CN115718985A - Reconstruction and extension highway model optimization method based on GIS - Google Patents
Reconstruction and extension highway model optimization method based on GIS Download PDFInfo
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Abstract
The application provides a reconstruction and extension road model optimization method based on a GIS (geographic information system), which comprises the following steps: preprocessing original GIS data; the original GIS data comprises design route data and elevation data; classifying and sorting the geographic information; carrying out data format conversion and type conversion processing; defining a coordinate system and converting coordinate data; establishing a road model; the road model comprises a newly-built road model and an existing road model; and performing connection processing on the new model and the old model. According to the method, the minimum two algorithm is adopted to fit the linear shape of the longitudinal section of the road on the basis of the laser point cloud technology, and after optimization processing, the link optimization scheme of a new road model and an existing road model can be completed.
Description
Technical Field
The application relates to the technical field of computer-aided modeling, in particular to a reconstruction and extension road model optimization method based on a GIS.
Background
Along with the rapid increase of economy, the demand of roads is increasing day by day, and the increase of traffic volume greatly tests the current situation of the traffic capacity of the roads. Traffic flow is becoming saturated and existing roads are becoming increasingly difficult to withstand large volumes of traffic. In order to meet the demand of economic growth and improve the traffic capacity and service level of roads, the proportion of reconstruction and extension projects of roads is increasing year by year.
However, reconstruction and expansion projects face the problems of large scale of node overpasses, complicated ramp, large difficulty in sign and tear and the like, and the traffic-preserving design scheme also has many problems from theory to practical application. In order to respond to the national construction concept of intelligent roads and green roads, the GIS technology is introduced to assist in the design and verification of the reconstruction and expansion insurance scheme, and the GIS technology becomes an effective means for solving the problems in the prior art.
However, the current technology has the following problem that the new road model and the existing road model have a crossing phenomenon. Because the geometric dimensions of the newly-built road model and the laser point cloud model have deviation, the existing road model needs to be cut based on a unified coordinate system to realize the connection between the newly-built road model and the laser point cloud model, but a mature technology can not solve the problem at present.
Disclosure of Invention
The application provides a GIS-based reconstruction and extension road model optimization method which can be used for solving the technical problems that newly-built and existing road models are crossed and cannot be fused.
The application provides a reconstruction and extension road model optimization method based on a GIS (geographic information system), which comprises the following steps:
s1, preprocessing original GIS data; the original GIS data comprises design route data and elevation data;
s2, classifying and sorting the geographic information;
s3, performing data format conversion and type conversion processing;
s4, defining a coordinate system and converting coordinate data;
s5, establishing a road model; the road model comprises a newly-built road model and an existing road model;
and S6, performing connection processing on the new model and the old model.
Optionally, the preprocessing is performed on the original GIS data, and includes:
importing the design route data into a preset Excel table according to the pile number and the corresponding X coordinate value and Y coordinate value in a plane coordinate system to form a uniform format;
and summarizing the elevation data into a preset EICAD file according to the pile number and the corresponding elevation value to form a uniform format.
Optionally, the sorting and sorting of the geographic information includes:
s21, extracting geographic information from the provided original data; the geographic information comprises position information of a road, starting point pile number information, a route direction and a coordinate axis system;
s22, arranging and storing the extracted geographic information according to a set format standard; each type of geographic information is stored in a spatial data type.
Optionally, the data format conversion and type conversion processing includes:
converting the format of the original information into a preset format;
if the road element data type does not meet the requirement, converting the original data type into a preset type; the road element data are coordinate points corresponding to each stake number along the road.
Optionally, the coordinate system definition and the coordinate data conversion are performed, including:
defining a self-defined coordinate system meeting the requirements;
and converting the item coordinate into a custom coordinate system.
Optionally, the newly-built road model is created by the following method:
s511, preprocessing a plan view; controlling the position and the shape of the road based on the primary skeleton and the primary control parameters, and determining secondary skeleton elements and secondary control parameters according to the road data;
s512, creating a road cross section; establishing a road initial pile number point and a plane thereof based on a horizontal road center line of a primary skeleton, determining a road range, and then establishing a road cross section of a road initial position under the same reference;
the road cross section comprises: the paving layer comprises an upper base layer, a lower base layer, an upper roadbed and a lower roadbed;
s513, instantiating a road model; and based on the road side lines and the space road center lines of the skeleton lines as guide elements of the instantiation template, instantiating the initial cross section and the elevation according to actual requirements to obtain a specific road component.
