CN107101594B - Method for extracting lowest point of wheel flange of wheel track wheel space - Google Patents
Method for extracting lowest point of wheel flange of wheel track wheel space Download PDFInfo
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Abstract
The invention discloses a method for extracting the lowest point of a wheel flange in wheel track wheel space, which comprises the following steps: s1, arranging laser displacement sensors; s2, acquiring data of the laser displacement sensor and transforming three-dimensional coordinates; s3, determining a laser plane emitted by the laser displacement sensor; s4, determining the projection of the space rim data points and the end face projection straight line; s5, fitting a projection curve of the space wheel rim and primarily extracting the lowest point of the space wheel rim; and S6, extracting the final space rim lowest point. The method for extracting the lowest point of the wheel-rail wheel space rim has more accurate and practical extraction result, thereby providing reliable guarantee for the non-contact on-line accurate measurement of the overall dimension parameters of the wheel set and being very suitable for the rail traffic monitoring engineering technology.
Description
Technical Field
The invention belongs to the technical field of traffic monitoring engineering, and particularly relates to a method for extracting the lowest point of a wheel flange in a wheel track wheel space.
Background
In the basic traffic construction of subways, light rails and the like, the wheel set not only bears the whole weight of a train body, but also is responsible for transmitting acting force between the wheel set and a steel rail, so that the wheel set is an extremely important component in a train running structure and is an important factor influencing the safe operation of a train.
However, the wheel set continuously rubs against the surface of the steel rail in the running process of the train, so that the wheel set tread is easily abraded; further, when the wheelset passes through curves or switches, the rim portion of the wheelset is rubbed against the inner surface of the rail, and the rim is easily worn. Due to the wear of the wheel set tread and the wear of the wheel rim, the overall dimension of the wheel set is easily changed, and the safety of train operation is reduced.
Therefore, whether the overall dimension parameters (such as the thickness of the wheel rim, the height of the wheel rim, the diameter of the wheel and the like) of the wheel set can be timely, accurately and quickly detected so as to master the quality condition of the wheel set in real time and eliminate accident potential is a difficult problem to be solved in the development of rail transit. The accurate extraction of the lowest point of the wheel space rim is an important link for ensuring the accurate detection of the overall dimension parameters of the wheel set, however, no suitable method for accurately extracting the lowest point of the wheel space rim exists at present, so that the accuracy of the online monitoring of the rail vehicle is ensured.
Disclosure of Invention
In order to overcome the defects in the prior art, the invention provides a method for extracting the lowest point of the wheel flange of the wheel track wheel space, and the extracted result is more accurate and practical.
In order to solve the problems, the invention is realized according to the following technical scheme:
a method of extracting a lowest point of a wheel space rim of a wheel rail, comprising the steps of:
s1, arranging laser displacement sensors;
s2, laser displacement sensor data acquisition and three-dimensional coordinate transformation: after the laser displacement sensor detects the wheel rim of the wheel to be detected and acquires the coordinates of the detection point, the coordinates of the detection point are completely converted from the coordinate system of the laser displacement sensor to a geodetic coordinate system with the circle center of the wheel to be detected as the origin in a three-dimensional coordinate conversion mode;
s3, determining a laser plane emitted by the laser displacement sensor: for the same laser displacement sensor, selecting three points on the measured space rim data points to obtain a coordinate equation of a laser plane emitted by the laser sensor in the geodetic coordinate system;
s4, determining the projection of the spatial rim data points and the end face projection straight line: projecting the spatial rim data points measured by the laser displacement sensor to an xoz plane in the geodetic coordinate system; in the xoz plane, firstly setting a turning point threshold, and then finding out the turning point of the end face projection straight line, thereby solving an end face projection straight line equation;
s5, fitting of a space rim projection curve and preliminary extraction of a space rim lowest point: selecting a part of data point sections of the lowest point of the space wheel rim by taking the end face projection straight line as a reference, and carrying out curve fitting to obtain a projection coordinate value of the lowest point of the space wheel rim on a plane xoz;
s6, extracting the final space rim lowest point: and calculating the coordinate value of the lowest point of the space rim to be measured in the geodetic coordinate system according to the coordinate equation of the laser plane determined in the step S3 and the projection coordinate value of the lowest point of the space rim extracted in the step S5 on the xoz plane.
