CN107451095A - A kind of city rail vehicle wheel is to curve-fitting method - Google Patents
A kind of city rail vehicle wheel is to curve-fitting method Download PDFInfo
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- CN107451095A CN107451095A CN201710528467.7A CN201710528467A CN107451095A CN 107451095 A CN107451095 A CN 107451095A CN 201710528467 A CN201710528467 A CN 201710528467A CN 107451095 A CN107451095 A CN 107451095A
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
- G06F17/10—Complex mathematical operations
- G06F17/11—Complex mathematical operations for solving equations, e.g. nonlinear equations, general mathematical optimization problems
- G06F17/12—Simultaneous equations, e.g. systems of linear equations
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
- G06F17/10—Complex mathematical operations
- G06F17/15—Correlation function computation including computation of convolution operations
Abstract
The invention discloses a kind of city rail vehicle wheel to curve-fitting method.Method is:Wheel is obtained to surface data information point:Two-dimensional laser displacement transducer by being arranged in track both sides obtains data message of the wheel to surface;To surface data information pre-processing:The wheel detected is pre-processed to surface data, the wheel reconstructed is to surface curve;It is determined that treat matched curve section:According to the wheel reconstructed to surface curve, it is determined that wheel is to region to be fitted on curve;Wheel is to curve matching:Treating in the range of fitted area, using least square method supporting vector machine method, processing is being fitted to surface curve to wheel, obtains completely taking turns to surface curve;Calculate wheelset profile parameter:According to wheelset profile parameter definition criterion, wheelset profile parameter is calculated.The present invention obtains wheel to surface data information using two-dimensional laser displacement transducer, None-linear approximation problem is converted into linear approximation problem using the SVMs method of least square, fitting effect is good, result of calculation is accurate.
Description
Technical field
The invention belongs to traffic safety field of engineering technology, particularly a kind of city rail vehicle wheel is to curve-fitting method.
Background technology
Municipal rail train is the core of track traffic cause, to realize the modernization development of urban track traffic cause, it is necessary to
Advanced modernization municipal rail train is researched and developed, this is prerequisite, be can not be ignored.Municipal rail train is one
System, equipment amount is big, technical sophistication.Municipal rail train is typically run in running tunnel, when breaking down or emergency case occur
When, this running environment is unfavorable for evacuating personnel and the processing for case of emergency very much.Therefore, City Rail Transit System is built
If the top priority with operation stage is exactly " safety ".
Wheel carries the weight of whole train, takes turns the change to parameter to being municipal rail train EEF bogie important component
Affect the safe operation of train, it is therefore desirable to monitor its change in real time.Parameter measurement is mainly passed through for wheel at present and swashed
Light method.The discrete point coordinates of tread is obtained by laser displacement sensor measurement, it is necessary to be fitted to it, different approximating methods
It is all inadvisable to parameter result of calculation, curve over-fitting and poor fitting to affect final wheel.
Detecting system testing result is influenceed for wheelset profile detecting system detection wheel tread curve-fitting method
Research, has been achieved for some achievements in research.What equality people of Harbin Institute of Technology proposes a kind of based on least square plan
The wheel of conjunction is to wheel rim on-line detecting system, but this method has the problem of curve over-fitting, computational solution precision is low.
The content of the invention
Present invention aims at the city rail vehicle wheel that a kind of fitting effect of offer is good, computational accuracy is high to curve matching side
Method.
The technical solution for realizing the object of the invention is:A kind of city rail vehicle wheel is including following to curve-fitting method
Step:
Step 1, wheel is obtained to surface data information point:Obtained by the two-dimensional laser displacement transducer for being arranged in track both sides
Take data message of the wheel to surface;
Step 2, take turns to surface data information pre-processing:The wheel detected is pre-processed to surface data, obtains weight
The wheel of structure is to surface curve;
Step 3, it is determined that treating matched curve section:According to the wheel reconstructed to surface curve, it is determined that wheel on curve to waiting to be fitted
Region;
Step 4, take turns to curve matching:Treating in the range of fitted area, using least square method supporting vector machine method, to wheel pair
Surface curve is fitted processing, obtains completely taking turns to surface curve;
Step 5, wheelset profile parameter is calculated:According to wheelset profile parameter definition criterion, wheelset profile parameter is calculated.
