A GNSS bridge displacement monitoring method with additional finite element model spatial constraints

Abstract

This invention discloses a GNSS bridge displacement monitoring method with additional finite element model spatial constraints, comprising the following steps: setting positions corresponding to GNSS monitoring points in the finite element model, and calculating the baseline vector changes between these monitoring points in real time; collecting observation data of GNSS bridge monitoring points and constructing GNSS double-difference observation values ​​between each monitoring station and the reference station; introducing the baseline vectors between monitoring points obtained based on the finite element model as spatial constraints into the GNSS observation equations; solving the GNSS observation equations with additional finite element model spatial constraints using the Kalman filter method or the least squares method to obtain the bridge monitoring point displacement and ambiguity floating-point solutions, and their covariance matrices; fixing the ambiguity to integer solutions based on the ambiguity floating-point solutions and the covariance matrix; and outputting the GNSS bridge displacement after ambiguity fixation to obtain more stable and higher-precision bridge displacement monitoring results. This invention improves the accuracy, stability, and reliability of GNSS bridge health monitoring in complex environments.

Description

Technical Field

[0001] This invention relates to the field of GNSS high-precision bridge health monitoring technology, and in particular to a GNSS bridge displacement monitoring method with additional finite element model spatial constraints. Background Technology

[0002] During their service life, bridges are susceptible to horizontal and vertical displacement and deformation due to the combined effects of wind loads, vehicle loads, and temperature. High-precision monitoring of bridge displacement is crucial for ensuring bridge operational safety and transportation safety.

[0003] In the field of bridge health monitoring, GNSS (Global Navigation Satellite System) has become one of the main means of monitoring structural displacement and deformation due to its advantages of all-weather, continuous observation and high-precision positioning. However, the bridge structure itself and its above / surrounding environment (such as piers, guardrails, ramps, adjacent buildings and large vehicles) can cause GNSS signal blockage and severe multipath effects, leading to short-term abrupt changes or systematic errors in the observed values, thus significantly reducing the monitoring accuracy and stability of single stations or sparse station networks. Current improvement methods mainly adopt the fusion strategy of GNSS and inertial measurement units (IMU), which can reduce the impact of random noise and short-term blockage to a certain extent. However, they are still limited by factors such as sensor drift, time synchronization errors and complex calibration, making it difficult to achieve long-term high-precision monitoring of millimeter-level displacement and arcsecond-level attitude of long-span bridges.

[0004] A refined finite element (FE) structural model can characterize the stress-deformation response of a bridge under various loads (wind, vehicles, temperature, etc.) from both mechanical and structural geometric perspectives, exhibiting spatially correlated and physically interpretable displacement and stress fields. Organically coupling a high-precision finite element model with real-time GNSS observations provides physical priors and constraints for the observation model. The finite element model can serve as a spatial-mechanical constraint, helping to distinguish between displacements caused by actual structural deformation and anomalous observations caused by GNSS observation errors (such as multipath or local obstruction), thereby enabling the identification and elimination of observed values. Furthermore, the finite element model facilitates the input of physical quantities such as temperature field, wind pressure distribution, and traffic loads into the same solution framework, achieving integrated data assimilation and digital twin updates of "force-deformation-observation," which is of great significance for improving the physical consistency and fault diagnosis capabilities of long-term online monitoring. Currently, there is a lack of algorithms in published literature and engineering practice that can tightly integrate finite element models with high-precision GNSS solutions (such as RTK / PPP) in real-time or near-real-time environments.

[0005] Therefore, how to organically combine finite element models with GNSS monitoring data to further improve the accuracy and reliability of bridge displacement calculation is a technical problem that urgently needs to be solved. Summary of the Invention

[0006] Objective of the Invention: To address the shortcomings of existing technologies, this invention proposes a GNSS bridge displacement monitoring method with additional finite element model spatial constraints. By establishing a finite element model of the bridge, the displacement and deformation of the bridge under the coupled effects of wind, vehicles, and temperature are simulated to obtain baseline vector change information between various GNSS monitoring points on the bridge. This information is then used as a spatial constraint condition and introduced into the processing of GNSS observation data, thereby suppressing positioning deviations and anomalies caused by GNSS signal obstruction, multipath, and noise, and improving the accuracy and stability of GNSS bridge displacement monitoring results.