Further, in the step S1, the method for arranging the laser displacement sensor includes:
mounting the three laser displacement sensors on a straight line parallel to the rail on the inner side of the rail; three ofThe included angles between the laser displacement sensor and the plumb line are β respectively1、β2、β3The included angles between the three laser displacement sensors and a longitudinal horizontal line along the track direction are α respectively1、α2、α3。
Further, the rotation parameter and the displacement parameter of the three-dimensional coordinate transformation are related to the installation position and the installation angle of the laser displacement sensor.
Further, in step S2, the three-dimensional coordinate transformation method includes:
setting the coordinate system of the laser displacement sensor as O1-X1Y1Z1A geodetic coordinate system taking the wheel center of the standard wheel as an origin is O-XYZ; for a laser displacement sensor, at O1-X1Y1Z1In the coordinate system, the coordinate values outputted are (x, y,0), and according to the following formula,
converting to obtain the coordinate point (x) of the laser displacement sensor in the geodetic coordinate system O-XYZp,yp,zp)；
Wherein the content of the first and second substances,
wherein (ε)X,εY,εZ) The rotation angle parameters (Δ x, Δ y, Δ z) are relative translation parameters of the coordinate origin, which are respectively the rotation angle parameters of the transformation from the coordinate system of the laser displacement sensor to the geodetic coordinate system.
Further, in step S3, the specific method for determining the laser plane emitted by the laser displacement sensor includes:
selecting coordinate values of three data points of the space rim contour point measured by the laser displacement sensor in the geodetic coordinate system, and respectively recording the coordinate values as M1(x1,y1,z1)、M2(x2,y2,z2)、M3(x3,y3,z3) (ii) a Based on that the spatial contour points measured by the same laser displacement sensor are all on one laser emission plane, the three data points can determine that the coordinate equation of the laser plane emitted by the laser sensor in the geodetic coordinate system is as follows:
Ax+By+Cz+D＝0
wherein the content of the first and second substances,
further, in step S4, the specific method for determining the projection of the space rim data point and the end face projection straight line includes:
s41, in the established geodetic coordinate system, projecting the spatial rim data points measured by the laser displacement sensor to a plane xoz, namely defaulting the y coordinates of all coordinate values of the spatial rim data points to 0, and obtaining the projection of each spatial profile data point in the plane xoz;
s42, in plane xoz, according to the formula:
dx＝xi+1-xii＝1,2,…n
solving the difference dx of the x coordinate; wherein x isi,xi+1The x coordinate of the wheel set tread data point is shown, and n is the total data point;
s43, setting a turning point threshold DxThen, searching the obtained end surface projection straight turning point of dx; when | Dx | ≧ Dx, the index m of x at this time is noted, then the mean of the x-coordinates of these m spatial rim data points is the projection line equation of the end face in plane xoz, i.e.:
furthermore, the method for searching the obtained turning point of the end surface projection straight line of dx comprises a step-by-step method.
Further, in the step S5, the curve fitting includes 6 th order curve fitting.
Further, in step S5, the specific method of fitting the projected spacial rim curve and preliminarily extracting the lowest point of the spacial rim includes:
according to the end surface projection straight line equation X determined in the step S4, data points with X-axis coordinate values in the range of (X-23, X-3) are extracted and curve fitting is carried out, namely the fitting polynomial is as follows:
z＝a0+a1x+a2x2+a3x3+a4x4+a5x5+a6x6
the sum of the distances of the projected data points to the fitted curve, i.e., the sum of the partial variances, is:
to find out a meeting conditioniValue, peer-to-peer right fetch aiThe partial derivatives of (c) are obtained:
......
further simplification, obtaining:
......
conversion to matrix form:
thereby obtaining a coefficient matrix a ═ a0a1...... a6]TAnd further obtaining a fitting curve equation as follows:
z＝a0+a1x+a2x2+a3x3+a4x4+a5x5+a6x6
solving minimum value point (x) for the fitted curve equation0,z0) I.e. the projection coordinate value of the lowest point of the space rim on the xoz plane.