Further, the acquisition wheel described in step 1 is specially to surface data information point:Two inside and outside single-sided tracks
While it is respectively arranged the first two-dimensional laser displacement transducer S1, the second two-dimensional laser displacement transducer S2, the first two-dimensional laser displacement
Sensor S1, the second two-dimensional laser displacement transducer S2 laser emission point are not higher than orbit plane, the first two-dimensional laser displacement
Sensor S1 and the second two-dimensional laser displacement transducer S2 is distributed on the Orbital Symmetry, and the laser beam of injection coincides with same put down
Face, the plane and horizontal plane angle be θ, the first two-dimensional laser displacement transducer S1, the second two-dimensional laser displacement transducer S2 and
Plumb line angle is α;The wheel pair that first two-dimensional laser displacement transducer S1, the second two-dimensional laser displacement transducer S2 are detected
Surface data information is two-dimensional coordinate point, is respectively (u1 (i),v1 (i))、(u2 (j),v2 (j))。
Further, the wheel described in step 2 is specially to surface data information pre-processing:By two-dimensional laser displacement sensing
The coordinate system that device carries carries out coordinate rotation processing;By the track detected in detection process, wheel axis and brake part
It is removed interference processing;Existing space isolation between the two-dimensional laser displacement transducer of track both sides is subjected to coordinate translation
Processing, under unification to the same coordinate system;The complete wheel of reconstruct is finally given to surface curve data.
Further, matched curve section is treated in the determination described in step 3, is specially:It is inner to set the wheel tread without abrasion
Line l on the basis of face, then take turns and treat that matched curve section is [l-d to wheel rim2,l-d1], wherein d1∈(2,7),d2∈(35,40);Wheel pair
Tread treats that matched curve section is [l-70-d3,l-70+d4], wherein d3、d4∈(8,25)。
Further, least square method supporting vector machine method is used described in step 4, place is fitted to surface curve to wheel
Reason, sets the discrete data point for treating matched curve section as (x(i),y(i)), comprise the following steps that:
(4.1) fitting function form isWhereinIt is Feature Mapping, w and b are plan to be asked
Close parameter;Optimization aim is formula (1):
Wherein ξ=(ξ1,ξ2,…,ξl)T, ξ*=(ξ1 *,ξ2 *,…,ξl *)T, ξ, ξ*For relaxation factor, ε is approximation accuracy, γ
It is the penalty coefficient of setting;
(4.2) formula (1) is converted into equality constraint, optimization aim is converted into formula (2):
Wherein ξ=(ξ1,ξ2,…,ζl)T;
The Lagrangian functions of formula (2) are
Wherein α=(α1,α2,…,αl)T;α is Lagrange multiplier;
(4.3) obtained by formula (3)
I.e.
Wherein, N is number of samples, and l is sample dimension,Y=[y1,y2,…,yl
]T,ξ=(ξ1,ξ2,…,ξl)T, α=(α1,α2,…,αl)T;
Known by formula (5) Eliminate w, ξiObtain system of linear equations:
Know with reference to Mercer conditions:
Kernel function k () take gaussian kernel function exp (- | | xi-xj||2/(2σ2));
(4.4) A ≡ Ω+γ are remembered-1I, formula (5) are converted into formula (8)
Tried to achieve by formula (9) The curvilinear function to be then fitted is
Further, the calculating wheelset profile parameter described in step 5, it is specially:On the basis of tread matched curve is obtained,
Rule is defined according to tread datum mark, extracts benchmark point coordinates, obtains wheel to parameter.
Compared with prior art, its remarkable advantage is the present invention:(1) wheel is obtained to table using two-dimensional laser displacement transducer
Face data message, accuracy of detection are higher;(2) None-linear approximation problem is converted into line using the SVMs method of least square
Property approximation problem, using the optimal curve of acquisition as take turns it is higher to surface information, fitting precision, calculation error is small.
Brief description of the drawings
Fig. 1 is city rail vehicle wheel of the present invention to curve-fitting method flow chart.
Fig. 2 is two-dimensional laser displacement transducer coordinate fusion figure.
Fig. 3 is to treat fitted area tread wheel rim division figure.
Fig. 4 is wheel to curve-fitting results figure.
Embodiment
Below in conjunction with the accompanying drawings and specific embodiment the invention will be further described.
