CN107451095B - Urban rail vehicle wheel pair curve fitting method - Google Patents
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Abstract
The invention discloses a curve fitting method for wheel sets of urban rail vehicles. The method comprises the following steps: acquiring wheel set surface data information points: acquiring data information of the surface of the wheel pair through two-dimensional laser displacement sensors arranged on two sides of the track; preprocessing surface data information: preprocessing the detected wheel set surface data to obtain a reconstructed wheel set surface curve; determining a curve segment to be fitted: determining an area to be fitted on the wheel set curve according to the reconstructed wheel set surface curve; and (3) wheel pair curve fitting: fitting the wheel pair surface curve by adopting a least square support vector machine method in the range of the area to be fitted to obtain a complete wheel pair surface curve; calculating the size parameters of the wheel set: and calculating to obtain the wheel set size parameters according to the wheel set size parameter definition criterion. According to the method, the two-dimensional laser displacement sensor is used for acquiring the data information of the wheel set surface, the support vector machine method of least square is used for converting the nonlinear approximation problem into the linear approximation problem, the fitting effect is good, and the calculation result is accurate.
Description
Technical Field
The invention belongs to the technical field of traffic safety engineering, and particularly relates to a curve fitting method for wheel sets of urban rail vehicles.
Background
The urban rail train is the core of the rail transit industry, and in order to realize the modernized development of the urban rail transit industry, an advanced modernized urban rail train must be researched and developed, which is a prerequisite and cannot be ignored. The urban rail train is a complex and comprehensive system, and has large equipment quantity and complex technology. Urban rail trains generally run in an inter-regional tunnel, and when a fault occurs or an emergency occurs, the running environment is not favorable for people evacuation and emergency handling. Therefore, the primary task of the urban rail transit system in the construction and operation phases is "safety".
The wheel set is an important component of a running gear of an urban rail train, bears the weight of the whole train, and changes of parameters of the wheel set influence the safe running of the train, so that the changes of the parameters need to be monitored in real time. Currently, the wheel set parameter measurement is mainly carried out by a laser method. The coordinates of the discrete points of the tread are obtained through measurement of the laser displacement sensor, fitting needs to be carried out on the discrete points, different fitting methods influence the final wheel set parameter calculation result, and curve overfitting and curve underfitting are not advisable.
Some research results have been obtained aiming at the research on the influence of the wheel set size detection system to the detection result of the detection system by the wheel set tread curve fitting method. The Haerbin industry university provides a wheel set rim on-line detection system based on least square fitting, but the method has the problems of curve overfitting and low calculation result precision.
Disclosure of Invention
The invention aims to provide a curve fitting method for wheel pairs of urban rail vehicles, which is good in fitting effect and high in calculation accuracy.
The technical solution for realizing the purpose of the invention is as follows: a method for fitting curves of wheel sets of urban rail vehicles comprises the following steps:
step 1, acquiring wheel set surface data information points: acquiring data information of the surface of the wheel pair through two-dimensional laser displacement sensors arranged on two sides of the track;
step 2, wheel set surface data information preprocessing: preprocessing the detected wheel set surface data to obtain a reconstructed wheel set surface curve;
step 3, determining a curve segment to be fitted: determining an area to be fitted on the wheel set curve according to the reconstructed wheel set surface curve;
step 4, wheel pair curve fitting: fitting the wheel pair surface curve by adopting a least square support vector machine method in the range of the area to be fitted to obtain a complete wheel pair surface curve;
step 5, calculating the wheel set size parameters: and calculating to obtain the wheel set size parameters according to the wheel set size parameter definition criterion.