[0007] Technical solution: The present invention provides a GNSS bridge displacement monitoring method with additional finite element model spatial constraints, comprising the following steps:

[0008] 1) Select the nodes corresponding to the locations of the GNSS monitoring stations deployed on the bridge in the finite element model as observation points, calculate the displacement changes of the nodes caused by different temperature loads, wind loads, and vehicle loads, and obtain the baseline components between the monitoring stations.

[0009] 2) Based on the collected observation data of multi-constellation, multi-frequency carrier phase and pseudorange from the bridge GNSS monitoring station, construct the double-difference observation equations between the monitoring station and the reference station, as well as between satellites, and linearize the double-difference observation equations to obtain the linearized double-difference observation equations, namely the GNSS double-difference carrier phase and pseudorange observation equations.

[0010] 3) A GNSS observation model with additional finite element model spatial constraints is formed by the spatial constraints of the finite element model and the GNSS double-difference carrier phase.

[0011] 4) Solve the GNSS observation equations with additional finite element model spatial constraints to obtain the GNSS displacement and ambiguity floating-point solutions for the bridge monitoring points, as well as the variance-covariance matrix of the ambiguity floating-point solutions. ;

[0012] 5) Based on the floating-point solution of ambiguity and the updated variance-covariance matrix, fix the ambiguity as an integer solution; then convert the floating-point solution of ambiguity... The variance-covariance matrix of the ambiguity floating-point solution As input to the least squares downcorrelation adjustment method for ambiguity fixing, an integer solution for ambiguity is obtained; the displacement parameters are updated using the integer solution for ambiguity, and the displacement based on the integer solution for ambiguity is calculated as the GNSS bridge displacement after ambiguity fixing.

[0013] Step 1) includes the following steps:

[0014] Step 1.1) Temperature difference field Equivalent nodal forces are generated on the element:

[0015] (3)

[0016] in, This represents the equivalent nodal force vector for the element temperature load. Represents the unit volume. The strain-displacement matrix is... For the material constitutive matrix, The coefficient of thermal expansion of the material. Points inside the cell Temperature changes;

[0017] Substituting the obtained equivalent nodal force vector into equation (4), we get the first node. Second node :

[0018] (4)

[0019] in, The first node Extraction vectors corresponding to degrees of freedom For the second node Extraction vector corresponding to the degree of freedom; Represents the structural compliance matrix;

[0020] Step 1.2) The wind pressure distributed on the bridge The equivalent wind load nodal force vector is obtained. (5)

[0021] in, This represents the nodal force vector of the equivalent wind load. The unit's wind-receiving surface area. This is the element interpolation function, which maps distributed loads to the degrees of freedom of the nodes; Represents position Wind pressure distribution function varying over time;

[0022] Therefore, the first node under wind load is obtained. Second node Relative displacement changes : (6);

[0023] Step 1.3) Vehicle load is at several bridge deck locations. Concentrated load Function:

[0024] (7)

[0025] in, The equivalent nodal force vector of the vehicle load. For the first Concentrated loads on individual wheels or axles The position of the wheels or axles on the bridge. The interpolation function value;

[0026] Therefore, the first node under vehicle load is obtained. Second node relative displacement change : (8)

[0027] in, For a unit concentrated load acting at location At that time, the first node The static displacement response function; For a unit concentrated load acting at location At that time, the second node The static displacement response function;

[0028] Step 1.4) Obtain the wind-mill-temperature load on the first node. Second node b :

[0029] (9)

[0030] Baseline components between monitoring points (10)

[0031] in, Represents the baseline components in the station-centered horizontal coordinate system with the ground GNSS reference station as the origin. Represents the baseline component under no-load conditions. Represents the baseline displacement change caused by wind-mill-temperature load. The coordinate transformation matrix converts the baseline components from the bridge coordinate system represented in the finite element model to the station-centered horizontal coordinate system with the ground GNSS reference station as the origin.

[0032] In step 2), the linearized double-difference observation equation is obtained as follows:

[0033] (1)

[0034] in, For a pseudorange observation of a GNSS frequency, For a GNSS carrier phase observation at a frequency, the superscript is... Represents GNSS reference satellite, Represents satellites other than the GNSS reference satellite, subscript Represents the base station, subscript Representing the first monitoring station on the bridge, This represents the second monitoring station on the bridge. Represents the first monitoring station relative to the base station The baseline three-dimensional column components, Represents the second monitoring station relative to the base station The baseline three-dimensional column components, for Column vectors Represents the overall ambiguity throughout the week. This represents the noise in the observations. The linearized double-difference observation equation is the GNSS double-difference carrier phase and pseudorange observation equation.

