks and valleys of the input signal; The cubic spline interpolation method is used to obtain the upper envelope and the lower envelope; A stationary intrinsic mode function is obtained when the number of extreme points and zero crossings differs by no more than one and the average value of the envelope formed by the local maximum and minimum points is always zero.

4. According to claim 3, a bridge multi-modal frequency identification method based on PPP-RTK is characterized in that: The method further comprises: A valid intrinsic mode function is selected according to a threshold value of the correlation coefficient of the intrinsic mode function.

5. According to the PPP-RTK-based bridge multi-modal frequency identification method of claim 1, it is characterized in that: The method further comprises: The partial ambiguity resolution strategy is used for ambiguity resolution.

6. A bridge multi-modal frequency identification system based on PPP-RTK, characterized in that: include: The first main module is used to obtain files containing rapid satellite orbits, clocks and observatory products; The second main module is used to process the local reference station network data in a non-differential and non-combined PPP-AR model in turn based on the acquired files, and obtain the fixed oblique ionospheric delay and the fixed tropospheric delay through ambiguity resolution; The third main module is used to calculate the single-difference ionosphere and troposphere products based on the interpolation of the ionosphere and troposphere, and to resolve the ambiguity based on the calculated single-difference ionosphere and troposphere 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 the instantaneous centimeter-level high-precision positioning results into a series of frequency band signals corresponding to different modes; A fifth main module, used for processing the frequency band signals of different modes into stable intrinsic mode functions through empirical mode decomposition; a sixth main module for extracting a free decay signal from a selected intrinsic mode function using a random decrement technique; The seventh main module is used to construct a Hilbert analytical function based on the free decay signal to determine the multi-modal frequency.

7. An execution device, characterized in that: The invention comprises a memory and a processor, wherein the memory stores program instructions executed by the processor, and the processor calls the program instructions to execute the steps of a bridge multi-modal frequency identification method based on PPP-RTK 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, and the computer instructions enable the computer to execute the steps of the bridge multi-modal frequency identification method based on PPP-RTK as described in any one of claims 1 to 5.

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