CN115597569B - Method for measuring relative position relation between pile and ship by using section scanner - Google Patents
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Abstract
The invention discloses a method for measuring the relative position relation between a pile and a ship by using a section scanner, which comprises the following steps: step 1: the arrangement of a scanner; step 2: establishing a conversion model; step 3: collecting data by a scanner; step 4: segment identification of the scanned data; step 5: the calculation of the ellipse center is performed under the condition that the ellipse major half axis, azimuth angle and minor half axis are known. Step 6: and judging whether the calculated elliptical center is the pile center corresponding to the pile body according to the fitted middle error, and determining the position of the pile body center under the ship body coordinate system. The invention adopts a section scanner, the scanning surface of the scanner is approximately parallel to the plane of the ship body and is arranged at the position where the pile body can be scanned, and the coordinates of the pile center relative to the ship body are calculated through the coordinates of a series of points scanned onto the pile body by the scanner, so that the coordinates of the pile center in the scanning plane are calculated, and the problem of measuring the relative position relationship between the pile and the ship is solved.
Description
Technical Field
The invention relates to the technical field of piling and positioning in water engineering, in particular to a method for measuring the relative position relationship between a pile and a ship by using a section scanner.
Background
In the process of constructing a river-crossing and sea-crossing bridge at a port and a wharf, piles are driven to a designed position and posture by using a pile driving ship on water, and the work is generally completed by the pile driving ship. The position of the pile needs to be determined before piling, wherein the position of the vessel can be obtained by satellite positioning, and if the relative position relationship of the pile and the vessel can be determined, the position of the pile can be obtained, so how to determine the relative position relationship of the pile and the vessel is the key of piling positioning.
But the relative position relationship between the pile and the pile driving ship in the traditional pile driving positioning process is determined by means of 2 distance meters. Because the diameter of the piles is different and the difference is larger, for example, the diameter of the pile is 3.2 meters, and the pile is thin with the diameter of tens of centimeters; the point location obtained by the measurement of the fixed distance meter is not ideal for determining the position of the pile center, and the positioning accuracy is affected.
Disclosure of Invention
1. Technical problem to be solved
The invention aims to solve the problems that in the prior art, the relative position relationship between a pile and a pile driving ship is measured by means of 2 distance meters, the position of a point position obtained by measurement of a fixed distance meter is not ideal for determining the center of the pile, and the positioning accuracy is affected.
2. Technical proposal
In order to achieve the above purpose, the present invention adopts the following technical scheme:
the method for measuring the relative position relation between the pile and the ship by using the section scanner comprises the following steps:
step 1: the scanner is arranged, and an observation bracket is arranged at a proper position on a ship deck near the pile frame and used for installing the scanner;
Step 2: setting up a conversion model, setting at least 2 characteristic points on a ship body, measuring the coordinates of the characteristic points under a ship body coordinate system by using a total station, starting a scanner, scanning the characteristic points to at least 2 characteristic points with known ship body coordinates, calculating the coordinates of the characteristic points under the scanner coordinate system by using the data of the scanner, calculating coordinate conversion parameters according to a similar conversion model by using the coordinates of the at least 2 characteristic points under the 2 coordinate systems, and further obtaining the coordinates of the center of the scanner under the ship body coordinate system and the included angle between the scanner coordinate system and the ship body coordinate system, thereby converting the coordinates under the scanner coordinate into the ship body coordinate system:
Step 3: collecting data by a scanner;
step 4: segment identification of the scanned data;
step 5: the pile body is scanned by using a scanner, the diameter and the inclination angle of the pile can be used as known values, a cylinder inclined at a certain angle represents an ellipse on the plane of the scanner, the scanned data is used for fitting the ellipse, the azimuth angle of the major axis and the minor axis of the ellipse in the fitting process is used as the known values, and then the coordinate of the center of the ellipse is calculated;
step 6: and judging whether the calculated elliptical center is the pile center corresponding to the pile body according to the fitted middle error, and determining the position of the pile body center under the ship body coordinate system.
Preferably, in the step 1, an observation support is disposed at a proper position on a deck of the hull near the pile frame and used for installing the scanner, and the installed scanner is required to scan pile bodies under different pile driving states, including straight piles, upward piles and downward piles, so that the scanner is ensured to scan the pile bodies.