Further, the step 1 of acquiring wheel set surface data information points specifically includes: a first two-dimensional laser displacement sensor S1 and a second two-dimensional laser displacement sensor S2 are respectively arranged on the inner side and the outer side of a unilateral track, the laser emission points of the first two-dimensional laser displacement sensor S1 and the second two-dimensional laser displacement sensor S2 are not higher than the plane of the track, the first two-dimensional laser displacement sensor S1 and the second two-dimensional laser displacement sensor S2 are symmetrically distributed around the track, the emitted laser beams are superposed on the same plane, the included angle between the plane and the horizontal plane is theta,the included angles between the first two-dimensional laser displacement sensor S1 and the second two-dimensional laser displacement sensor S2 and a plumb line are α, and the wheel set surface data information detected by the first two-dimensional laser displacement sensor S1 and the second two-dimensional laser displacement sensor S2 is a two-dimensional coordinate point which is (u) respectively1 (i),v1 (i))、(u2 (j),v2 (j))。
Further, the wheel set surface data information preprocessing described in step 2 specifically includes: carrying out coordinate rotation processing on a coordinate system of the two-dimensional laser displacement sensor; removing interference on the track, the wheel axis and the brake part detected in the detection process; carrying out coordinate translation processing on space isolation existing between two-dimensional laser displacement sensors on two sides of a track, and unifying the space isolation to the same coordinate system; and finally, obtaining the reconstructed complete wheel set surface curve data.
Further, the determining a curve segment to be fitted in step 3 specifically includes: setting the inner end surface of the wheel set tread without abrasion as a datum line l, and setting the section of a curve to be fitted of the wheel set rim as [ l-d ]2,l-d1]Wherein d is1∈(2,7),d2∈ (35,40), and the curve segment to be fitted of the wheel set tread is l-70-d3,l-70+d4]Wherein d is3、d4∈(8,25)。
Further, the least square support vector machine method is adopted in the step 4, the surface curve is fitted through the wheel, and discrete data points of a curve segment to be fitted are set to be (x)(i),y(i)) The method comprises the following specific steps:
(4.1) fitting the functional form to
Wherein
Is a feature mapping, w and b are fitting parameters to be solved; the optimization objective is formula (1):
wherein ξ ═ (ξ)1,ξ2,…,ξl)T，ξ*＝(ξ1 *,ξ2 *,…,ξl *)T，ξ、ξ*Is a relaxation factor and is an approximation precision, and gamma is a set penalty coefficient;
(4.2) converting equation (1) into an equality constraint, and converting the optimization objective into equation (2):
wherein ξ ═ (ξ)1,ξ2,…,ζl)T；
The Lagrangian function of formula (2) is
Wherein α ═ (α)1,α2,…,αl)Tα is Lagrange multiplier;
(4.3) from formula (3)
Namely, it is
Wherein N is the number of samples, l is the dimension of the samples,
y＝[y1,y2,…,yl]T，
ξ＝(ξ1,ξ2,…,ξl)T，α＝(α1,α2,…,αl)T；
is shown by the formula (5)
Elimination of w, ξiObtaining a linear equation system:
combined with Mercer conditions:
taking the Gaussian kernel function exp (- | x) as the kernel function k (·,. cndot.)i-xj||2/(2σ2))；
(4.4) note A ≡ Ω + γ-1I, conversion of formula (5) to formula (8)
Obtained from the formula (9)
The curve function to be fitted is then
Further, the step 5 of calculating the wheel set size parameter specifically includes: and on the basis of obtaining the tread fitting curve, extracting the coordinates of the reference points according to the tread reference point definition rule, and obtaining the wheel set parameters.
Compared with the prior art, the invention has the following remarkable advantages: (1) the two-dimensional laser displacement sensor is used for acquiring the surface data information of the wheel set, so that the detection precision is high; (2) the support vector machine method of least square is used for converting the nonlinear approximation problem into the linear approximation problem, the obtained optimal curve is used as the wheel set surface information, the fitting precision is high, and the calculation error is small.
Drawings
FIG. 1 is a flow chart of a curve fitting method for wheel pairs of urban rail vehicles.
Fig. 2 is a coordinate fusion diagram of a two-dimensional laser displacement sensor.