[0035] In step 3), the finite element model from step 1) is used to obtain the first monitoring station a of the bridge. The baseline component is The spatial constraints of the finite element model are then expressed as:

[0036] (12)

[0037] This represents the first monitoring station a relative to the base station. The baseline components, This represents the second monitoring station b relative to the base station. The baseline components;

[0038] Assuming observation The double-difference observation equation for a satellite is expressed as follows: (13)

[0039] The observation vector in formula (13) Represented as

[0040] (14)

[0041] The coefficient matrix in formula (13) ,in , and Represented as:

[0042] (15)

[0043] (16)

[0044] (17)

[0045] in, Represents a three-dimensional row vector. represent The identity matrix; The coefficient matrix representing the displacement parameters. The coefficient matrix representing the ambiguity parameters. This represents the spatial constraint coefficient matrix obtained through the finite element model.

[0046] The column vector of parameters to be estimated in formula (13) for

[0047] (18)

[0048] in, , To observe noise, and it follows a normal distribution. ;

[0049] The covariance matrix is ​​represented as:

[0050] (19)

[0051] in, Represented by vector Each element is a diagonal matrix formed by the main diagonal elements; Formula (13) is the GNSS observation equation with additional finite element model spatial constraints.

[0052] In step 4), the Kalman filter method or the least squares method is used to solve the GNSS observation equations with additional finite element model spatial constraints.

[0053] Step 4) includes the following steps:

[0054] 4.1) Assumptions At time t, the state vector of the GNSS observation equation is Then the Kalman filter prediction stage obtains The state vector at time t is , This represents the state vector at time k predicted from the state vector at time k-1.

[0055] (20)

[0056] in, for Time to The state transition matrix at time t; Let be the process noise matrix, with a mean of 0 and a variance of . The normal distribution, i.e. ; Variance-covariance matrix in the prediction phase Represented as: (twenty one)

[0057] represent The variance-covariance matrix of the state vector at time step. represent Time to The state vector transition matrix at time t, denoted here as the identity matrix;

[0058] 4.2) During the update phase, the observation residuals The calculation is as follows:

[0059] (twenty two)

[0060] The representation constructed using formula (13) The coefficient matrix of the observation vector at each time step; The representative is constructed using formula (13). The coefficient matrix of the state vector at any given time;

[0061] The variance-covariance matrix corresponding to formula (22) for: (twenty three)

[0062] in, represent The transpose of the matrix, represent The noise matrix of the observations at time t; represent The variance-covariance matrix at time t;

[0063] Kalman filter gain matrix The calculation is as follows: (twenty four)

[0064] in, represent The inverse matrix;

[0065] Updated state vector for: (25)

[0066] Updated variance-covariance matrix for: (26)

[0067] Where E represents the identity matrix;

[0068] Obtain GNSS displacement And ambiguity floating-point solution .

[0069] In step 5), the updated variance-covariance matrix contains the variances and covariances of the displacement and ambiguity parameters:

[0070] (27)

[0071] Updated The variance-covariance matrix between the state vectors at time t. , , , , , , Representative parameters , , The variance and covariance matrix between them.

[0072] In step 5), , resolve ambiguity floating point and the variance and covariance matrix of the ambiguity floating-point solution N As input to the ambiguity fixing method—least squares downcorrelation adjustment—integer solutions for ambiguity are obtained. :

[0073] (28)

[0074] In step 5), LAMBDA is used to fix the ambiguity as an integer solution, and the Ratio threshold is 3.

[0075] In step 5), the displacement parameters are updated using the fuzzy integer solution, and the displacement based on the fuzzy integer solution is calculated. and :

[0076] (29)

[0077] represent Time Node The floating-point solution baseline component, represent Time Node The floating-point solution baseline component, The amount of correction represents the baseline component. , This represents the baseline vector after the ambiguity is fixed.

[0078] In step (3), the spatial displacement information between monitoring points obtained based on the finite element model is used as a pseudo-observation value, and the noise of the pseudo-observation value is set according to the accuracy of the finite element model.

[0079] Furthermore, step (3) introduces spatial constraints for the finite element model:

[0080] (2)

[0081] in, The first monitoring station of the bridge obtained through finite element model Second monitoring station The spatial three-dimensional column vector. This constraint will serve as a virtual observation equation, which, together with the GNSS double-difference carrier phase and pseudorange observation equations, constitutes a GNSS observation model with additional finite element model spatial constraints.