Optionally, the existing road model is created by the following method:
s521, erecting a base station and preparing measurement data equipment;
s522, after preparing the measurement data equipment, acquiring measurement data; utilizing laser point cloud data, denoising, filtering, interpolating and establishing TIN to generate a digital elevation model;
further, the laser point cloud data mainly comprises inertial navigation data, image data and point cloud original data; the plane precision and the elevation precision of the laser point cloud data are better than +/-5 cm and +/-2 cm respectively;
s523, performing monomer treatment; and denoising and filtering the collected laser point cloud data.
Optionally, performing join processing on the new model and the old model includes:
s611, n-1 measurement data points (x) are known i ，y i ) (i = l,2,3,.., n-1), fitting a polynomial according to a least squares method as:
P m-1 (x)＝a 0 +a 1 x+a 2 x 2 +…+a m-1 x m-1
wherein: xi is the pile number of the ground line, yi is the elevation corresponding to the pile number, the number of terms of a least square method fitting polynomial is m, the maximum times of the polynomial fitting is m-1,m which is not more than n, m is not more than 30, a0, a1, a2, …, and am-1 is a parameter to be determined;
and determining the square sum of the distances from each point to the fitted road vertical line according to undetermined parameters:
q is related to a j (j =0,1, …, n), so the polynomial fitting problem is reduced to the minimum solution of the multivariate function, let:
obtaining:
degeneracy will be expressed in a matrix to yield the following formula:
the Van der Monte matrix is simplified to obtain:
and then ordering:
the above matrix can be written as XA = Y;
according to the least square principle, A = (X' X) -1 X' Y, solving to obtain parameters a0, a1, a2, …, am-1;
according to the undetermined parameters, when the actual elevation difference is large, the least square curve fitting frequency takes a large value, when the actual elevation difference is small, the ground line shape is smooth, and the least square curve fitting frequency should take a small value;
s612, fitting the linear straight line segment of the road:
assuming the initial slope equation to be:
y＝ax+b
wherein x and y are the pile number and elevation of the initial slope point, a and b are undetermined coefficients, and a is the slope rate;
according to the principle of least square curve fitting:
according to undetermined parameters, taking minimum values to obtain coefficients a and b;
determining a regression line according to the recurved point of the route curve:
y＝aix+bi，i＝1,2,3,4,…,n
and generating an intersection point according to the intersection of two adjacent straight lines, wherein the coordinates of the intersection point are as follows in sequence:
obtaining a unary linear regression graph according to the coordinate points;
s613, fitting the linear vertical curve segment of the road:
determining the longitudinal slopes of adjacent straight line sections at two ends of a route curve slope point as i1 and i2 respectively;
calculating a gradient difference Δ i = (i 2-i 1); when the delta i is "+", the curve is a concave vertical curve, and when the delta i is "-", the curve is a convex vertical curve;
the curvature is known from the definition of curvature:
wherein k (k ≠ 0) is the curvature at any point (x, y) on the vertical curve;
the vertical curve has the following relationship between the curvature radius at this point and the curvature k:
R＝1/k
according to a curve fitting equation:
P m-1 (x)＝a 0 +a 1 x+a 2 x 2 +…+a m-1 x m-1
obtaining:
first derivative:
y'＝a 1 +a 2 x+a 3 x 2 +…+a m-1 x m-2
second derivative:
y"＝a 2 +a 3 x+a 4 x 2 …+a m-1 x m-3
according to the undetermined parameters, determining the radius of a vertical curve at a variable slope point (ZHi, hi):
and fitting the linear vertical curve section of the road according to the radius of the vertical curve.
Optionally, the new model and the old model are subjected to join processing, including the following constraints:
and (3) height control point constraint: the measurement control point is arranged on a relatively fixed and easily-recognized structure, so that the linear position is close to the control point, and then the optimization and adjustment are carried out according to the actual condition;
and (3) index constraint of the minimum slope length: when the slope length is smaller than the minimum slope length required by the specification or a road section with frequent slope change exists, deleting unreasonable slope change points or reducing the fitting times of the slope change points to reduce fitting;
and (3) index constraint of the maximum longitudinal slope: if the longitudinal slope gradient value is not in the range specified by the maximum longitudinal slope and the minimum longitudinal slope gradient value required by the specification, the longitudinal slope gradient value is required to be adjusted in order to meet the specification requirement;
index constraint of vertical curve radius: and (4) checking the radius value of the vertical curve, and determining whether the minimum required value of the radius of the vertical curve in the road grade required by the specification is reached.