FIG. 3 is a partial view of the tread rim of the region to be fitted.
Fig. 4 is a graph of wheel-set curve fitting results.
Detailed Description
The invention is further described with reference to the accompanying drawings and the specific embodiments.
With reference to fig. 1, the method for fitting curves of wheel sets of urban rail vehicles comprises the following steps:
step 1, acquiring wheel set surface data information points: acquiring data information of the surface of the wheel pair through two-dimensional laser displacement sensors arranged on two sides of the track;
a first two-dimensional laser displacement sensor S1 and a second two-dimensional laser displacement sensor S2 are respectively arranged on the inner side and the outer side of a single-side track, the laser emission points of the first two-dimensional laser displacement sensor S1 and the second two-dimensional laser displacement sensor S2 are not higher than a track plane, the first two-dimensional laser displacement sensor S1 and the second two-dimensional laser displacement sensor S2 are symmetrically distributed about the track, emitted laser beams are superposed on the same plane, the included angle between the plane and the horizontal plane is theta, the included angles between the first two-dimensional laser displacement sensor S1 and the second two-dimensional laser displacement sensor S2 and a vertical line are α, and wheel set surface data information detected by the first two-dimensional laser displacement sensor S1 and the second two-dimensional laser displacement sensor S2 is (u, u1 (i),v1 (i))、(u2 (j),v2 (j))。
Step 2, wheel set surface data information preprocessing: preprocessing the detected wheel set surface data to obtain a reconstructed wheel set surface curve;
the two-dimensional laser displacement sensor is provided with a coordinate system and needs to be subjected to coordinate rotation processing; the interference of parts such as a track, a wheel axis, a brake and the like can be generated in the detection process, and the interference needs to be removed; space isolation exists between the laser displacement sensors on the two sides of the track, coordinate translation processing needs to be carried out, and the laser displacement sensors are unified to a same coordinate system;
therefore, coordinate rotation processing is carried out on a coordinate system of the two-dimensional laser displacement sensor; removing interference on the track, the wheel axis and the brake part detected in the detection process; carrying out coordinate translation processing on space isolation existing between two-dimensional laser displacement sensors on two sides of a track, and unifying the space isolation to the same coordinate system; and finally, the reconstructed complete wheel set surface curve data is obtained, as shown in figure 2.
Step 3, determining a curve segment to be fitted: determining an area to be fitted on the wheel set curve according to the reconstructed wheel set surface curve;
the wheel set surface curve consists of a gentle curve and an arc curve, and the datum points for calculating the diameter of the wheel set, the height of the wheel rim and the thickness of the wheel rim are only on part of the wheel set surface curve, so that the method for fitting only part of the curve segments is as follows.
From the wheel set surface data information points, it can be determined that the inner end surface of the wheel set tread without abrasion is a datum line l, and the section of the curve to be fitted of the wheel set rim is [ l-d ]2,l-d1]Wherein d is1∈(2,7),d2∈ (35,40), and the curve segment to be fitted of the wheel set tread is l-70-d3,l-70+d4]Wherein d is3、d4∈ (8,25), the partitioning results are shown in fig. 3.