Compared with the prior art, the invention has the beneficial technical effects that:
the method for extracting the lowest point of the wheel flange in the wheel track wheel space provided by the invention has the advantages that the sensor is convenient to arrange, the structure and the principle are extremely simple, more importantly, the extracted result is extremely accurate and practical, and reliable guarantee can be provided for the non-contact online accurate measurement of the overall dimension parameter of the wheel pair. Specifically, for example: (1) the invention adopts a three-dimensional space transformation technology, takes the wheel center of the wheel to be measured as the origin of a coordinate system, thereby effectively eliminating the extraction error of the lowest point of the wheel rim caused by incomplete parallel of the wheel and the track; (2) according to the space geometric relationship between the wheel rim space contour data points and the laser plane of the laser displacement sensor, the lowest point of the wheel rim is obtained by the method of calculating the extreme point through space curve projection and curve fitting.
In conclusion, the invention is very suitable for the actual requirements of modern traffic engineering construction, and has wide market prospect in the technical field of traffic safety monitoring engineering.
Drawings
Embodiments of the invention are described in further detail below with reference to the attached drawing figures, wherein:
FIG. 1 is a schematic representation of the steps of one embodiment of the method of extracting the lowest point of the wheel rim of a wheel space of a wheel track according to the present invention;
FIG. 2 is a schematic view showing the installation of the laser displacement sensor according to embodiment 1;
FIG. 3 is a schematic diagram of three-dimensional coordinate transformation described in embodiment 1;
FIG. 4 is a schematic representation of the spatial rim data points measured by a sensor according to embodiment 1 in the geodetic coordinate system;
FIG. 5 is a schematic diagram of a sensor of embodiment 1 projecting a data point of a space rim onto xoz plane and finding a projected straight line of the end face;
FIG. 6 is a graph of the projection of data points of the spatial rim measured by a sensor as described in example 1 and a 6 th order curve fit.
Description of reference numerals:
1. a wheel; 2. a laser displacement sensor; 21. a first laser displacement sensor; 22. a second laser displacement sensor; 23. a third laser displacement sensor; 3. a track.
Detailed Description
In the following description, numerous specific details are set forth in order to provide a thorough understanding of the present invention, but the present invention may be embodied in many different forms without departing from the spirit or scope of the present invention, which should not be construed as limited to the specific embodiments set forth herein.
As shown in FIG. 1, the invention discloses a method for extracting the lowest point of a wheel flange of a wheel space of a wheel rail, which comprises the following steps:
s1, arranging the laser displacement sensors, wherein the specific method comprises the following steps:
three laser displacement sensors are arranged on a straight line which is arranged on the inner side of the track and is parallel to the track, and the included angles between the three laser displacement sensors and the plumb line are β respectively1、β2、β3The included angles between the three laser displacement sensors and the longitudinal horizontal line along the track direction are α respectively1、α2、α3。
S2, laser displacement sensor data acquisition and three-dimensional coordinate transformation: after the laser displacement sensor detects the wheel rim of the wheel to be detected and acquires the coordinates of the detection point, the coordinates of the detection point are completely converted from the coordinate system of the laser displacement sensor to a geodetic coordinate system with the circle center of the wheel to be detected as the origin in a three-dimensional coordinate conversion mode;
in step S2, the rotation parameter and the displacement parameter of the three-dimensional coordinate transformation are related to the installation position and the installation angle of the laser displacement sensor; the three-dimensional coordinate transformation method specifically includes:
let the coordinate system of the laser displacement sensor itself be O1-X1Y1Z1A geodetic coordinate system taking the wheel center of the standard wheel as an origin is O-XYZ; for a laser displacement sensor, at O1-X1Y1Z1In the coordinate system, the coordinate values outputted are (x, y,0), and according to the following formula,
converting to obtain the coordinate point (x) of the laser displacement sensor in the geodetic coordinate system O-XYZp,yp,zp)；
Wherein the content of the first and second substances,
wherein (ε)X,εY,εZ) The rotation angle parameters (delta x, delta y and delta z) are relative translation parameters of the coordinate origin, and the rotation angle parameters are respectively converted from the coordinate system of the laser displacement sensor to the geodetic coordinate system.