The method for reconstructing and expanding the road model based on the GIS comprises the steps of firstly preprocessing original GIS data collected on a project site, wherein the original GIS data comprises design route data and an elevation value; secondly, classifying, sorting and organizing the construction conditions according to the classification coding rules of the geographic information according to the influence factors of the construction scheme; then converting the format and the type of the data; defining a coordinate system for the data through a coordinate conversion tool according to the project coordinate system; the method comprises the steps of establishing a newly-built highway model based on a modeling principle of 'skeleton + template', fitting the linear shape of the longitudinal section of the road by adopting a minimum two algorithm based on a laser point cloud technology, and finishing a link optimization scheme of the newly-built highway model and the existing highway model after optimization processing. By the method, the problem of linear fitting of the longitudinal section can be solved, repeated modification and adjustment are avoided, and the design efficiency is greatly improved.
Drawings
FIG. 1 is a flowchart of a method for reconstructing and extending a road model optimization method based on GIS according to the present invention;
FIG. 2 is a flowchart of a method for creating a new road model according to the present invention;
FIG. 3 is a flow chart of a method for creating an existing road model according to the present invention;
FIG. 4 is a schematic diagram of a road linear straight segment fit provided by the present invention;
FIG. 5 is a schematic diagram of a road linear vertical curve segment fitting provided by the present invention;
FIG. 6 is a schematic diagram of road vertical section line fitting provided by the present invention.
Detailed Description
To make the objects, technical solutions and advantages of the present application more clear, embodiments of the present application will be described in further detail below with reference to the accompanying drawings.
Embodiments of the present application will be described below with reference to the accompanying drawings.
The application provides a reconstruction and extension road model optimization method based on a GIS (geographic information system), which comprises the following steps:
s1, preprocessing original GIS data; the raw GIS data includes design route data and elevation data.
And (5) preprocessing original GIS data. Because original GIS data of a project site are provided by different units and professionals, the compatibility of the data is different and cannot be directly used, and the format of the data needs to be preprocessed to be processed into a preset format.
Specifically, the design route data is imported into a preset Excel table according to the pile number and the corresponding X coordinate value and Y coordinate value in a plane coordinate system to form a uniform format;
and summarizing the elevation data into a preset EICAD file according to the pile number and the corresponding elevation value to form a uniform format.
And S2, classifying and sorting the geographic information, and classifying, sorting and organizing the construction conditions according to the classification coding rules of the geographic information according to the influence factors of the construction scheme.
S21, extracting geographic information from the provided original data; the geographic information comprises position information of a road, starting point pile number information, a route direction and a coordinate axis system;
s22, arranging and storing the extracted geographic information according to a set format standard; each type of geographic information is stored in a spatial data type.
And S3, performing data format conversion and type conversion processing.
Converting the format of the original information into a preset format; most of the collected geographic information data are in a CAD format and cannot meet GIS integration requirements, so that the CAD information is required to be converted into a format which can be identified and accepted by a GIS platform on the basis of ensuring that the information is not lost and disordered, and subsequent processing and docking work are facilitated.
If the road element data type does not meet the requirement, converting the original data type into a preset type; the road element data are coordinate points corresponding to each stake number along the road. The road element data type is a coordinate point corresponding to each stake number along the line, and a closed road route is required for displaying in the GIS platform.
And S4, defining a coordinate system and converting coordinate data.
Specifically, defining a self-defined coordinate system meeting the requirements;
and converting the item coordinate into a custom coordinate system.
Since the project coordinate system actually used in the project cannot be accurately determined from the coordinates of the geographic information data, a coordinate system needs to be defined for the data by a coordinate transformation tool from the project coordinate system obtained from a surveying and mapping unit when processing the data.
The coordinate conversion tool is hypergraph software, can realize the conversion of various coordinate systems, and can realize the quick and accurate coordinate system conversion from modeling software to a GIS platform or from the GIS platform to a Web platform. Which is not within the scope of the claims.
And S5, establishing a road model. The establishment of the new road model is completed by adopting a modeling principle based on a framework and a template and taking a developed quick instantiation tool as an assistant. The existing road model is created by acquiring an old road point cloud model through a laser point cloud technology, and forming a structural model capable of bearing data information through extracting road characteristic information and classifying and individualizing.