Step 4, wheel pair curve fitting: in the range of the area to be fitted, fitting the wheel pair surface curve by adopting a least square support vector machine method to obtain a complete wheel pair surface curve, and setting discrete data points of the curve section to be fitted as (x)(i),y(i)) The method comprises the following steps:
(4.1) fitting the functional form to
Wherein
Is the feature mapping, w and b are the fitting parameters to be solved. The optimization objective is formula (1):
wherein ξ ═ (ξ)1,ξ2,…,ξl)T，ξ*＝(ξ1 *,ξ2 *,…,ξl *)T，ξ、ξ*Is a relaxation factor and is an approximation precision, and gamma is a set penalty coefficient;
(4.2) converting equation (1) into an equality constraint, and converting the optimization objective into equation (2):
wherein ξ ═ (ξ)1,ξ2,…,ζl)T；
The Lagrangian function of formula (2) is
Wherein α ═ (α)1,α2,…,αl)Tα is Lagrange multiplier;
(4.3) from formula (3)
Namely, it is
Wherein N is the number of samples, l is the dimension of the samples,
y＝[y1,y2,…,yl]T，
ξ＝(ξ1,ξ2,…,ξl)T，α＝(α1,α2,…,αl)T；
is shown by the formula (5)
Elimination of w, ξiObtaining a linear equation system:
combined with Mercer conditions:
taking the Gaussian kernel function exp (- | x) as the kernel function k (·,. cndot.)i-xj||2/(2σ2))；
(4.4) note A ≡ Ω + γ-1I, conversion of formula (5) to formula (8)
Obtained from the formula (9)
The curve function to be fitted is then
The curve fitting results are shown in fig. 4.
Step 5, calculating the wheel set size parameters: and calculating to obtain the wheel set size parameters according to the wheel set size parameter definition criterion. The method specifically comprises the following steps: and on the basis of obtaining the tread fitting curve, extracting the coordinates of the reference points according to the tread reference point definition rule, and obtaining the wheel set parameters.
Example 1
The method comprises the steps of collecting multiple groups of wheel set surface detection data by taking wheel set surface information data collected by a set of wheel set size online detection system installed in a vehicle overhaul warehouse of a subway company as a research object, and explaining the method by using one group of data.
By using the wheel set surface data information points, it can be determined that the inner end surface of the wheel set tread without wear is a datum line l, and the section of the curve to be fitted of the wheel set rim is [ l-d ]2,l-d1]Wherein d is1∈(2,7),d2∈ (35,40), and the curve segment to be fitted of the wheel set tread is l-70-d3,l-70+d4]Wherein d is3、d4∈(8,25)。
Preprocessing the data to obtain a coordinate point of the tread data as shown in the formula (10)
The wheel rim data coordinate point is shown as formula (11)
Fitting the tread data points and the wheel rim data points by using a least square support vector machine respectively, wherein the result is as follows:
tread partThe fitting function is
The rim portion fitting function is
After the surface curve is subjected to segmented fitting, coordinate values of positions of the datum points are searched, and the first wheel rim datum point is (-281.3786,303.5439), the second wheel rim datum point is (-296.3054,322.9051), and the first tread datum point is (-337.9701,332.7283). And calculating to obtain each parameter of the wheel set by combining the wheel set size parameter definition and the wheel set benchmark reference point. The result was a rim height of 28.7965mm and a rim thickness of 29.1733 mm.
In conclusion, the two-dimensional laser displacement sensor is used for acquiring the data information of the wheel set surface, so that the detection precision is high; the support vector machine method of least square is used for converting the nonlinear approximation problem into the linear approximation problem, the obtained optimal curve is used as the wheel set surface information, the fitting precision is high, and the calculation error is small.