S3, determining a laser plane emitted by the laser displacement sensor: for the same laser displacement sensor, selecting three points on the measured spatial rim data points to obtain a coordinate equation of a laser plane emitted by the laser sensor in a geodetic coordinate system;
in step S3, the specific method for determining the laser plane emitted by the laser displacement sensor includes:
selecting three of the space rim contour points measured by the laser displacement sensorThe coordinate values of the data points in the geodetic coordinate system are respectively marked as M1(x1,y1,z1)、M2(x2,y2,z2)、M3(x3,y3,z3) (ii) a Based on the fact that the space contour points measured by the same laser displacement sensor are all on one laser emission plane, the coordinate equation of the laser plane emitted by the laser sensor in the geodetic coordinate system can be determined by the three data points as follows:
Ax+By+Cz+D＝0
wherein the content of the first and second substances,
s4, determining the projection of the spatial rim data points and the end face projection straight line: in a geodetic coordinate system, projecting a spatial rim data point measured by a laser displacement sensor to an xoz plane; in the xoz plane, firstly setting a turning point threshold, and then finding out the turning point of the end face projection straight line, thereby solving an end face projection straight line equation;
in step S4, the method for determining the projection of the space rim data point and the end face projection straight line includes:
s41, in the established geodetic coordinate system, projecting the spatial rim data points measured by the laser displacement sensor into a plane xoz, namely defaulting the y coordinates of all coordinate values of the spatial rim data points to 0, and obtaining the projection of each spatial profile data point in the plane xoz;
s42, in plane xoz, according to the formula:
dx＝xi+1-xii＝1,2,…n
solving the difference dx of the x coordinate; wherein x isi,xi+1The x coordinate of the wheel set tread data point is shown, and n is the total data point;
s43, setting a turning point threshold DxThen, searching the obtained end surface projection straight turning point of dx; when | Dx | ≧ Dx, the index m of x at that time is noted, then the mean of the x coordinates of the m spatial rim data points is the projection line equation of the end face in the plane xoz, i.e.：
In the above sub-step S43, the method for finding the inflection point of the end projection straight line of dx includes a step-by-step method.
S5, fitting of a space rim projection curve and preliminary extraction of a space rim lowest point: selecting partial data point sections of the lowest point of the space wheel rim by taking the end surface projection straight line as a reference, and carrying out curve fitting to obtain the projection coordinate value of the lowest point of the space wheel rim on the xoz plane;
in step S5, the curve fitting is specifically 6 th order curve fitting; the concrete method for fitting the projection curve of the space rim and preliminarily extracting the lowest point of the space rim comprises the following steps:
according to the end surface projection straight line equation X determined in the step S4, data points with X-axis coordinate values in the range of (X-23, X-3) are extracted and curve fitting is carried out, namely the fitting polynomial is as follows:
z＝a0+a1x+a2x2+a3x3+a4x4+a5x5+a6x6
the sum of the distances of the projected data points to the fitted curve, i.e., the sum of the partial variances, is:
to find out a meeting conditioniValue, peer-to-peer right fetch aiThe partial derivatives of (c) are obtained:
......
further simplification, obtaining:
......
conversion to matrix form:
thereby obtaining a coefficient matrix a ═ a0a1...... a6]TAnd further obtaining a fitting curve equation as follows:
z＝a0+a1x+a2x2+a3x3+a4x4+a5x5+a6x6
for the fitted curve equation, minimum value point (x) is obtained0,z0) It is the projection coordinate value of the lowest point of the space wheel rim on the xoz plane.