Preferably, in the step 2, a certain number of common control points are needed for the conversion between the plane coordinate systems, and the conversion parameters are solved and then the coordinate conversion can be performed.
Preferably, the mathematical model of the planar coordinate transformation can be generally classified into a similarity transformation and an affine transformation.
Preferably, the solving process of the similar transformation coordinate transformation parameters specifically comprises the following steps:
In the middle of Is the coordinates in the new coordinate system (O 2-X2Y2)/(For the coordinates in the old coordinate system (O 1-X1Y1), the dimensional changes δμ and the rotation angles α and O 1 are the coordinates/>, in the new coordinate system (O 2-X2Y2)Collectively referred to as the conversion parameters between the two coordinate systems;
Weighing scale As translation parameters, alpha is rotation parameters, and delta mu is scale parameters; assuming a=x 0,b＝Y0, c= (1+δμ) cos α, d= (1+δμ) sin α, then equation (3-2) can be transformed into
Let n common points in two coordinate systemsAnd/>The error equation may be listed:
Namely:
The most probable solution of the conversion parameters:
wherein: p is a weight matrix determined by errors in coordinates, and is generally taken as an identity matrix.
Preferably, the fitting of the ellipse in the step 5 is performed by the following 2 methods:
Method 1: a least square method according to an elliptic general equation;
The general equation for an ellipse is f i (m, n, a, b, θ) =0, where Δx i＝m-xi,Δyi＝n-yi;
Equation (6) is a nonlinear function, which is developed by a taylor series and taken once at the approximation of the parameter, which can be obtained by a linear least squares method,
Wherein:
method 2: a least square method based on the vertical distance from the point to the ellipse;
v i is defined as the vertical distance from the point to the ellipse, the parameters of the ellipse are obtained by using an indirect adjustment method,
Wherein f i 1 (m, n, a, b, θ) is the vertical distance from the point to the ellipse, the parameter takes the initial value m 0、n0、a0、b0、θ0 through iterative calculation, and the partial derivative is adopted here because f i 1 is difficult to calculate;
li＝fi 1(m0,n0,a0,b0,θ0)#(21)
the calculation method of f i 1 (m, n, a, b, θ) is as follows: in an elliptical coordinate system, a perpendicular line of an ellipse is drawn through points (x, y), an included angle between the perpendicular line and an x axis is B, and h is a perpendicular distance f i 1 between the points and the ellipse, so that the three-dimensional coordinate system is obtained:
Wherein:
Iterative calculation:
h(0)=0
Preferably, the step 6 further includes detecting an ellipse, and the detection procedure of the ellipse specifically includes the following steps:
Step 6.1: dividing the scanning points in one section of the scanner according to the rotation direction of the scanner, if the distance difference between two adjacent points is too large, the two points can be considered to be not on the same elliptical arc, the distance threshold can be set, the section point is divided into a plurality of point sets, the plurality of point sets are respectively processed, if the number of the point sets is too small, no ellipse is considered to exist, and the processing can be omitted;
Step 6.2: hough transform is used for detection, parameters m and n are divided with a certain starting point, an end point and a step length, a two-dimensional accumulator (which can be regarded as a two-dimensional array, each item of which corresponds to one value of m and n) is constructed, n k can be calculated when m k is known for any point (x i,yi), namely formula (23), for any point (x i,yi), each m k value of the division is taken, the corresponding value of n k is calculated, if n k has a real number solution, the corresponding item of m k、nk in the two-dimensional accumulator is added by one and is brought into all points, m k、nk at the local maximum value is regarded as the coordinate of the ellipse,
Step 6.3: arc segment segmentation traversal, setting the maximum value and the minimum value of the points of a segmentation point set, firstly fixing the sequence number of a starting point, moving the sequence number of an ending point backwards by a fixed step length, changing the arc segment point from the minimum value to the maximum value, moving the starting point after the fixed step length, and repeating the steps.
Preferably, in the step 6.2, after the values of the parameters m and n are obtained by hough transform, the parameters may be used to determine the points on the elliptical arc segment (the points are removed by the distance threshold from the point to the ellipse or the range of the maximum arc segment that may be scanned), the calculated parameters are set as initial values, the points on the arc segment are fitted by indirect adjustment method, and the least square solution of the center coordinates of the ellipse is obtained, so as to improve the accuracy, and the error in three times is used to perform coarse removal, so as to prevent the coarse difference from affecting the fitting accuracy.