Claims (5)
1. A method for fitting curves of wheel sets of urban rail vehicles is characterized by comprising the following steps:
step 1, acquiring wheel set surface data information points: acquiring data information of the surface of the wheel pair through two-dimensional laser displacement sensors arranged on two sides of the track;
step 2, wheel set surface data information preprocessing: preprocessing the detected wheel set surface data to obtain a reconstructed wheel set surface curve;
step 3, determining a curve segment to be fitted: determining an area to be fitted on the wheel set curve according to the reconstructed wheel set surface curve;
step 4, wheel pair curve fitting: fitting the wheel pair surface curve by adopting a least square support vector machine method in the range of the area to be fitted to obtain a complete wheel pair surface curve;
step 5, calculating the wheel set size parameters: calculating to obtain wheel set size parameters according to the wheel set size parameter definition criterion;
and 4, fitting the surface curve by using a least square support vector machine method, and setting discrete data points of a curve segment to be fitted as (x)(i),y(i)) The method comprises the following specific steps:
(4.1) fitting the functional form to
Wherein
Is a feature mapping, w and b are fitting parameters to be solved; the optimization objective is formula (1):
wherein ξ ═ (ξ)1,ξ2,…,ξl)T，ξ*＝(ξ1 *,ξ2 *,…,ξl *)T，ξ、ξ*Is a relaxation factor and is an approximation precision, and gamma is a set penalty coefficient;
(4.2) converting equation (1) into an equality constraint, and converting the optimization objective into equation (2):
wherein ξ ═ (ξ)1,ξ2,…,ζl)T；
The Lagrangian function of formula (2) is
Wherein α ═ (α)1,α2,…,αl)Tα is Lagrange multiplier;
(4.3) from formula (3)
Namely, it is
Wherein N is the number of samples, l is the dimension of the samples,
y＝[y1,y2,…,yl]T，
ξ＝(ξ1,ξ2,…,ξl)T，α＝(α1,α2,…,αl)T；
is shown by the formula (5)
Elimination of w, ξiObtaining a linear equation system:
combined with Mercer conditions:
taking the Gaussian kernel function exp (- | x) as the kernel function k (·,. cndot.)i-xj||2/(2σ2))；
(4.4) note A ≡ Ω + γ-1I, conversion of formula (5) to formula (8)
Is obtained from the formula (9)To obtain
The curve function to be fitted is then
2. The curve fitting method for urban rail vehicle wheel pair according to claim 1, wherein the wheel pair surface data information points obtained in step 1 are specifically obtained by respectively arranging a first two-dimensional laser displacement sensor S1 and a second two-dimensional laser displacement sensor S2 on the inner side and the outer side of a unilateral track, the laser emission points of the first two-dimensional laser displacement sensor S1 and the second two-dimensional laser displacement sensor S2 are not higher than the plane of the track, the first two-dimensional laser displacement sensor S1 and the second two-dimensional laser displacement sensor S2 are symmetrically distributed about the track, emitted laser beams are superposed on the same plane, the included angle between the plane and the horizontal plane is theta, the included angles between the first two-dimensional laser displacement sensor S1 and the second two-dimensional laser displacement sensor S2 and the plumb line are α, the wheel pair surface data information detected by the first two-dimensional laser displacement sensor S1 and the second two-dimensional laser displacement sensor S2 are two-dimensional coordinate points (u is1 (i),v1 (i))、(u2 (j),v2 (j))。
3. The method for fitting curves to wheel pairs of urban rail vehicles according to claim 1, wherein the wheel pair surface data information preprocessing of step 2 specifically comprises: carrying out coordinate rotation processing on a coordinate system of the two-dimensional laser displacement sensor; removing interference on the track, the wheel axis and the brake part detected in the detection process; carrying out coordinate translation processing on space isolation existing between two-dimensional laser displacement sensors on two sides of a track, and unifying the space isolation to the same coordinate system; and finally, obtaining the reconstructed complete wheel set surface curve data.
4. The method for fitting curves of wheel pairs of urban rail vehicles according to claim 1, wherein the determination of the curve segment to be fitted in step 3 is specifically as follows: setting the inner end surface of the wheel set tread without abrasion as a datum line l, and setting the section of a curve to be fitted of the wheel set rim as [ l-d ]2,l-d1]Wherein d is1∈(2,7),d2∈ (35,40), and the curve segment to be fitted of the wheel set tread is l-70-d3,l-70+d4]Wherein d is3、d4∈(8,25)。
5. The method for fitting curves of wheel pairs of urban rail vehicles according to claim 1, wherein the step 5 of calculating wheel pair size parameters specifically comprises: and on the basis of obtaining the tread fitting curve, extracting the coordinates of the reference points according to the tread reference point definition rule, and obtaining the wheel set parameters.
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| WO2013043087A1 (en) * | 2011-09-23 | 2013-03-28 | Volvo Construction Equipment Ab | Method for selecting an attack pose for a working machine having a bucket |
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