The road model comprises a new road model and an existing road model
The new road model is created by the following method:
s511, preprocessing a plan view; controlling the position and the shape of the road based on the primary skeleton and the primary control parameters, and determining secondary skeleton elements and secondary control parameters according to the road data;
according to the project plan, preparation is carried out before model creation based on primary and secondary skeleton element linear shapes, the continuity and integrity of the skeleton linear shape need to be guaranteed, if the linear shape is discontinuous or incomplete, the road design line needs to be repaired again, and then the road design line is led into professional design software.
The primary skeleton elements and the primary control parameters are mainly used for controlling the position or the shape of a road, and the primary skeleton elements and the primary control parameters created by the route model are shown in the following table:
table 1: first level skeleton element and first level control parameter table
The secondary skeleton elements and the secondary control parameters mainly analyze the data of the road to obtain the secondary skeleton elements and the secondary control parameters, and the secondary skeleton elements and the secondary control parameters are shown in the following table:
TABLE 2 Secondary framework elements and secondary control parameters table
| Second grade skeleton element | Secondary control parameter |
| Road left and right side line<Curve> | Width of road |
| Road guardrail line<Curve> | Width of guard rail from edge |
S512, creating a road cross section; establishing a road initial pile number point and a plane thereof based on a horizontal road center line of a primary skeleton, determining a road range, and then establishing a road cross section of a road initial position under the same reference;
the road cross section comprises: the paving layer comprises an upper base layer, a lower base layer, an upper roadbed and a lower roadbed.
S513, instantiating a road model; and based on the road side lines and the space road center lines of the skeleton lines as guide elements of the instantiation template, instantiating the initial cross section and the elevation according to actual requirements to obtain a specific road component.
The existing road model is created by the following method:
s521, erecting a base station and preparing measurement data equipment;
surveying the survey area and selecting a control point; centering and leveling the tripod; arranging a GPS; after the measuring instrument is obliquely high; starting up, and waiting to receive signals; installing unmanned aerial vehicle equipment and connecting a power supply; opening a wing paddle and an unmanned aerial vehicle switch; connecting a notebook and a remote system in a login device; starting a laser and a camera; the remote controller is connected with an iPad (ground control station).
The method adopts control software to set flight routes and flight parameters, monitors the flight attitude of the airplane and the acquisition condition of equipment in the flight process, and reduces emergent events through necessary manual intervention.
The flight parameters mainly comprise the flight height, the flight speed, the lateral overlapping degree, the course overlapping degree and the like.
The prepared map data is used for performing on-site exploration, the road traffic condition in the acquisition range is confirmed, the relevance among lines is acquired, and marks are made on the map.
S522, after preparing the measurement data equipment, acquiring measurement data; generating a high-precision digital elevation model by utilizing high-precision laser point cloud data through denoising, filtering, interpolation and TIN establishment;
further, the laser point cloud data mainly comprises inertial navigation data, image data and point cloud original data; the plane precision and the elevation precision of the laser point cloud data are better than +/-5 cm and +/-2 cm respectively;
s523, performing monomer treatment; and denoising and filtering the acquired laser point cloud data. The problems of edge sawtooth, uncut texture, complicated vector surface stacking process and the like in the monomer extraction process can be solved, and the data processing efficiency is improved.
And S6, carrying out connection processing on the new model and the old model.
