Modeling method of displacement vector dynamic space model based on GNSS (Global Navigation Satellite System) platform

Abstract

The invention provides a displacement vector dynamic space model modeling method based on a GNSS platform. The displacement vector dynamic space model modeling method comprises the following steps that S1, initial point position coordinates X1 of all observation stations are obtained and stored through GNSS satellite navigation signal receiving equipment; s2, after a data acquisition period T0, obtaining and storing a new observation station coordinate X2; s3, defining the direction of the Cartesian coordinate system; s4, obtaining a spatial trend structure function based on the displacement vector data of each observation station and the initial observation station coordinate X1; s5, performing detrending processing on the displacement vector data, and calculating a spatial autocorrelation function of the data; s6, establishing a displacement vector space distribution model in x, y and z directions, and obtaining displacement vectors of each non-direct measurement point in the x, y and z directions in the space; s7, calculating a total displacement vector of each non-direct measurement point; and S8: updating the initial point position coordinate of each observation station as X2, taking X2 as a new initial point position coordinate X1, and repeating the steps S2 to S7. According to the invention, dynamic and high-precision spatial modeling of the displacement vector is realized.

Description

Technical Field

[0001] The present invention relates to the technical field of engineering monitoring, and in particular to a displacement vector dynamic space modeling method based on a GNSS platform. Background Art

[0002] In traditional intelligent monitoring, data space modeling is mainly implemented through the following steps: First, select devices such as resistive displacement sensors, capacitive displacement sensors, inductive displacement sensors, and photoelectric displacement sensors, and install these sensors at specific locations of the engineering structure to monitor displacement data. Then, the sensor starts working to collect displacement quantity (scalar displacement) data. These data are transmitted to the data processing center or monitoring system. Then, in the data processing center, the collected scalar displacement data is preliminarily sorted and analyzed, and the spatial distribution of monitoring data is established using spatial modeling methods. Among them, the initial measuring station coordinates are used as the known point coordinates in the interpolation calculation.

[0003] How to use scattered monitoring data to construct a spatial distribution model of displacement is a technical problem that needs to be solved in intelligent monitoring. At present, there are two main technical difficulties in spatial modeling of displacement:

[0004] (1) Displacement is a vector with directional characteristics. The spatial distribution model of displacement should fully reflect the directionality of displacement, which is helpful for a more comprehensive engineering risk assessment, such as more accurately determining the potential sliding direction of a landslide. Traditional intelligent monitoring sensors, such as resistive displacement sensors, capacitive displacement sensors, inductive displacement sensors, and photoelectric displacement sensors, can usually only monitor the amount of displacement (i.e., scalar displacement), but ignore the directionality of displacement.

[0005] (2) Compared with the spatial modeling of other objects (such as atmospheric monitoring data), the spatial modeling of displacement is accompanied by the dynamic change of the coordinates of the measuring points, that is, as the displacement changes, the coordinates of the measuring points will also change. Since spatial coordinates are important parameters in spatial modeling, the update of coordinates should be fully considered when performing spatial modeling of displacement. Traditional displacement sensing equipment cannot locate and update the coordinate information of the measuring station.

[0006] Based on the above two points, there is still a lack of effective methods and models in constructing displacement spatial distribution models. To this end, the present invention proposes a displacement vector dynamic spatial modeling method based on a GNSS platform. Summary of the invention

[0007] The purpose of the present invention is to propose a displacement vector dynamic spatial modeling method based on a GNSS platform, which effectively realizes the dynamic and high-precision spatial modeling of the displacement vector by organically combining the GNSS real-time positioning technology with the unbiased interpolation technology.