[0082] Working Principle: This invention provides a GNSS bridge displacement monitoring method with additional finite element model spatial constraints. The method sets positions corresponding to GNSS monitoring points within the finite element model and calculates baseline vector changes between these monitoring points in real time. It collects observation data from GNSS bridge monitoring points and constructs double-difference GNSS observations between each monitoring station and the base station. The baseline vector information between monitoring points obtained from the finite element model is used as a spatial constraint and introduced into the GNSS observation equations. The Kalman filter method or least squares method is used to solve the GNSS observation equations with additional finite element model spatial constraints, obtaining the bridge monitoring point displacement and ambiguity floating-point solutions, along with their covariance matrices. Based on the ambiguity floating-point solutions and the covariance matrix, the ambiguity is fixed to an integer solution. The GNSS bridge displacement calculation results with fixed ambiguity are output, resulting in more stable and higher-precision bridge displacement monitoring results.

[0083] The GNSS bridge health monitoring system with additional finite element model spatial constraints used in this invention includes:

[0084] Finite element model: used to output baseline vector change information between bridge monitoring stations in real time;

[0085] Observation module: used to construct double-difference observations between the monitoring station and the reference station, and between different satellites;

[0086] The parameterization module is used to add the baseline components obtained from the finite element model as spatial constraints to the GNSS observation model.

[0087] Solution module: Kalman filtering or least squares is used to solve the GNSS observation model;

[0088] Ambiguity fixing module: used to execute the LAMBDA algorithm and output ambiguity integer solutions;

[0089] Output module: Used to update position and attitude parameters using ambiguity integer solutions.

[0090] Beneficial effects: Compared with the prior art, the present invention has the following advantages:

[0091] (1) The monitoring accuracy of the present invention is higher: The present invention calculates the baseline component change between monitoring stations in real time through the bridge finite element model, and introduces the baseline component change as a spatial constraint into GNSS precision data processing, thereby correcting and avoiding the positioning deviation caused by GNSS in complex environment due to signal blockage, multipath effect and noise interference, and improving the accuracy and reliability of bridge displacement calculation.

[0092] (2) The stability of the bridge displacement monitoring results of the present invention is better: The physical constraints of the finite element model used in the present invention provide reliable prior information for GNSS observation, avoiding large fluctuations in the single GNSS solution results due to changes in the external environment, thereby improving the continuity and stability of displacement calculation.

[0093] (3) Adapting to complex working conditions: By comprehensively considering the coupling effect of wind load, vehicle load and temperature effect through the finite element model, the present invention maintains high monitoring accuracy under various complex operating conditions and is suitable for long-term health monitoring of long bridges in harsh environments.

[0094] (4) Significant integration advantages: This invention realizes the organic integration of numerical simulation method and GNSS measured data, giving full play to the ability of finite element model to characterize structural deformation law and the advantages of GNSS for real-time displacement monitoring, and overcoming the limitations of finite element model and GNSS when used alone.

[0095] (5) High engineering application value: The optimized GNSS displacement calculation results can be directly used for bridge structural health status assessment and safety early warning, improving the scientificity and reliability of operation and maintenance management, and has broad engineering application prospects. Attached Figure Description

[0096] Figure 1 This is a diagram showing the spatial baseline components of the bridge finite element model of the present invention.

[0097] Figure 2 This is a flowchart of the GNSS bridge displacement monitoring method with additional finite element model spatial constraints according to the present invention. Detailed Implementation

[0098] The technical solution of the present invention will be further described below with reference to the accompanying drawings.

[0099] like Figures 1 to 2 As shown, the GNSS bridge displacement monitoring method with additional finite element model spatial constraints of the present invention includes the following steps:

[0100] 1) In the finite element model of the bridge, nodes corresponding to the locations of GNSS monitoring stations deployed on the actual bridge are selected as observation points. The displacement changes of these nodes under different "temperature-wind-vehicle" loads are calculated in real time through the finite element model, including the horizontal, vertical, and three-dimensional displacement components; that is, the displacement changes of nodes caused by different temperature loads, wind loads, and vehicle loads are calculated through the finite element model, and the baseline components between monitoring stations are obtained.

[0101] Furthermore, by comparing the displacement values ​​of each node, the baseline components between different monitoring stations are obtained. .