S6, extracting the final space rim lowest point: the coordinate equation of the laser plane determined in the above step S3 (Ax + By + Cz + D is 0), and the projection coordinate value (x) of the lowest point of the spatial rim extracted in the above step S5 on the xoz plane0,z0) And calculating the coordinate value P (x) of the lowest point of the space rim to be measured in the geodetic coordinate system0,y0,z0) It is the final captured spacial rim nadir.
Example 1
As shown in fig. 2 to 6, three laser displacement sensors 2 are installed inside the track 3 along a direction parallel to the track 3, wherein the included angles between the first laser displacement sensor 21, the second laser displacement sensor 22 and the third laser displacement sensor 23 and the plumb line are all 45 °, that is, β1、β2、β3Is 45 degrees; the first laser displacement sensor 21 and the third laser displacement sensor 23 form an angle of 45 degrees with the longitudinal horizontal line along the direction of the track 3Assemblies, i.e. α1、α3Are all 45 deg., and the second laser displacement sensor 22 is installed in parallel along the longitudinal horizontal line in the direction of the rail 3, i.e., α2Is 0 deg..
Hereinafter, the lowest point of the rim of the wheel 1 measured by the second laser displacement sensor 22 is obtained by taking the second laser displacement sensor 22 as an example.
(1) For the second laser displacement sensor 22, O is in itself1-X1Y1Z1In the coordinate system, the output coordinate value is (x, y, 0); first, clockwise around X1Rotation of the shaft
Then clockwise around Y1Shaft rotation β2Finally clockwise around Z1The axis is rotated by pi, thereby obtaining rotation parameters
εY＝-β2,εZAnd (pi), obtaining a coordinate rotation transformation matrix according to the rotation parameters:
the coordinate system O of the second laser displacement sensor 22 itself1-X1Y1Z1Translation matrix [ delta x delta y delta z ] of points between the coordinate system and the earth coordinate system O-XYZ]T＝[328.42 -0.5846 -640.3469]T(ii) a The coordinate point (x) of the second laser displacement sensor 22 in the geodetic coordinate system O-XYZ can be obtained through conversion by the coordinate rotation conversion matrix and the translation matrixp,yp,zp) And then:
thus, the smallest Z-axis data point coordinate value is directly obtained as P1:(42.8475,0.5846,-422.9682)。
(2) Selecting 3 groups of data from the coordinate values of the space rim contour point measured by the second laser displacement sensor 22 in the geodetic coordinate system, and calculating to obtain a coordinate equation of a laser plane emitted by the second laser displacement sensor 22 in the geodetic coordinate system as
y＝0.5846
(3) In the established geodetic coordinate system, the spatial rim data points measured by the second laser displacement sensor 22 are projected to the xoz plane; in the xoz plane, the end surface projection line equation is solved as:
x＝54.3173
(4) taking data with the horizontal distance between the projection straight lines of the opposite end faces being 2mm and 23mm, and carrying out 6-order curve fitting to obtain a fitting curve equation:
z＝-3.0684×10-7x6+8.4615×10-5x5-0.0096x4+0.5747x3-19.0927x2+332.6156x-2781.4
and (4) solving minimum points of the fitted curve equation to obtain the projection coordinates (42.7791-422.9832) of the lowest point of the wheel rim of the wheel 1.
(5) And (3) substituting the projection coordinate of the lowest point of the wheel rim of the wheel 1 obtained in the step (4) into the laser plane equation determined in the step (2) to obtain the final coordinate value of the lowest point of the space wheel rim measured by the second laser displacement sensor 22 as P (42.7791,0.5846, -422.9832).