[0008] To achieve the above object, the technical solution of the present invention is: a displacement vector dynamic space modeling method based on a GNSS platform, comprising the following steps:

[0009] S1: a certain number of GNSS satellite navigation signal receiving devices are dispersedly arranged to obtain and store the initial point coordinates X1 of each measuring station; X1 is a matrix for storing the initial point coordinates of each measuring station; the point coordinates are three-dimensional coordinates in the x, y and z directions;

[0010] S2: After a data collection cycle T0, obtain and store the new station coordinates X2;

[0011] S3: Define the direction of the Cartesian coordinate system, calculate the displacement vector of each measuring station in the x, y and z directions based on X1 and X2, and define the direction by the positive and negative signs;

[0012] S4: Based on the displacement vector data of each measuring station and the initial measuring station coordinate X1, the overall distribution trend of the displacement vector of each measuring station in space is analyzed to obtain the spatial trend structure function;

[0013] S5: Detrending the displacement vector data and calculating the spatial autocorrelation function of the data;

[0014] S6: Based on the unbiased interpolation technology and the initial point coordinates X1, the spatial distribution models of the displacement vectors in the x, y and z directions are established respectively, and the predicted displacement vectors in the x, y and z directions of each point in the space that is not directly measured are obtained;

[0015] S7: using a spatial geometry method, based on the predicted displacement vectors of each indirect measurement point in the space in the x, y and z directions, calculate the predicted total displacement vector of each indirect measurement point;

[0016] S8: Update the initial point coordinates of each measuring station to X2, use X2 as the new initial point coordinates X1, and repeat S2 to S7 to achieve dynamic spatial modeling of the displacement vector.

[0017] Preferably, the spatial trend structure function of S4 adopts a linear regression function, and after the order of the linear regression function is determined by successively comparing the fitting effects of linear functions of each order, the parameters of the linear regression function are calculated based on the least squares method.

[0018] Preferably, the linear regression function determines the order by successively comparing the fitting effects of linear functions of different orders:

[0019] The fitting effect of the trend function is judged based on the leave-one-out crossover method, and the leave-one-out crossover coefficient S cv As the basis for judgment, S cvThe larger the value, the better the fitting effect of the trend function:

[0020]

[0021] In the formula, The residual vector representing the data is equal to the displacement vector of each station minus the corresponding spatial trend structure function value; n is the total number of stations;

[0022] At the same time, we can judge whether the trend function is overfitting by using the Wald statistic and the interpolation P of the F distribution. F Make a judgment, when P F When >0.05, it is considered that the order of the spatial trend structure function is too high and there is an overfitting problem;

[0023] According to S cv and P F The fitting effects of linear functions of different orders are compared successively to determine the most appropriate order of linear regression function.

[0024] Preferably, the detrending process in S5 is to use the monitoring data minus the value of the trend structure function, which is calculated by the following formula:

[0025] z(X)=u(X)+ε(X)(2)

[0026] Where X represents the point coordinates (x, y, z); z(X) represents the displacement vector data at coordinate X; u(X) represents the trend structure function, obtained by S4; ε(X) represents the regression deviation after detrending.

[0027] Preferably, the spatial autocorrelation function in S5 adopts a theoretical spatial autocorrelation function, including any one of an exponential function, a Gaussian function, and a Matérn equation.

[0028] Preferably, the spatial autocorrelation function in S5 is in the form of a Gaussian function, specifically:

[0029]

[0030] In the formula, τ x , τ y and τ z represents the distance between any two points in the x, y and z directions; ρ is the spatial autocorrelation coefficient; θ x ,θ y and θ z It represents the spatial autocorrelation distance parameter of spatial data in the x, y and z directions. The subscript r indicates that when predicting displacement vectors in different directions, the autocorrelation coefficient and spatial autocorrelation distance parameter are different.

[0031] Preferably, the establishment of the spatial distribution model of the displacement vectors in the x, y and z directions in S6 is specifically as follows:

[0032] S6.1. Calculate the covariance moment V0 between the measuring station positions corresponding to the x, y and z directions, and the covariance matrix V between the measuring station and the points not directly monitored. c :

[0033]

[0034] Where ρ represents the autocorrelation coefficient, which is calculated by Formula 3; d represents the number of measuring stations; n represents the number of points not directly monitored; σ represents the standard deviation of the data in the x-direction, y-direction, or z-direction, which is obtained from the displacement vectors in the x-direction, y-direction, or z-direction obtained from all measuring stations;

[0035] S6.2. The covariance moments V0 and V corresponding to the x, y and z directions are c Substitute them into formula 4 to obtain the vector β containing the interpolation weight corresponding to the x, y and z directions:

[0036]

[0037] Where l is a vector whose elements are all 1, λ represents the Lagrange multiplier, and Vc(k) is the kth column of the covariance matrix Vc;