[0102] Step 1) is as follows:

[0103] Step 1.1) The displacement change caused by temperature load is obtained as follows:

[0104] Temperature difference field Equivalent nodal forces are generated on the element:

[0105] (3)

[0106] in, This represents the equivalent nodal force vector for the element temperature load. Represents the unit volume. This is a strain-displacement matrix that correlates nodal displacements with element strains. This is the material constitutive matrix (elastic matrix), i.e., the stress-strain relationship matrix. The coefficient of thermal expansion of the material. For a point inside the unit Temperature changes.

[0107] Substituting the obtained equivalent nodal force vector into equation (4) yields the first node. Second node Relative displacement change under temperature load :

[0108] (4)

[0109] The first node Extraction vectors corresponding to degrees of freedom For the second node Extraction vector corresponding to the degree of freedom; It represents the structural flexibility matrix (the inverse of the stiffness matrix).

[0110] Step 1.2) The displacement change process caused by wind load is as follows:

[0111] Wind pressure distributed on the bridge The equivalent wind load nodal force vector is obtained. :

[0112] (5)

[0113] in, This represents the nodal force vector of the equivalent wind load. Unit wind-receiving surface area, This is the element interpolation function, which maps distributed loads to nodal degrees of freedom; Represents the wind pressure distribution function (as a function of location) (and changes over time).

[0114] Therefore, the first node under wind load is obtained. Second node Relative displacement changes :

[0115] (6)

[0116] Step 1.3) The displacement change process caused by vehicle load is as follows:

[0117] Vehicle loads are considered at several bridge deck locations. Concentrated load The combined effect can be described as follows:

[0118] (7)

[0119] in, The equivalent nodal force vector of the vehicle load. For the first Concentrated loads on individual wheels or axles The position of the wheels or axles on the bridge. This is the interpolation function value used to map concentrated loads to nodes.

[0120] Therefore, the first node under vehicle load is obtained. Second node relative displacement change :

[0121] (8)

[0122] in, Nodes under vehicle load , The relative displacement changes between them; and These represent the locations where the unit concentrated load acts. At that time, node , The static displacement response function.

[0123] In summary, the wind-mill-temperature load on the nodes , The overall displacement change is as follows:

[0124] (9)

[0125] The first bridge monitoring station obtained based on the finite element model Second monitoring station baseline components for:

[0126] (10)

[0127] in, The reference coordinate system is the station-centered horizontal coordinate system with the ground GNSS reference station as the origin. Represents the baseline component under no-load conditions. Represents the baseline displacement change caused by wind-mill-temperature load. This is a coordinate transformation matrix used to convert the baseline components from the bridge coordinate system represented in the finite element model to the station-centered horizontal coordinate system with the ground GNSS reference station as the origin.

[0128] Baseline components between monitoring points obtained by finite element model calculation This method not only reflects the overall deformation pattern of the bridge under the coupled effects of wind, vehicles, and temperature, but also provides reliable prior constraints for the spatial relationships between GNSS monitoring points. The baseline components between monitoring points extracted using this method will serve as important inputs for subsequent GNSS data fusion and optimization calculations.

[0129] 2) Based on the collected multi-constellation, multi-frequency carrier phase and pseudorange observation data from the bridge GNSS monitoring station, double-difference observation equations are constructed between the monitoring station and the reference station, as well as between satellites, to eliminate systematic errors caused by satellite clock bias and atmospheric delay. The double-difference observation equations are then linearized, resulting in the following linearized double-difference observation equations:

[0130] (1)

[0131] in, This represents a pseudorange observation value at a specific GNSS frequency. Represents the carrier phase observation value at a certain frequency of GNSS, superscript Represents GNSS reference satellite, Represents satellites other than the GNSS reference satellite, subscript Represents the base station, subscript This represents the first monitoring station located on the bridge. This represents the second monitoring station located on the bridge. Represents the first monitoring station relative to the base station The baseline three-dimensional column components, Represents the second monitoring station relative to the base station The baseline three-dimensional column components are usually represented as the East-North-High component with the reference station as the origin. Represents the corresponding coefficient matrix, which is Column vectors Represents the overall ambiguity throughout the week. This represents the noise in the observed values.

[0132] Furthermore, in step 2), the number of monitoring stations is ≥2, and the distance between the base station and the monitoring station is less than 5km.