Specifically, S611, n-1 measurement data points (x) are known i ，y i ) (i = l,2,3,.., n-1), fitting a polynomial according to a least squares method as:
P m-1 (x)＝a 0 +a 1 x+a 2 x 2 +…+a m-1 x m-1
wherein: xi is the pile number of the ground line, yi is the elevation corresponding to the pile number, the number of terms of a least square method fitting polynomial is m, the maximum times of the polynomial fitting is m-1,m which is not more than n, m is not more than 30, a0, a1, a2, …, and am-1 is a parameter to be determined;
and determining the square sum of the distances from each point to the fitted road vertical line according to undetermined parameters: i.e. the sum of the squared deviations is:
q is with respect to a j (j =0,1, …, n), so the polynomial fitting problem is reduced to the minimum solution of the multivariate function, let:
obtaining:
degeneracy will be expressed in a matrix to yield the following formula:
the Van der Monte matrix is simplified to obtain:
and then ordering:
the above matrix can be written as XA = Y;
according to the least square principle, A = (X' X) -1 X' Y, solving to obtain parameters a0, a1, a2, …, am-1;
according to the parameters to be determined, when the number of times of fitting the linear shape of the longitudinal section by adopting a least square method is lower, the fitting curve is smoother, the extreme points of the curve are fewer, otherwise, the higher the number of times of fitting is, the more the fitting curve is unsmooth, and the more the extreme points of the curve are; when the height difference on the spot is large, the fitting frequency of the least square curve takes a large value, when the height difference on the spot is small, the ground line shape is smooth, and the fitting frequency of the least square curve should take a small value;
referring to fig. 4 of the drawings, a schematic diagram of a display device,
s612, fitting the linear straight line segment of the road:
assuming the initial slope equation to be:
y＝ax+b
wherein x and y are the pile number and elevation of the initial slope point, a and b are undetermined coefficients, and a is the slope rate;
according to the principle of least square curve fitting:
according to undetermined parameters, taking minimum values to obtain coefficients a and b;
determining a regression line according to a reverse bending point of the route curve:
y＝aix+bi，i＝1,2,3,4,…,n
the intersection point is generated according to the intersection of two adjacent straight lines, and the coordinates of the intersection point are as follows in sequence:
obtaining a unary linear regression graph according to the coordinate points;
as shown in figure 5 of the drawings,
s613, fitting the linear vertical curve segment of the road:
determining the longitudinal slopes of adjacent straight line sections at two ends of a route curve slope point as i1 and i2 respectively;
calculating a gradient difference Δ i = (i 2-i 1); when the delta i is "+", the curve is a concave vertical curve, and when the delta i is "-", the curve is a convex vertical curve;
since the fitted curve is continuously derivable, the curvature is known from its definition:
wherein k (k ≠ 0) is the curvature at any point (x, y) on the vertical curve;
the radius of curvature of the vertical curve at this point has the following relationship with the curvature k:
R＝1/k
according to a curve fitting equation:
P m-1 (x)＝a 0 +a 1 x+a 2 x 2 +…+a m-1 x m-1
obtaining:
first derivative:
y'＝a 1 +a 2 x+a 3 x 2 +…+a m-1 x m-2
second derivative:
y"＝a 2 +a 3 x+a 4 x 2 …+a m-1 x m-3
according to the undetermined parameters, determining the radius of a vertical curve at a variable slope point (ZHi, hi):
and fitting the linear vertical curve segments of the road according to the radius of the vertical curve.
And performing linking processing on the new model and the old model, wherein the linking processing comprises the following constraint conditions:
and (3) height control point constraint: in order to obtain more accurate field sampling points, measuring control points are arranged on a relatively fixed and easily-identified structure, so that linear positions are close to the control points, and then optimization adjustment is carried out according to actual conditions;
and (3) index constraint of the minimum slope length: before solving the elevation of the variable slope point, the slope length must be constrained, when the slope length is smaller than the minimum slope length required by specifications or a road section with frequent slope change exists, the constraint of the slope length is damaged, unreasonable variable slope points are deleted, or the fitting times of the variable slope points are reduced to reduce the fitting;
and (3) index constraint of the maximum longitudinal slope: if the longitudinal slope gradient value is not in the range specified by the maximum longitudinal slope and the minimum longitudinal slope gradient value required by the specification, the longitudinal slope gradient value is required to be adjusted in order to meet the specification requirement;
index constraint of vertical curve radius: checking the radius value of the vertical curve, and determining whether the minimum required value of the radius of the vertical curve in the road grade meeting the standard requirement is reached
The method for reconstructing and expanding the road model based on the GIS comprises the following steps of firstly, preprocessing original GIS data acquired on a project site, wherein the original GIS data comprises design route data and an elevation value; secondly, classifying, sorting and organizing the construction conditions according to the classification coding rules of the geographic information according to the influence factors of the construction scheme; then converting the format and the type of the data; defining a coordinate system for the data through a coordinate conversion tool according to the project coordinate system; the method comprises the steps of establishing a newly-built highway model based on a modeling principle of 'skeleton + template', fitting the linear shape of the longitudinal section of the road by adopting a minimum two algorithm based on a laser point cloud technology, and finishing a link optimization scheme of the newly-built highway model and the existing highway model after optimization processing. By the method, the problem of linear fitting of the longitudinal section can be solved, repeated modification and adjustment are avoided, and the design efficiency is greatly improved.