[0038] S6.3, using the vectors β corresponding to the x, y and z directions, calculate the coordinates X of the unmeasured point p The predicted deviation ε(X p ) x,p ,ε(X p ) y,p ,ε(X p ) z,p :

[0039]

[0040] Where the subscript r is used to refer to any of the x, y, and z directions; ε r represents a vector, which contains the regression deviation of the displacement vector in the r direction monitored by each measuring station, calculated by formula 2;

[0041] S6.4, based on the predicted deviation ε(X p ) x,p ,ε(X p ) y,p ,ε(X p ) z,p , respectively obtain the coordinates X of the points not directly measured p The prediction results in the x, y and z directions are p )x,p 、z(X p ) y,p 、z(X p ) z,p , that is, the displacement vector in the x, y, and z directions at the coordinate point p:

[0042] z(X p ) r,p =u r (X p )+ε(X p ) r,p (6)

[0043] In the formula, u r (.) represents the trend structure function in the r direction.

[0044] Compared with the prior art, the present invention has the following beneficial effects:

[0045] The method of the present invention uses unbiased interpolation technology as the basis for spatial modeling of displacement, and combines the function of the GNSS device platform to measure point coordinates in real time, effectively solving the problem existing in traditional displacement spatial modeling technology, that is, when the position of the measuring station changes, the known point coordinates in the interpolation calculation cannot be updated in time. In addition, the present invention uses the real-time point coordinate measurement function of the GNSS device and combines the spatial geometry calculation method to successfully solve the problem that the displacement direction is difficult to consider in displacement spatial modeling.

[0046] In summary, this method effectively realizes the dynamic and high-precision spatial modeling of displacement vectors by organically combining GNSS real-time positioning technology with unbiased interpolation technology. BRIEF DESCRIPTION OF THE DRAWINGS

[0047] Figure 1 The figure is a flow chart of the method of the present invention. DETAILED DESCRIPTION

[0048] The following is combined with Figure 1 , the technical solution of the present invention is specifically described.

[0049] The present invention proposes a displacement vector dynamic space modeling method based on a GNSS platform, comprising the following steps:

[0050] S1: A certain number of GNSS satellite navigation signal receiving devices are dispersedly arranged to obtain and store the initial point coordinates X1 of each measuring station. X1 is a matrix used to store the initial point coordinates of each measuring station. The point coordinates are three-dimensional coordinates in the x, y and z directions;

[0051] S2: After a data collection cycle, obtain and store the new station coordinates X2;

[0052] S3: Define the direction of the Cartesian coordinate system, calculate the displacement vector of each measuring station in the x, y and z directions based on X1 and X2, and define the direction by the positive and negative signs;

[0053] S4: Based on the displacement vector data of each measuring station and the initial measuring station coordinate X1, the overall distribution trend of the displacement vector of each measuring station in space is analyzed to obtain the spatial trend structure function;

[0054] S5: Detrending the displacement vector data and calculating the spatial autocorrelation function of the data;

[0055] S6: Based on the unbiased interpolation technology and the initial station coordinates X1, the spatial distribution models of displacement vectors in the x, y and z directions are established respectively, and the predicted displacement vectors of each potential point (or point not directly measured) in the space in the x, y and z directions are obtained;

[0056] S7: using a spatial geometry method, based on the predicted displacement vectors of each indirect measurement point in the space in the x, y and z directions, calculate the predicted total displacement vector of each indirect measurement point;

[0057] S8: Update the coordinates of each measuring station to X2, use X2 as the new initial coordinate, and repeat S2 to S7 to achieve dynamic spatial modeling of the displacement vector.

[0058] Each step is described in detail below.

[0059] S1. A certain number of GNSS satellite navigation signal receiving devices are dispersedly arranged to obtain and store the initial point coordinates X1 of each measuring station. X1 is a matrix used to store the initial point coordinates of each measuring station. The point coordinates are three-dimensional coordinates in the x, y and z directions. The present invention does not limit the type of GNSS satellite navigation signal receiving device used, nor does it limit the method of GNSS measuring point coordinates. The arrangement of the measuring stations should be arranged according to the actual engineering conditions, and there is no limitation on the arrangement of the measuring stations.

[0060] S2. After a data collection cycle, obtain and store the new station coordinates X2. The data collection cycle T0 is set by the user according to the needs.