[0133] (3) Set up the finite element model in step 1) to obtain the first monitoring station of the bridge. Second monitoring station The baseline component is The corresponding noise is The spatial constraints of the finite element model are expressed as follows:

[0134] (12)

[0135] Represents monitoring station a relative to the base station The baseline components, Represents monitoring station b relative to the base station The baseline component.

[0136] Assuming observation The double-difference observation equation for a satellite is expressed as follows:

[0137] (13)

[0138] The observation vector in formula (13) Represented as:

[0139] (14)

[0140] The coefficient matrix in formula (13) ,in , and Represented as:

[0141] (15)

[0142] (16)

[0143] (17)

[0144] in, Represents a three-dimensional row vector. represent The identity matrix. The coefficient matrix representing the displacement parameters. The coefficient matrix representing the ambiguity parameters. This represents the spatial constraint coefficient matrix obtained through the finite element model.

[0145] The column vector of parameters to be estimated in formula (13) for

[0146] (18)

[0147] in, , . To observe noise, and it follows a normal distribution. .

[0148] The covariance matrix is ​​represented as:

[0149] (19)

[0150] in, Represented by vector Each element is a diagonal matrix formed by the main diagonal elements. Thus, formula (13) is the GNSS observation equation with additional finite element model spatial constraints.

[0151] 4) Solving formula (13) uses Kalman filtering or least squares method. This invention takes Kalman filtering as an example to solve the GNSS observation equation with additional finite element model spatial constraints, and obtains the GNSS displacement and ambiguity floating-point solution of the bridge monitoring point, as well as the variance and covariance matrix of the ambiguity floating-point solution. .

[0152] Assumption At time t, the state vector of the GNSS observation equation is Then the Kalman filter prediction stage obtains State vector at time step for: This represents the state vector at time k predicted from the state vector at time k-1.

[0153] (20)

[0154] in, for Time to The state transition matrix at time t is represented as an identity matrix if it is modeled as a random walk process. Let be the process noise matrix, with a mean of 0 and a variance of . The normal distribution, i.e. The variance-covariance matrix during the prediction phase. Represented as:

[0155] (twenty one)

[0156] represent The variance-covariance matrix of the state vector at time step. represent Time to The state vector transition matrix at time t is represented here as the identity matrix.

[0157] During the update phase, the observed residuals The calculation is as follows:

[0158] (twenty two)

[0159] The representative is constructed using formula (13). The vector of observations at each time point, The representative is constructed using formula (13). The coefficient matrix of the state vector at any given time.

[0160] The variance-covariance matrix corresponding to formula (22) for:

[0161] (twenty three)

[0162] represent The transpose of the matrix, represent The noise matrix of the observations at time t; represent The variance-covariance matrix at time t;

[0163] Kalman filter gain matrix The calculation is as follows:

[0164] (twenty four)

[0165] represent inverse matrix

[0166] Updated state vector for:

[0167] (25)

[0168] Updated variance-covariance matrix The calculation is as follows:

[0169] (26)

[0170] E represents the identity matrix;

[0171] Thus, the GNSS displacement with additional finite element model spatial constraints is obtained. And ambiguity floating-point solution .

[0172] 5) Determine the ambiguity using floating-point resolution. and the variance and covariance matrix of the ambiguity floating-point solution N As input to the ambiguity fixing method - least squares reduced correlation adjustment method, the ambiguity integer solution is obtained; the displacement parameter is updated using the ambiguity integer solution, and the displacement based on the ambiguity integer solution is the GNSS bridge displacement after ambiguity fixing.

[0173] Based on the floating-point solution of ambiguity and the updated variance-covariance matrix, the ambiguity is fixed as an integer solution to improve the accuracy of GNSS displacement monitoring; specifically as follows: the updated variance-covariance matrix includes the variance and covariance of displacement and ambiguity parameters:

[0174] (27)

[0175] Updated The variance-covariance matrix between the state vectors at time t. , , , , , , Representative parameters , , The variance and covariance matrix between them.

[0176] in , resolve ambiguity floating point and the variance and covariance matrix of the ambiguity floating-point solution N As input to the ambiguity fixing method—Least-Squares Ambiguity Decorrelation (LAMBDA)—the following integer solutions for ambiguity are obtained:

[0177] (28)

[0178] in, This represents the integer ambiguity solution. When using LAMBDA to fix ambiguity, the Ratio threshold for determining whether the ambiguity is fixed is 3.