Those skilled in the art will clearly understand that the techniques in the embodiments of the present application may be implemented by way of software plus a required general hardware platform. Based on such understanding, the technical solutions in the embodiments of the present application may be substantially or partially embodied in the form of a software product, which may be stored in a storage medium, such as a ROM/RAM, a magnetic disk, an optical disk, or the like, and includes several instructions for enabling a computer device (which may be a personal computer, a server, or a network device) to execute the method according to the embodiments or some parts of the embodiments of the present application.
The above-described embodiments of the present application do not limit the scope of the present application.
Claims (9)
1. A reconstruction and extension road model optimization method based on GIS is characterized by comprising the following steps:
s1, preprocessing original GIS data; the original GIS data comprises design route data and elevation data;
s2, classifying and sorting the geographic information;
s3, performing data format conversion and type conversion processing;
s4, defining a coordinate system and converting coordinate data;
s5, establishing a road model; the road model comprises a newly-built road model and an existing road model;
and S6, carrying out connection processing on the new model and the old model.
2. The method of claim 1, wherein preprocessing the raw GIS data comprises:
importing the design route data into a preset Excel table according to the pile number and the corresponding X coordinate value and Y coordinate value in a plane coordinate system to form a uniform format;
and summarizing the elevation data into a preset EICAD file according to the pile number and the corresponding elevation value to form a uniform format.
3. The method of claim 1, wherein sorting the geographic information comprises:
s21, extracting geographic information from the provided original data; the geographic information comprises position information of a road, starting point pile number information, a route direction and a coordinate axis system;
s22, arranging and storing the extracted geographic information according to a set format standard; each type of geographic information is stored in a spatial data type.
4. The method of claim 1, wherein performing the data format conversion and type conversion comprises:
converting the format of the original information into a preset format;
if the road element data type does not meet the requirement, converting the original data type into a preset type; the road element data are coordinate points corresponding to each stake number along the road.
5. The method of claim 1, wherein performing coordinate system definition and coordinate data transformation comprises:
defining a self-defined coordinate system meeting the requirements;
and converting the item coordinate into a custom coordinate system.
6. The method of claim 1, wherein the newly created road model is created by:
s511, preprocessing a plan view; controlling the position and the shape of the road based on the primary skeleton and the primary control parameters, and determining secondary skeleton elements and secondary control parameters according to the road data;
s512, creating a road cross section; establishing a road initial pile number point and a plane thereof based on a horizontal road center line of a primary skeleton, determining a road range, and then establishing a road cross section of a road initial position under the same reference;
the cross-section of the road comprises: the paving layer comprises an upper base layer, a lower base layer, an upper roadbed and a lower roadbed;
s513, instantiating a road model; and based on the road side lines and the space road center lines of the skeleton lines as guide elements of the instantiation template, instantiating the initial cross section and the elevation according to actual requirements to obtain a specific road component.
7. The method of claim 1, wherein the existing road model is created by:
s521, erecting a base station and preparing measurement data equipment;
s522, after preparing the measurement data equipment, acquiring measurement data; utilizing laser point cloud data, denoising, filtering, interpolating and establishing TIN to generate a digital elevation model;
further, the laser point cloud data mainly comprises inertial navigation data, image data and point cloud original data; the plane precision and the elevation precision of the laser point cloud data are better than +/-5 cm and +/-2 cm respectively;
s523, performing monomer treatment; and denoising and filtering the collected laser point cloud data.