3. Advantageous effects
Compared with the prior art, the invention has the advantages that:
In the invention, a section scanner is adopted, the scanning surface of the scanner is approximately parallel to the plane of the ship body, and the section scanner is arranged at a position where the pile body can be scanned. The coordinates of the pile center relative to the ship body are calculated through the coordinates of a series of points scanned by the scanner, and the coordinates of the pile center in the scanning plane are calculated because the scanner can obtain the coordinates of a series of points on the surface of the pile body at the same time, so that the problem of measuring the relative position relationship between the pile and the ship is solved.
Drawings
FIG. 1 is a diagram showing the relative position between piles and vessels measured by a laser section scanner according to the present invention;
FIG. 2 is a schematic diagram of a scan range and a scan coordinate system definition according to the present invention;
FIG. 3 is a schematic view of an ellipse in a planar rectangular coordinate system;
FIG. 4 is a schematic flow chart of ellipse detection according to the present invention;
Fig. 5 is a diagram of flying spot situation of non-adjacent objects according to the present invention.
Fig. 6 is a schematic diagram of a hough transform accumulator according to the present invention;
FIG. 7 is a graph of segment segmentation according to the present invention;
Fig. 8 is a graph of ellipse fitting results proposed by the present invention.
Detailed Description
The following description of the embodiments of the present invention will be made clearly and completely with reference to the accompanying drawings, in which it is apparent that the embodiments described are only some embodiments of the present invention, but not all embodiments.
Example 1:
Referring to fig. 1-4, a method for determining the relative positional relationship of a pile and a vessel using a section scanner, comprising the steps of:
Step 1: arranging a scanner, arranging an observation support at a proper position on a ship deck near a pile frame for installing the scanner, wherein the installed scanner is required to scan pile bodies in different pile driving states, and the scanner comprises a straight pile, a pitching pile and a pitching pile, so that the scanner can scan the pile bodies;
step 2: establishing a conversion model, setting at least 2 characteristic points on a ship body, measuring the coordinates of the characteristic points under a ship body coordinate system by using a total station, starting a scanner, scanning the characteristic points to at least 2 characteristic points with known ship body coordinates, calculating the coordinates of the characteristic points under the scanner coordinate system by using the data of the scanner, calculating coordinate conversion parameters according to a similar conversion model by using the coordinates of the at least 2 characteristic points under the 2 coordinate systems, and further obtaining the coordinates of the center of the scanner under the ship body coordinate system and the included angles between the scanner coordinate system and the ship body coordinate system, so that the coordinates under the scanner coordinate system can be converted into the ship body coordinate system;
the conversion between the plane coordinate systems needs a certain number of common control points, the conversion parameters are solved, then the coordinate conversion can be carried out, and the mathematical model of the plane coordinate conversion can be generally divided into similar conversion and affine conversion;
the solving process of the similar transformation coordinate transformation parameters comprises the following steps:
In the middle of Is the coordinates in the new coordinate system (O 2-X2Y2)/(For the coordinates in the old coordinate system (O 1-X1Y1), the dimensional changes δμ and the rotation angles α and O 1 are the coordinates/>, in the new coordinate system (O 2-X2Y2)Collectively referred to as the conversion parameters between the two coordinate systems;
Weighing scale As translation parameters, alpha is rotation parameters, and delta mu is scale parameters; assuming a=x 0,b＝Y0, c= (1+δμ) cos α, d= (1+δμ) sin α, then equation (3-2) can be transformed into
Let n common points in two coordinate systemsAnd/>The error equation may be listed:
Namely:
The most probable solution of the conversion parameters:
wherein: p is a weight matrix determined by errors in coordinates, and is generally taken as an identity matrix:
Step 3: collecting data by a scanner;
step 4: segment identification of the scanned data;
step 5: the pile body is scanned by using a scanner, the diameter and the inclination angle of the pile can be used as known values, a cylinder inclined at a certain angle represents an ellipse on the plane of the scanner, the scanned data is used for fitting the ellipse, the azimuth angle of the major axis and the minor axis of the ellipse in the fitting process is used as the known values, and then the coordinate of the center of the ellipse is calculated;
step 6: and judging whether the calculated elliptical center is the pile center corresponding to the pile body according to the fitted middle error, and determining the position of the pile body center under the ship body coordinate system.