[0061] S3. Define the direction of the Cartesian coordinate system, calculate the displacement vector of each measuring station in the x, y and z directions based on X1 and X2, and define the direction by positive and negative signs. The Cartesian coordinate system is a mathematical three-dimensional Cartesian coordinate system, where x is the horizontal direction in the plane, y is the vertical direction in the plane, and z is the direction perpendicular to the xy plane. The positive and negative nature of the displacement direction is achieved by defining the positive direction of the coordinate. For example, in the x direction, moving to the right is defined as positive, and moving to the left is defined as negative.

[0062] S4. Based on the displacement vector data of each measuring station and the initial measuring station coordinate X1, the overall distribution trend of the displacement vector of each measuring station in space is analyzed to obtain the spatial trend structure function. The calculation of the spatial trend function can be achieved through regression analysis. The regression function can generally adopt a linear function (linear polynomial equation). When calculating, the order of the linear regression function must first be determined. After the form of the linear regression function is determined, the parameters of the regression function can be calculated based on the least squares method. The method of the present invention determines the order of the regression function according to the following principles:

[0063] The present invention determines the fitting effect of the trend function based on the leave-one-out crossover method, wherein the leave-one-out crossover coefficient S cv As the basis for judgment, S cv The larger the value, the better the fitting effect of the trend function:

[0064]

[0065] In formula 1, Residual vector represents the data, which is equal to the displacement vector of each station minus the corresponding spatial trend structure function value; n is the total number of stations. In addition, it is also necessary to determine whether the trend function has an overfitting problem. In this regard, the interpolation P of the Wald statistic and the F distribution can be used. F Make a judgment, when P F When >0.05, it can be considered that the order of the spatial trend structure function is too high and there is an overfitting problem. According to the above parameters, the fitting effects of linear functions of different orders are compared one by one to determine the most suitable linear regression function. The specific process is as follows:

[0066] Determine a smaller order i and determine P based on the order i F and S cv If P F If >0.05, the order is reduced. Otherwise, the order is increased to i+1, and the S after the increase is compared. cv Value, if S cv Increased and its P F If the value meets the requirements, continue to upgrade until S cv (i+1) cv (i) or P F >0.05.

[0067] S5. Detrend the displacement vector data and calculate the spatial autocorrelation function of the data. Detrend refers to subtracting the value of the trend function from the monitoring data, which can be calculated by the following formula:

[0068] z(X)=u(X)+ε(X)(2)

[0069] ​In the above formula, X represents the point coordinates (x, y, z); z(X) represents the monitoring data at coordinate X, that is, the displacement vector data of S3; u(X) represents the trend structure function, which is obtained from S4; ε(X) represents the regression deviation after detrending.

[0070] The spatial autocorrelation function form of the data may adopt a theoretical spatial autocorrelation function, such as an exponential function and a Gaussian function, or may adopt a Matérn equation with a flexible control mechanism. The patent of the present invention does not limit the form of the spatial autocorrelation function.

[0071] The calculation of spatial autocorrelation function mainly involves the calculation of parameters in the spatial autocorrelation function. For example, the exponential function and Gaussian function need to calculate the "spatial autocorrelation distance" parameter in the function. The Matérn equation needs to calculate the formal parameters of the equation control equation form and the spatial autocorrelation distance parameter. The calculation of parameters in the equation can be done by optimizing calculation methods, such as the maximum likelihood estimation method.

[0072] This embodiment takes the Gaussian function as an example:

[0073]

[0074] In formula 3, τ x , τ y and τ z represents the distance between any two points in the x, y and z directions; ρ is the spatial autocorrelation coefficient; θ x ,θ y and θ z It represents the spatial autocorrelation distance parameter of spatial data in the x, y and z directions. The subscript r indicates that when predicting displacement vectors in different directions, the autocorrelation coefficient and spatial autocorrelation distance parameter are different.

[0075] S6. Based on the unbiased interpolation technology and the initial station coordinates X1, the displacement vector spatial distribution models in the x, y and z directions are established respectively to obtain the displacement vectors in the x, y and z directions of each potential point (or point not directly measured) in the space. In this step, the unbiased interpolation technology is used to obtain the displacement vector spatial distribution model in the x, y and z directions, and the calculation method and steps are consistent (Formulas 4, 5 and 6).