[0179] Update displacement parameters using fuzzy integer solutions, and calculate displacement based on fuzzy integer solutions. and :

[0180] (29)

[0181] represent Time Node The floating-point solution baseline component, represent Time Node The floating-point solution baseline component, The amount of correction represents the baseline component. , This represents the baseline vector after the ambiguity is fixed.

[0182] In step (5), the ambiguity fixing method adopts the least squares uncorrelation adjustment method; where the Ratio threshold is 3.

Claims

1. A GNSS bridge displacement monitoring method with additional finite element model spatial constraints, characterized in that, Includes the following steps: 1) Select the nodes corresponding to the locations of the GNSS monitoring stations deployed on the bridge in the finite element model as observation points, calculate the displacement changes of the nodes caused by different temperature loads, wind loads, and vehicle loads, and obtain the baseline components between the monitoring stations. 2) Based on the collected multi-constellation, multi-frequency carrier phase and pseudorange observation data of the bridge GNSS monitoring station, construct the double-difference observation equations between the monitoring station and the reference station, as well as between satellites, and linearize the double-difference observation equations to obtain the GNSS double-difference carrier phase and pseudorange observation equations. 3) A GNSS observation model with additional finite element model spatial constraints is constructed by the spatial constraints of the finite element model and the GNSS double-difference carrier phase and pseudorange observation equations. 4) Solve the GNSS observation equations with additional finite element model spatial constraints to obtain the GNSS displacement and ambiguity floating-point solutions for the bridge monitoring points, as well as the variance-covariance matrix of the ambiguity floating-point solutions. ; 5) Based on the floating-point solution of ambiguity and the updated variance-covariance matrix, the ambiguity is fixed as an integer solution; The ambiguity floating-point solution and its variance-covariance matrix are given. As input to the least squares downcorrelation adjustment method, a method for fixing ambiguity, we obtain integer solutions for ambiguity. The displacement parameters are updated using the integer solution of ambiguity, and the displacement based on the integer solution of ambiguity is the GNSS bridge displacement after the ambiguity is fixed.

2. The GNSS bridge displacement monitoring method with additional finite element model spatial constraints according to claim 1, characterized in that: Step 1) includes the following steps: Step 1.1) Temperature difference field Equivalent nodal forces are generated on the element: (3) in, This represents the equivalent nodal force vector for the element temperature load. Represents the unit volume. The strain-displacement matrix is... For the material constitutive matrix, The coefficient of thermal expansion of the material. Points inside the cell Temperature changes; Substituting the obtained equivalent nodal force vector into equation (4), we get the first node. Second node Relative displacement change under temperature load : (4) in, The first node Extraction vectors corresponding to degrees of freedom For the second node Extraction vector corresponding to the degree of freedom; Represents the structural compliance matrix; Step 1.2) The wind pressure distributed on the bridge The equivalent wind load nodal force vector is obtained. (5) in, This represents the nodal force vector of the equivalent wind load. The unit's wind-receiving surface area. This is the element interpolation function, which maps distributed loads to the degrees of freedom of the nodes; Represents position Wind pressure distribution function varying over time; Therefore, the first node under wind load is obtained. Second node Relative displacement changes : (6); Step 1.3) Vehicle load is at several bridge deck locations. Concentrated load Function: (7) in, The equivalent nodal force vector of the vehicle load. For the first Concentrated loads on individual wheels or axles The position of the wheels or axles on the bridge. The interpolation function value; Therefore, the first node under vehicle load is obtained. Second node relative displacement change : (8) in, For a unit concentrated load acting at location At that time, the first node The static displacement response function; For a unit concentrated load acting at location At that time, the second node The static displacement response function; Step 1.4) Obtain the wind-mill-temperature load on the first node. Second node Comprehensive displacement change : (9) Baseline components between monitoring points (10) in, Represents the baseline components in the station-centered horizontal coordinate system with the ground GNSS reference station as the origin. Represents the baseline component under no-load conditions. Represents the baseline displacement change caused by wind-mill-temperature load. The coordinate transformation matrix converts the baseline components from the bridge coordinate system represented in the finite element model to the station-centered horizontal coordinate system with the ground GNSS reference station as the origin.

3. The GNSS bridge displacement monitoring method with additional finite element model spatial constraints according to claim 1, characterized in that: In step 2), the linearized double-difference observation equation is obtained as follows: (1) in, For a pseudorange observation of a GNSS frequency, For a GNSS carrier phase observation at a frequency, the superscript is... Represents GNSS reference satellite, Represents satellites other than the GNSS reference satellite, subscript Represents the base station, subscript Representing the first monitoring station on the bridge, This represents the second monitoring station on the bridge. Represents the first monitoring station relative to the base station The baseline three-dimensional column components, Represents the second monitoring station relative to the base station The baseline three-dimensional column components, for Column vector, Represents the overall ambiguity throughout the week. This represents the noise in the observed values.