In the invention, a section scanner is adopted, the scanning surface of the scanner is approximately parallel to the plane of the ship body, and the section scanner is arranged at a position where the pile body can be scanned. The coordinates of the pile center relative to the ship body are calculated through the coordinates of a series of points scanned by the scanner, and the coordinates of the pile center in the scanning plane are calculated because the scanner can obtain the coordinates of a series of points on the surface of the pile body at the same time, so that the problem of measuring the relative position relationship between the pile and the ship is solved.
Example 2:
It has the implementation content of the above embodiments, where reference may be made to the foregoing description for specific implementation of the above embodiments, and the details of the embodiments herein are not repeated; in the embodiment of the present application, however, it is different from the above embodiment in that:
in the invention, the fitting of the ellipse specifically comprises the following steps:
step 5.1: a least square method according to an elliptic general equation;
The general equation for an ellipse is f i (m, n, a, b, θ) =0, where Δx i＝m-xi,Δyi＝n-yi;
equation (6) is a nonlinear function, which is obtained by expanding the parameters by a Taylor series and taking a term once at the approximate value of the parameters, equation (7) can be obtained by a linear least square method,
Wherein:
Step 5.2: a least square method based on the vertical distance from the point to the ellipse;
v i is defined as the vertical distance from the point to the ellipse, the parameters of the ellipse are obtained by using an indirect adjustment method,
Wherein f i 1 (m, n, a, b, θ) is the vertical distance from the point to the ellipse, the initial value m 0、n0、a0、b0、θ0 can be taken as the parameter through iterative calculation, and the partial derivative is difficult to calculate due to f i 1, so that a numerical derivative method is adopted;
li＝fi 1(m0,n0,a0,b0,θ0)#(21)
the calculation method of f i 1 (m, n, a, b, θ) is as follows: in an elliptical coordinate system, a perpendicular line of an ellipse is drawn through points (x, y), an included angle between the perpendicular line and an x axis is B, and h is a perpendicular distance f i 1 between the points and the ellipse, so that the three-dimensional coordinate system is obtained:
Wherein:
Iterative calculation:
h(0)=0
Example 3:
It has the implementation content of the above embodiments, where reference may be made to the foregoing description for specific implementation of the above embodiments, and the details of the embodiments herein are not repeated; in the embodiment of the present application, however, it is different from the above embodiment in that:
referring to fig. 5-7, the ellipse detection process specifically includes the following steps:
Step 6.1: in one section of the scanner, scanning points are sequentially acquired according to the rotation direction of the scanner, and if the distances between two adjacent points are too large, the two points can be considered to be not on the same elliptical arc. A distance threshold may be set to divide the breakpoint into a plurality of point sets, thereby processing the plurality of point sets separately. If the number of points in the point set is too small, it is considered that there is no ellipse, and the processing may be omitted. In actual engineering, if the tangent plane of the cylinder is not adjacent to other objects, the points on the ellipse can be divided into independent point sets by utilizing the distance threshold value, so that the flow of ellipse detection is greatly simplified. Due to the problems of measuring precision, working mode and the like of the scanner, the situation that flying spots may occur to non-adjacent objects, a multi-point distance threshold value is set, and if the distances between a plurality of adjacent points are all larger than the threshold value, the segmentation is carried out;
Step 6.2: hough transform is used for detection, parameters m and n are divided with a certain starting point, an end point and a step length, a two-dimensional accumulator (which can be regarded as a two-dimensional array, each item of which corresponds to one value of m and n) is constructed, n k can be calculated when m k is known for any point (x i,yi), namely formula (23), for any point (x i,yi), each m k value of the division is taken, the corresponding value of n k is calculated, if n k has a real number solution, the corresponding item of m k、nk in the two-dimensional accumulator is added by one and is brought into all points, m k、nk at the local maximum value is regarded as the coordinate of the ellipse,
After the values of the parameters m and n are obtained by Hough transformation, the parameters can be used for determining the points on the elliptical arc segments (the points are removed by the distance threshold value from the points to the ellipse or the range of the maximum arc segment which can be scanned), the calculated parameters are set as initial values, the points on the arc segments are fitted by an indirect adjustment method, and the least square solution of the center coordinates of the ellipse is obtained, so that the accuracy is improved, the rough removal is performed by using the error in three times, and the influence of the rough removal on the fitting accuracy is prevented;
Step 6.3: after the arc segment is segmented through the distance threshold, if the segmented single point set contains points on the ellipse and points of other ground objects, the large point set is segmented for multiple times to obtain a plurality of small point sets, ellipse fitting is carried out on each small point set, and the ellipse with the smallest error is taken as the detected ellipse. Points on the ellipse are continuously acquired during scanning, so that the points in the middle of the starting point and the ending point are used as a point set divided at one time through setting the sequence numbers of the starting point and the ending point each time. Setting the maximum value and the minimum value of the points of the dividing point set, firstly fixing the sequence number of the starting point, moving the sequence number of the ending point backwards by a fixed step length, and converting the arc segment point from the minimum value to the maximum value. The starting point is removed after a fixed step size and the above steps are repeated. To increase the detection speed, the points in each small point set are sampled with a fixed step length and then fitted.