The lowest point coordinate value P directly read by comparing with the second laser displacement sensor 221(42.8475,0.5846, -422.9682), it is seen that the present invention is more consistent with the practical requirements of extracting the lowest point of the rim.
Finally, it is to be noted that: other parts of the method for extracting the lowest point of the wheel flange of the wheel space of the wheel rail according to the invention are referred to in the prior art.
The above description is only a preferred embodiment of the present invention, and is not intended to limit the present invention in any way, so that any modification, equivalent change and modification made to the above embodiment according to the technical spirit of the present invention are within the scope of the technical solution of the present invention.
Claims (7)
1. A method of extracting a lowest point of a wheel space rim of a wheel rail, comprising the steps of:
s1, arranging the laser displacement sensors, wherein the arranging method comprises the following steps:
the three laser displacement sensors are arranged on a straight line which is arranged on the inner side of the track and is parallel to the track, and the included angles between the three laser displacement sensors and the plumb line are β respectively1、β2、β3The included angles between the three laser displacement sensors and a longitudinal horizontal line along the track direction are α respectively1、α2、α3；
S2, laser displacement sensor data acquisition and three-dimensional coordinate transformation: the rotation parameter and the displacement parameter of the three-dimensional coordinate transformation are related to the installation position and the installation angle of the laser displacement sensor;
after the laser displacement sensor detects the wheel rim of the wheel to be detected and acquires the coordinates of the detection point, the coordinates of the detection point are completely converted from the coordinate system of the laser displacement sensor to a geodetic coordinate system with the circle center of the wheel to be detected as the origin in a three-dimensional coordinate conversion mode;
s3, determining a laser plane emitted by the laser displacement sensor: for the same laser displacement sensor, selecting three points on the measured space rim data points to obtain a coordinate equation of a laser plane emitted by the laser sensor in the geodetic coordinate system;
s4, determining the projection of the spatial rim data points and the end face projection straight line: projecting the spatial rim data points measured by the laser displacement sensor to an xoz plane in the geodetic coordinate system; in the xoz plane, firstly setting a turning point threshold, and then finding out the turning point of the end face projection straight line, thereby solving an end face projection straight line equation;
s5, fitting of a space rim projection curve and preliminary extraction of a space rim lowest point: selecting a part of data point sections of the lowest point of the space wheel rim by taking the end face projection straight line as a reference, and carrying out curve fitting to obtain a projection coordinate value of the lowest point of the space wheel rim on a plane xoz;
s6, extracting the final space rim lowest point: and calculating the coordinate value of the lowest point of the space rim to be measured in the geodetic coordinate system according to the coordinate equation of the laser plane determined in the step S3 and the projection coordinate value of the lowest point of the space rim extracted in the step S5 on the xoz plane.
2. The method of extracting a wheel rail wheel space rim nadir according to claim 1 wherein in step S2, the three dimensional coordinate transformation comprises:
setting the coordinate system of the laser displacement sensor as O1-X1Y1Z1A geodetic coordinate system taking the wheel center of the standard wheel as an origin is O-XYZ; for a laser displacement sensor, at O1-X1Y1Z1In the coordinate system, the coordinate values outputted are (x, y,0), and according to the following formula,
converting to obtain the coordinate point (x) of the laser displacement sensor in the geodetic coordinate system O-XYZp,yp,zp)；
Wherein the content of the first and second substances,
wherein (ε)X,εY,εZ) The rotation angle parameters (Δ x, Δ y, Δ z) are relative translation parameters of the coordinate origin, which are respectively the rotation angle parameters of the transformation from the coordinate system of the laser displacement sensor to the geodetic coordinate system.