8. The method of claim 1, wherein concatenating the new model and the old model comprises:
s611, n-1 measurement data points (x) are known i ，y i ) (i = l,2,3,.., n-1), fitting a polynomial according to a least squares method as:
P m-1 (x)＝a 0 +a 1 x+a 2 x 2 +…+a m-1 x m-1
wherein: xi is the pile number of the ground line, yi is the elevation corresponding to the pile number, the number of terms of a least square method fitting polynomial is m, the maximum times of the polynomial fitting is m-1,m which is not more than n, m is not more than 30, a0, a1, a2, …, and am-1 is a parameter to be determined;
and determining the square sum of the distances from each point to the fitted road vertical line according to undetermined parameters:
q is with respect to a j (j =0,1, …, n), so the polynomial fitting problem is reduced to a multivariate functionSolving the minimum value of the number, and enabling:
obtaining:
degeneracy will be expressed in a matrix to yield the following formula:
the Van der Monte matrix is simplified to obtain:
and then ordering:
the above matrix can be written as XA = Y;
according to the least square principle, A = (X' X) -1 X' Y, solving to obtain parameters a0, a1, a2, …, am-1;
according to the undetermined parameters, when the actual elevation difference is large, the least square curve fitting frequency takes a large value, when the actual elevation difference is small, the ground line shape is smooth, and the least square curve fitting frequency should take a small value;
s612, fitting the linear straight line segment of the road:
assuming the initial slope line equation to be:
y＝ax+b
wherein x and y are the pile number and elevation of the initial slope point, a and b are undetermined coefficients, and a is the slope rate;
according to the principle of least square curve fitting:
according to undetermined parameters, taking minimum values to obtain coefficients a and b;
determining a regression line according to the recurved point of the route curve:
y＝aix+bi，i＝1,2,3,4,…,n
the intersection point is generated according to the intersection of two adjacent straight lines, and the coordinates of the intersection point are as follows in sequence:
obtaining a unary linear regression graph according to the coordinate points;
s613, fitting the linear vertical curve segment of the road:
determining the longitudinal slopes of adjacent straight line sections at two ends of a route curve slope point as i1 and i2 respectively;
calculating a gradient difference Δ i = (i 2-i 1); when the delta i is "+", the curve is a concave vertical curve, and when the delta i is "-", the curve is a convex vertical curve;
the curvature is known from the definition of curvature:
wherein k (k ≠ 0) is the curvature at any point (x, y) on the vertical curve;
the radius of curvature of the vertical curve at this point has the following relationship with the curvature k:
R＝1/k
according to a curve fitting equation:
P m-1 (x)＝a 0 +a 1 x+a 2 x 2 +…+a m-1 x m-1
obtaining:
first derivative:
y'＝a 1 +a 2 x+a 3 x 2 +…+a m-1 x m-2
second derivative:
y"＝a 2 +a 3 x+a 4 x 2 …+a m-1 x m-3
according to the undetermined parameters, determining the radius of a vertical curve at a variable slope point (ZHi, hi):
and fitting the linear vertical curve segments of the road according to the radius of the vertical curve.
9. The method of claim 8, wherein the new model and the old model are connected, and the method comprises the following constraints:
and (3) height control point constraint: the measurement control point is arranged on a relatively fixed and easily recognized structure, so that the linear position is close to the control point, and then the measurement control point is optimized and adjusted according to actual conditions;
the index constraint of the minimum slope length is as follows: when the slope length is smaller than the minimum slope length required by the specification or a road section with frequent slope change exists, deleting unreasonable slope change points or reducing the fitting times of the slope change points to reduce fitting;
and (3) index constraint of the maximum longitudinal slope: if the longitudinal slope gradient value is not in the range specified by the maximum longitudinal slope and the minimum longitudinal slope gradient value required by the specification, the longitudinal slope gradient value is required to be adjusted in order to meet the specification requirement;
index constraint of vertical curve radius: and (4) checking the radius value of the vertical curve, and determining whether the minimum required value of the radius of the vertical curve in the road grade required by the specification is reached.
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Cited By (3)
| Publication number | Priority date | Publication date | Assignee | Title |
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| CN116150928A (en) * | 2023-04-14 | 2023-05-23 | 江苏狄诺尼信息技术有限责任公司 | Intelligent generation and optimization method for road vertical section based on Monte Carlo simulation |
| CN117892389A (en) * | 2023-12-19 | 2024-04-16 | 国网湖北省电力有限公司超高压公司 | Modeling method and system based on two-dimensional slope |
| CN118246106A (en) * | 2024-03-08 | 2024-06-25 | 北京市市政工程设计研究总院有限公司 | Route modeling method in building information model |
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Cited By (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN116150928A (en) * | 2023-04-14 | 2023-05-23 | 江苏狄诺尼信息技术有限责任公司 | Intelligent generation and optimization method for road vertical section based on Monte Carlo simulation |
| CN116150928B (en) * | 2023-04-14 | 2023-07-25 | 江苏狄诺尼信息技术有限责任公司 | Intelligent generation and optimization method for road vertical section based on Monte Carlo simulation |
| CN117892389A (en) * | 2023-12-19 | 2024-04-16 | 国网湖北省电力有限公司超高压公司 | Modeling method and system based on two-dimensional slope |
| CN118246106A (en) * | 2024-03-08 | 2024-06-25 | 北京市市政工程设计研究总院有限公司 | Route modeling method in building information model |
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