With reference to Fig. 1, a kind of city rail vehicle wheel of the present invention comprises the following steps to curve-fitting method:
Step 1, wheel is obtained to surface data information point:Obtained by the two-dimensional laser displacement transducer for being arranged in track both sides
Take data message of the wheel to surface;
The first two-dimensional laser displacement transducer S1, the second two-dimensional laser displacement are respectively arranged on the inside and outside both sides of single-sided tracks
Sensor S2, the first two-dimensional laser displacement transducer S1, the second two-dimensional laser displacement transducer S2 laser emission point are not higher than
Rail plane, the first two-dimensional laser displacement transducer S1 and the second two-dimensional laser displacement transducer S2 are distributed on the Orbital Symmetry,
The laser beam of injection coincides with same plane, and the plane and horizontal plane angle are θ, the first two-dimensional laser displacement transducer S1, the
Two two-dimensional laser displacement transducer S2 and vertical line angle are α.First two-dimensional laser displacement transducer S1, the second two-dimensional laser position
The wheel that displacement sensor S2 is detected is respectively (u to surface data information1 (i),v1 (i))、(u2 (j),v2 (j))。
Step 2, take turns to surface data information pre-processing:The wheel detected is pre-processed to surface data, obtains weight
The wheel of structure is to surface curve;
Two-dimensional laser displacement transducer carries coordinate system, it is necessary to do coordinate rotation processing in itself;Can be by detection process
The interference of the parts such as track, wheel axis and brake is, it is necessary to remove these interference;The laser displacement sensor of track both sides it
Between Existential Space isolation, it is necessary to do coordinate translation processing, it is unified under the same coordinate system;
Therefore, coordinate system two-dimensional laser displacement transducer carried carries out coordinate rotation processing;It will be examined in detection process
Track, wheel axis and the brake part measured is removed interference processing;By the two-dimensional laser displacement sensing of track both sides
Existing space isolation carries out coordinate translation processing between device, under unification to the same coordinate system;Finally give the complete wheel of reconstruct
To surface curve data, as shown in Figure 2.
Step 3, it is determined that treating matched curve section:According to the wheel reconstructed to surface curve, it is determined that wheel on curve to waiting to be fitted
Region;
Wheel is made up of to surface curve easy curve and circular curve, thick to diameter, wheel rim height and wheel rim for calculating wheel
Datum mark only in part wheel in surface curve, so it is as follows that method only need to be fitted to partial trace section.
By taking turns to surface data information point, it may be determined that line l on the basis of the wheel tread inner face without abrasion, then wheel is to wheel rim
It is [l-d to treat matched curve section2,l-d1], wherein d1∈(2,7),d2∈(35,40);Wheel tread treats that matched curve section is [l-
70-d3,l-70+d4], wherein d3、d4∈ (8,25), division result is as shown in Figure 3.
Step 4, take turns to curve matching:Treating in the range of fitted area, using least square method supporting vector machine method, to wheel pair
Surface curve is fitted processing, obtains completely taking turns to surface curve, sets the discrete data point for treating matched curve section as (x(i),y(i)), it is specific as follows:
(4.1) fitting function form isWhereinIt is Feature Mapping, w and b are plan to be asked
Close parameter.Optimization aim is formula (1):
Wherein ξ=(ξ1,ξ2,…,ξl)T, ξ*=(ξ1 *,ξ2 *,…,ξl *)T, ξ, ξ*For relaxation factor, ε is approximation accuracy, γ
It is the penalty coefficient of setting;
(4.2) formula (1) is converted into equality constraint, optimization aim is converted into formula (2):
Wherein ξ=(ξ1,ξ2,…,ζl)T;
The Lagrangian functions of formula (2) are
Wherein α=(α1,α2,…,αl)T;α is Lagrange multiplier;
(4.3) obtained by formula (3)
I.e.
Wherein, N is number of samples, and l is sample dimension,Y=[y1,y2,…,yl
]T,ξ=(ξ1,ξ2,…,ξl)T, α=(α1,α2,…,αl)T;
Known by formula (5) Eliminate w, ξiObtain system of linear equations:
Know with reference to Mercer conditions:
Kernel function k () take gaussian kernel function exp (- | | xi-xj||2/(2σ2));
(4.4) A ≡ Ω+γ are remembered-1I, formula (5) are converted into formula (8)
Tried to achieve by formula (9) The curvilinear function to be then fitted is
Curve-fitting results are as shown in Figure 4.
Step 5, wheelset profile parameter is calculated:According to wheelset profile parameter definition criterion, wheelset profile parameter is calculated.
Specially:On the basis of tread matched curve is obtained, rule is defined according to tread datum mark, extracts benchmark point coordinates, obtains wheel
To parameter.
Embodiment 1
Surface is believed with the wheel that a set of wheelset profile on-line detecting system of certain MTR's car inspection and repair storehouse installation gathers
Breath data are research object, gather multigroup wheel to Surface testing data, method explanation is carried out with one of which data.