[0076] The following is an explanation of the steps of the modeling method using the vector displacement in the x direction as an example:

[0077]

[0078] z(X p ) x,p =u(X p )+ε(X p ) x,p (6)

[0079] In the above formula, z(X p ) x,p Indicates that the coordinates of the point X are not directly measured p The prediction result at ε x represents a vector, which contains the vector displacement regression deviation in the x direction monitored by each station, calculated by formula 2; ε(X p ) x,p Indicates the coordinates of the unmeasured point X p The predicted deviation at ; β is a vector containing interpolation weights; l is a vector whose elements are all 1; λ represents the Lagrange multiplier; V0 represents the covariance matrix between the station positions; V c Vc represents the covariance matrix between the measuring station and the points not directly monitored, ( k ) is the kth column of the covariance matrix Vc. V0 and V c They are calculated by the following formulas:

[0080]

[0081] In the above formula, ρ represents the autocorrelation coefficient, which is calculated by Formula 3; d represents the number of measuring stations; n represents the number of points not directly monitored; σ represents the standard deviation of the data, which is obtained by the x-direction displacement vector obtained from all measuring stations.

[0082] S7, using a spatial geometry method, based on the displacement vectors of each point in the space in the x, y and z directions, calculate the total displacement vector of each point. The calculation method used in this step is the spatial geometry and vector calculation method at the middle school stage, and the calculation method is relatively simple, so it will not be described in detail here.

[0083] S8, update the coordinates of each measuring station to X2, use X2 as the new initial coordinate, and repeat S2 to S7 to achieve dynamic spatial modeling of the displacement vector. In this step, the number of repetitions can be determined by the user according to the specific engineering situation and requirements.

[0084] The present invention relies on the function of real-time measurement of point coordinates possessed by the GNSS equipment platform, uses spatial geometry calculation methods, calculates vector displacement based on coordinates, and combines unbiased interpolation technology to achieve spatial distribution modeling of vector displacement.

[0085] The present invention utilizes the real-time point coordinate measurement function of the GNSS device and combines it with the unbiased interpolation estimation technology to realize the dynamic update of the measuring station coordinates in the displacement space modeling process, effectively solving the problem in the traditional displacement space modeling technology that when the measuring station position changes, the known point coordinates in the interpolation calculation cannot be updated.

[0086] The above are preferred embodiments of the present invention. Any changes made according to the technical solution of the present invention, as long as the resulting functions do not exceed the scope of the technical solution of the present invention, belong to the protection scope of the present invention.

Claims

1. A displacement vector dynamic space modeling method based on a GNSS platform, characterized in that: The following steps are involved: S1: a certain number of GNSS satellite navigation signal receiving devices are dispersedly arranged to obtain and store the initial point coordinates X1 of each measuring station; X1 is a matrix for storing the initial point coordinates of each measuring station; the point coordinates are three-dimensional coordinates in the x, y and z directions; S2: After a data collection cycle T0, obtain and store the new station coordinates X2; S3: Define the direction of the Cartesian coordinate system, calculate the displacement vector of each measuring station in the x, y and z directions based on X1 and X2, and define the direction by the positive and negative signs; S4: Based on the displacement vector data of each measuring station and the initial measuring station coordinate X1, the overall distribution trend of the displacement vector of each measuring station in space is analyzed to obtain the spatial trend structure function; S5: Detrending the displacement vector data and calculating the spatial autocorrelation function of the data; S6: Based on the unbiased interpolation technology and the initial point coordinates X1, the spatial distribution models of the displacement vectors in the x, y and z directions are established respectively, and the predicted displacement vectors in the x, y and z directions of each point in the space that is not directly measured are obtained; S7: using a spatial geometry method, based on the predicted displacement vectors of each indirect measurement point in the space in the x, y and z directions, calculating the predicted total displacement vector of each indirect measurement point; S8: Update the initial point coordinates of each measuring station to X2, use X2 as the new initial point coordinates X1, and repeat S2 to S7 to achieve dynamic spatial modeling of the displacement vector.