3. The method of extracting the lowest point of the wheel-rail wheel-space rim of claim 1, wherein in the step S3, the specific method of determining the laser plane emitted by the laser displacement sensor comprises:
selecting the laser displacement sensor to measureThe coordinate values of three data points of the space rim contour point in the geodetic coordinate system are respectively marked as M1(x1,y1,z1)、M2(x2,y2,z2)、M3(x3,y3,z3) (ii) a Based on that the spatial contour points measured by the same laser displacement sensor are all on one laser emission plane, the three data points can determine that the coordinate equation of the laser plane emitted by the laser sensor in the geodetic coordinate system is as follows:
Ax+By+Cz+D＝0
wherein the content of the first and second substances,
4. the method for extracting the lowest point of the wheel-side rim of the wheel-side rail according to claim 1, wherein the step S4 is performed by a specific method for determining the projection of the data points of the wheel-side rim and the end projection straight line of the wheel-side rail, which comprises the following steps:
s41, in the established geodetic coordinate system, projecting the spatial rim data points measured by the laser displacement sensor to a plane xoz, namely defaulting the y coordinates of all coordinate values of the spatial rim data points to 0, and obtaining the projection of each spatial profile data point in the plane xoz;
s42, in plane xoz, according to the formula:
dx＝xi+1-xii＝1,2,…n
solving the difference dx of the x coordinate; wherein x isi,xi+1The x coordinate of the wheel set tread data point is shown, and n is the total data point;
s43, setting a turning point threshold DxThen, searching the obtained end surface projection straight turning point of dx; when | Dx | ≧ Dx, the index m of x at this time is noted, then the mean of the x-coordinates of these m spatial rim data points is the projection line equation of the end face in plane xoz, i.e.:
5. the method of extracting a wheel rail wheel space rim nadir according to claim 4, wherein: the method for searching the obtained turning point of the end surface projection straight line of dx comprises a step-by-step method.
6. The method of extracting a wheel rail wheel space rim nadir according to claim 4 or 5, wherein: in step S5, the curve fitting includes 6 th order curve fitting.
7. The method for extracting the lowest point of the wheel-rail wheel spatial rim according to claim 6, wherein in the step S5, the concrete method for fitting the projected curve of the spatial rim and preliminarily extracting the lowest point of the spatial rim comprises the following steps:
according to the end surface projection straight line equation X determined in the step S4, data points with X-axis coordinate values in the range of (X-23, X-3) are extracted and curve fitting is carried out, namely the fitting polynomial is as follows:
z＝a0+a1x+a2x2+a3x3+a4x4+a5x5+a6x6
the sum of the distances of the projected data points to the fitted curve, i.e., the sum of the partial variances, is:
to find out a meeting conditioniValue, peer-to-peer right fetch aiThe partial derivatives of (c) are obtained:
further simplification, obtaining:
conversion to matrix form:
thereby obtaining a coefficient matrix a ═ a0a1...... a6]TAnd further obtaining a fitting curve equation as follows:
z＝a0+a1x+a2x2+a3x3+a4x4+a5x5+a6x6
solving minimum value point (x) for the fitted curve equation0,z0) I.e. the projection coordinate value of the lowest point of the space rim on the xoz plane.
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| CN109334709B (en) * | 2018-12-09 | 2023-07-14 | 马鞍山市雷狮轨道交通装备有限公司 | Device and method for measuring wheel rim parameters |
| CN111336948B (en) * | 2020-03-02 | 2021-11-02 | 武汉理工大学 | Non-calibration handheld profile detection method and device based on imaging plane conversion |
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| CN104590314B (en) * | 2015-01-16 | 2017-05-17 | 南京理工大学 | Device and method for measuring diameter of urban rail vehicle wheel based on multiple sensors |
| CN105292180A (en) * | 2015-11-13 | 2016-02-03 | 南京理工大学 | Non-contact wheel set dimension online detection method and device based on various sensors |
| CN106091951B (en) * | 2016-05-27 | 2018-11-13 | 南京理工大学 | A kind of municipal rail train wheel rim parameter on-line detecting system and method |
| CN106017354A (en) * | 2016-07-26 | 2016-10-12 | 广州地铁集团有限公司 | Train wheelset tread three-dimensional contour automatic measurement method and system |
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