4. The GNSS bridge displacement monitoring method with additional finite element model spatial constraints according to claim 1, characterized in that: In step 3), the finite element model from step 1) is used to obtain the first monitoring station a of the bridge. The baseline components are The spatial constraints of the finite element model are then expressed as: (12) This represents the first monitoring station a relative to the base station. The baseline components, This represents the second monitoring station b relative to the base station. The baseline components; Assuming observation The double-difference observation equation for a satellite is expressed as follows: (13) The observation vector in formula (13) Represented as (14) The coefficient matrix in formula (13) ,in , and Represented as: (15) (16) (17) in, Represents a three-dimensional row vector. represent The identity matrix; The coefficient matrix representing the displacement parameters. The coefficient matrix representing the ambiguity parameters. This represents the spatial constraint coefficient matrix obtained through the finite element model. The column vector of parameters to be estimated in formula (13) for (18) in, , To observe noise, and it follows a normal distribution. ; The covariance matrix is ​​represented as: (19) in, Represented by vector Each element is a diagonal matrix formed by the main diagonal elements; Formula (13) is the GNSS observation equation with additional finite element model spatial constraints.

5. The GNSS bridge displacement monitoring method with additional finite element model spatial constraints according to claim 1, characterized in that: In step 4), the Kalman filter method or the least squares method is used to solve the GNSS observation equations with additional finite element model spatial constraints.

6. The GNSS bridge displacement monitoring method with additional finite element model spatial constraints according to claim 5, characterized in that: Step 4) includes the following steps: 4.1) Assumptions At time t, the state vector of the GNSS observation equation is Then the Kalman filter prediction stage obtains The state vector at time t is , This represents the state vector at time k predicted from the state vector at time k-1. (20) in, for Time to The state transition matrix at time t; Let be the process noise matrix, with a mean of 0 and a variance of . The normal distribution, i.e. ; Variance-covariance matrix in the prediction phase Represented as: (twenty one) represent The variance-covariance matrix of the state vector at time step. represent Time to The state vector transition matrix at time t, denoted here as the identity matrix; 4.2) During the update phase, the observation residuals The calculation is as follows: (22) The representation constructed using formula (13) The coefficient matrix of the observation vector at each time step; The representative is constructed using formula (13). The coefficient matrix of the state vector at any given time; The variance-covariance matrix corresponding to formula (22) for: (twenty three) in, represent The transpose of the matrix, represent The noise matrix of the observations at time t; represent The variance-covariance matrix at time t; Kalman filter gain matrix The calculation is as follows: (twenty four) in, represent The inverse matrix; Updated state vector for: (25) Updated variance-covariance matrix for: (26) Where E represents the identity matrix; Obtain GNSS displacement And ambiguity floating-point solution .

7. The GNSS bridge displacement monitoring method with additional finite element model spatial constraints according to claim 1, characterized in that: In step 5), the updated variance-covariance matrix contains the variances and covariances of the displacement and ambiguity parameters: (27) Updated The variance-covariance matrix between the state vectors at time t. , , , , , , Representative parameters , , The variance and covariance matrix between them.

8. The GNSS bridge displacement monitoring method with additional finite element model spatial constraints according to claim 1, characterized in that: In step 5), , resolve ambiguity floating point and the variance and covariance matrix of the ambiguity floating-point solution N As input to the ambiguity fixing method—least squares downcorrelation adjustment—integer solutions for ambiguity are obtained. : (28)。 9. The GNSS bridge displacement monitoring method with additional finite element model spatial constraints according to claim 1, characterized in that: In step 5), LAMBDA is used to fix the ambiguity as an integer solution, and the Ratio threshold is 3.

10. The GNSS bridge displacement monitoring method with additional finite element model spatial constraints according to claim 1, characterized in that: In step 5), the displacement parameters are updated using the fuzzy integer solution, and the displacement based on the fuzzy integer solution is calculated. and : (29) represent Time Node The floating-point solution baseline component, represent Time Node The floating-point solution baseline component, The amount of correction represents the baseline component. , This represents the baseline vector after the ambiguity is fixed.

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