2. The displacement vector dynamic space modeling method based on the GNSS platform according to claim 1 is characterized in that: The spatial trend structure function of S4 adopts a linear regression function. After the order of the linear regression function is determined by successively comparing the fitting effects of linear functions of each order, the parameters of the linear regression function are calculated based on the least squares method.

3. The displacement vector dynamic space modeling method based on the GNSS platform according to claim 2 is characterized in that: The linear regression function determines the order by successively comparing the fitting effects of linear functions of various orders: The fitting effect of the trend function is judged based on the leave-one-out crossover method, and the leave-one-out crossover coefficient S cv As the basis for judgment, S cv The larger the value, the better the fitting effect of the trend function: In the formula, The residual vector representing the data is equal to the displacement vector of each station minus the corresponding spatial trend structure function value; n is the total number of stations; At the same time, we can judge whether the trend function is overfitting by using the Wald statistic and the interpolation P of the F distribution. F Make a judgment, when P F When >0.05, it is considered that the order of the spatial trend structure function is too high and there is an overfitting problem; According to S cv and P F The fitting effects of linear functions of different orders are compared successively to determine the most appropriate order of linear regression function.

4. The displacement vector dynamic space modeling method based on the GNSS platform according to claim 1 is characterized in that: The detrending process in S5 is to use the monitoring data to subtract the value of the trend structure function, which is calculated by the following formula: z(X)=u(X)+ε(X) (2) Where X represents the point coordinates (x, y, z); z(X) represents the displacement vector data at coordinate X; u(X) represents the trend structure function, obtained by S4; ε(X) represents the regression deviation after detrending.

5. The displacement vector dynamic space modeling method based on the GNSS platform according to claim 1 is characterized in that: The spatial autocorrelation function in S5 adopts a theoretical spatial autocorrelation function, including any one of an exponential function, a Gaussian function, and a Matérn equation.

6. The displacement vector dynamic space modeling method based on the GNSS platform according to claim 4 is characterized in that: The spatial autocorrelation function in S5 adopts the form of Gaussian function, specifically: In the formula, τ x , τ y and τ z represents the distance between any two points in the x, y and z directions; ρ is the spatial autocorrelation coefficient; θ x ,θ y and θ z It represents the spatial autocorrelation distance parameter of spatial data in the x, y and z directions. The subscript r indicates that when predicting displacement vectors in different directions, the autocorrelation coefficient and spatial autocorrelation distance parameter are different.

7. The method for modeling a displacement vector dynamic space model based on a GNSS platform according to claim 6, characterized in that: The establishment of the spatial distribution model of the displacement vectors in the x, y and z directions in S6 is specifically as follows: S6.

1. Calculate the covariance moment V0 between the measuring station positions corresponding to the x, y and z directions, and the covariance matrix V between the measuring station and the points not directly monitored. c : Where ρ represents the autocorrelation coefficient, which is calculated by Formula 3; d represents the number of measuring stations; n represents the number of points not directly monitored; σ represents the standard deviation of the data in the x-direction, y-direction, or z-direction, which is obtained from the displacement vectors in the x-direction, y-direction, or z-direction obtained from all measuring stations; S6.

2. The covariance moments V0 and V corresponding to the x, y and z directions are c Substitute them into formula 4 to obtain the vector β containing the interpolation weight corresponding to the x, y and z directions: Where l is a vector whose elements are all 1, λ represents the Lagrange multiplier, and V c (k) is the kth column of the covariance matrix Vc; S6.3, using the vectors β corresponding to the x, y and z directions, calculate the coordinates X of the unmeasured point p The predicted deviation ε(X p ) x,p ,ε(X p ) y,p ,ε(X p ) z,p : Where the subscript r is used to refer to any of the x, y, and z directions; ε r represents a vector, which contains the regression deviation of the displacement vector in the r direction monitored by each measuring station, calculated by formula 2; S6.4, based on the predicted deviation ε(X p ) x,p ,ε(X p ) y,p ,ε(X p ) z,p , respectively obtain the coordinates of the points not directly measured X p The prediction results in the x, y and z directions are p ) x,p 、z(X p ) y,p 、z(X p ) z,p , that is, the displacement vector in the x, y, and z directions at the coordinate point p: z(X p ) r,p =u r (X p )+ε(X p ) r,p (6) In the formula, u r (.) represents the trend structure function in the r direction.

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