Example 4:
It has the implementation content of the above embodiments, where reference may be made to the foregoing description for specific implementation of the above embodiments, and the details of the embodiments herein are not repeated; in the embodiment of the present application, however, it is different from the above embodiment in that:
Elliptical detection results:
To verify the accuracy of the detection and fitting of the different methods, the test was performed using analog data. The random error with an error of 2cm was added to each scan point of the simulated section, and the calculation results are shown in tables 1 and 2 and fig. 8. The two fitting methods were compared.
Table 1 ellipse 1 (θ= -43.91 °, a=1.2029m, b=0.6587 m, m=2.0 m, n=1.5 m)
Table 2 ellipses 2 (θ= -34.39 °, a=1.1731 m, b=0.7498 m, m= -3.0m, n=2.0 m)
The foregoing is only a preferred embodiment of the present invention, but the scope of the present invention is not limited thereto, and any person skilled in the art, who is within the scope of the present invention, should make equivalent substitutions or modifications according to the technical scheme of the present invention and the inventive concept thereof, and should be covered by the scope of the present invention.
Claims (7)
1. The method for measuring the relative position relation between the pile and the ship by using the section scanner is characterized by comprising the following steps of:
step 1: the scanner is arranged, and an observation bracket is arranged at a proper position on a ship deck near the pile frame and used for installing the scanner;
Step 2: setting up a conversion model, setting at least 2 characteristic points on a ship body, measuring the coordinates of the characteristic points under a ship body coordinate system by using a total station, starting a scanner, scanning the characteristic points to at least 2 characteristic points with known ship body coordinates, calculating the coordinates of the characteristic points under the scanner coordinate system by using the data of the scanner, calculating coordinate conversion parameters according to a similar conversion model by using the coordinates of the at least 2 characteristic points under the 2 coordinate systems, and further obtaining the coordinates of the center of the scanner under the ship body coordinate system and the included angle between the scanner coordinate system and the ship body coordinate system, thereby converting the coordinates under the scanner coordinate into the ship body coordinate system:
Step 3: collecting data by a scanner;
step 4: segment identification of the scanned data;
Step 5: scanning a pile body by using a scanner, wherein the diameter and the inclination angle of the pile are taken as known values, a cylinder inclined at a certain angle represents an ellipse on the plane of the scanner, fitting the ellipse by using scanned data, taking the azimuth angle of a long and short half axes and a long axis of the ellipse in the fitting process as the known values, and then calculating the coordinate of the center of the ellipse;
Step 6: judging whether the calculated ellipse center is the pile center corresponding to the pile body according to the fitted middle error, determining the position of the pile body center under the ship body coordinate system, and detecting the ellipse, wherein the ellipse detection flow specifically comprises the following steps:
Step 6.1: dividing the cross section of the scanner through a distance threshold, acquiring scanning points in sequence according to the rotation direction of the scanner, if the distance difference between two adjacent points is too large, considering that the two points are not on the same elliptical arc, setting the distance threshold, dividing the cross section point into a plurality of point sets, respectively processing the plurality of point sets, and if the point number of the point sets is too small, considering that no ellipse exists, and omitting the processing;
Step 6.2: the Hough transform is used for detection, parameters m and n are divided with a certain starting point, an end point and a step length to construct a two-dimensional accumulator, the two-dimensional accumulator is regarded as a two-dimensional array, each item corresponds to one value of m and n, n k is calculated for any point (x i,yi) when m k is known, namely formula (23), for any point (x i,yi), each divided value of m k is taken, the corresponding value of n k is calculated, if n k has a real solution, the corresponding item of m k、nk in the two-dimensional accumulator is added by one to be brought into all points, and m k、nk at the local maximum value is considered as the coordinate of the ellipse,
Step 6.3: arc segment segmentation traversal, setting the maximum value and the minimum value of the points of a segmentation point set, firstly fixing the sequence number of a starting point, moving the sequence number of an ending point backwards by a fixed step length, changing the arc segment point from the minimum value to the maximum value, moving the starting point after the fixed step length, and repeating the steps.
2. The method for determining the relative positional relationship between piles and vessels by using a section scanner according to claim 1, wherein in the step 1, an observation support is provided at a proper position on a deck of a hull near a pile frame for installing the scanner, and the installed scanner is required to scan pile bodies under different pile driving conditions, including vertical piles, upward piles and downward piles, so that the scanner can scan pile bodies.
3. The method for determining pile-ship relative position relationship by using section scanner according to claim 1, wherein said conversion between planar coordinate systems in step2 requires a certain number of common control points, and the conversion parameters are solved before coordinate conversion.
4. A method for determining pile-to-vessel relative position using a section scanner according to claim 3, wherein the mathematical model of the transformation between planar coordinate systems is divided into a similarity transformation and an affine transformation.
5. The method for determining the relative positional relationship between a pile and a ship by using a section scanner according to claim 4, wherein the similar transformation coordinate transformation parameter solving process specifically comprises:
In the middle of Is the coordinates in the new coordinate system (O 2-X2Y2)/(For the coordinates in the old coordinate system (O 1-X1Y1), the dimensional changes δμ and the rotation angles α and O 1 are the coordinates/>, in the new coordinate system (O 2-X2Y2)Collectively referred to as the conversion parameters between the two coordinate systems; weighing scaleAs translation parameters, alpha is rotation parameters, and delta mu is scale parameters; assuming e=x 0,f＝Y0, c= (1+δμ) cos α, d= (1+δμ) sin α, then equation (3-2) can be transformed into
Let n common points in two coordinate systemsAnd/>The error equation may be listed:
Namely:
The most probable solution of the conversion parameters:
wherein: p is a weight matrix determined by errors in coordinates, and P is taken as an identity matrix.
6. The method for determining the relative positional relationship between a pile and a ship by using a section scanner according to claim 1, wherein the ellipse fitting in the step 5 is performed by the following 2 methods:
Method 1: a least square method according to an elliptic general equation;
The general equation for an ellipse is f i (m, n, a, b, θ) =0, where Δx i＝m-xi,Δyi＝n-yi;
Equation (6) is a nonlinear function, which is developed by a taylor series and taken once at the approximation of the parameter, which can be obtained by a linear least squares method,
Wherein:
method 2: a least square method based on the vertical distance from the point to the ellipse;
v i is defined as the vertical distance from the point to the ellipse, the parameters of the ellipse are obtained by using an indirect adjustment method,
Wherein f i 1 (m, n, a, b, θ) is the vertical distance from the point to the ellipse, the parameter takes the initial value m 0、n0、a0、b0、θ0 through iterative calculation, and the partial derivative is adopted here because f i 1 is difficult to calculate;
li＝-fi 1(m0,n0,a0,b0,θ0) (21)
The calculation method of f i 1 (m, n, a, b, θ) is as follows: in an elliptical coordinate system, a perpendicular line of an ellipse is drawn through points (x, y), an included angle between the perpendicular line and an x axis is B, and h is a perpendicular distance f i 1 between the points and the ellipse, so that the three-dimensional coordinate system is obtained:
Wherein:
Iterative calculation:
7. The method according to claim 1, wherein in the step 6.2, after obtaining the values of the parameters m and n by hough transform, the points on the elliptical arc are determined by using the parameters, the points are eliminated by using the distance threshold from the point to the ellipse or the range of the maximum arc that can be scanned, the calculated parameters are set as initial values, the points on the arc are fitted by indirect adjustment method, the least square solution of the coordinates of the center of the ellipse is obtained, so as to improve the accuracy, the rough elimination is performed by using the error in three times, and the fitting accuracy is prevented from being affected by the rough.
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