By taking turns to surface data information point, it may be determined that line l on the basis of the wheel tread inner face without abrasion, take turns and wheel rim is treated
Matched curve section is [l-d2,l-d1], wherein d1∈(2,7),d2∈(35,40);Wheel tread treats that matched curve section is [l-70-
d3,l-70+d4], wherein d3、d4∈(8,25)。
Data are pre-processed, obtained shown in tread data coordinates point such as formula (10)
Shown in wheel rim data coordinates point such as formula (11)
SVMs is supported to be fitted respectively to tread data point and wheel rim data point using least square, as a result such as
Under:
Then tread portions fitting function is
Rim section fitting function is
After taking turns to surface curve piecewise fitting, the coordinate value of a reference point location is found, obtains the first wheel rim datum mark
For (- 281.3786,303.5439), the second wheel rim datum mark is (- 296.3054,322.9051), and the first tread datum mark is
(-337.9701,332.7283).With reference to wheelset profile parameter definition and wheel to reference point, wheel is calculated to each ginseng
Number.As a result it is the high 28.7965mm of wheel rim, wheel rim thickness 29.1733mm.
In summary, the present invention is higher to surface data information, accuracy of detection with two-dimensional laser displacement transducer acquisition wheel;
None-linear approximation problem is converted into linear approximation problem using the SVMs method of least square, by the optimal curve of acquisition
As wheel to surface information, fitting precision is higher, and calculation error is small.
Claims (6)
1. a kind of city rail vehicle wheel is to curve-fitting method, it is characterised in that comprises the following steps:
Step 1, wheel is obtained to surface data information point:Wheel is obtained by the two-dimensional laser displacement transducer for being arranged in track both sides
To the data message on surface;
Step 2, take turns to surface data information pre-processing:The wheel detected is pre-processed to surface data, reconstructed
Wheel is to surface curve;
Step 3, it is determined that treating matched curve section:According to the wheel reconstructed to surface curve, it is determined that wheel is to area to be fitted on curve
Domain;
Step 4, take turns to curve matching:Treating in the range of fitted area, using least square method supporting vector machine method, to taking turns to surface
Curve is fitted processing, obtains completely taking turns to surface curve;
Step 5, wheelset profile parameter is calculated:According to wheelset profile parameter definition criterion, wheelset profile parameter is calculated.
2. city rail vehicle wheel according to claim 1 is to curve-fitting method, it is characterised in that the acquisition described in step 1
Take turns to surface data information point, be specially:The first two-dimensional laser displacement transducer is respectively arranged on the inside and outside both sides of single-sided tracks
S1, the second two-dimensional laser displacement transducer S2, the first two-dimensional laser displacement transducer S1, the second two-dimensional laser displacement transducer S2
Laser emission point be not higher than orbit plane, the first two-dimensional laser displacement transducer S1 and the second two-dimensional laser displacement transducer S2
It is distributed on the Orbital Symmetry, the laser beam of injection coincides with same plane, and the plane is θ with horizontal plane angle, and first is two-dimentional
Laser displacement sensor S1, the second two-dimensional laser displacement transducer S2 and plumb line angle are α;First two-dimensional laser displacement passes
The wheel that sensor S1, the second two-dimensional laser displacement transducer S2 are detected is two-dimensional coordinate point to surface data information, is respectively (u1 (i),v1 (i))、(u2 (j),v2 (j))。
3. city rail vehicle wheel according to claim 1 is to curve-fitting method, it is characterised in that the wheel pair described in step 2
Surface data information pre-processing, it is specially:The coordinate system that two-dimensional laser displacement transducer is carried carries out coordinate rotation processing;Will
Track, wheel axis and the brake part detected in detection process is removed interference processing;By the two dimension of track both sides
Existing space isolation carries out coordinate translation processing between laser displacement sensor, under unification to the same coordinate system;Finally give
The complete wheel of reconstruct is to surface curve data.
4. city rail vehicle wheel according to claim 1 is to curve-fitting method, it is characterised in that the determination described in step 3
Matched curve section is treated, is specially:Line l on the basis of wheel tread inner face of the setting without abrasion, then take turns and matched curve is treated to wheel rim
Section is [l-d2,l-d1], wherein d1∈(2,7),d2∈(35,40);Wheel tread treats that matched curve section is [l-70-d3,l-70+
d4], wherein d3、d4∈(8,25)。
5. city rail vehicle wheel according to claim 1 is to curve-fitting method, it is characterised in that the use described in step 4
Least square method supporting vector machine method, processing is fitted to wheel to surface curve, and the discrete data point of matched curve section is treated in setting
For (x(i),y(i)), comprise the following steps that:
(4.1) fitting function form isWhereinIt is Feature Mapping, w and b are fitting ginseng to be asked
Number;Optimization aim is formula (1):
Wherein ξ=(ξ1,ξ2,…,ξl)T, ξ*=(ξ1 *,ξ2 *,…,ξl *)T, ξ, ξ*For relaxation factor, ε is approximation accuracy, and γ is to set
Fixed penalty coefficient;
(4.2) formula (1) is converted into equality constraint, optimization aim is converted into formula (2):
Wherein ξ=(ξ1,ξ2,…,ζl)T;
The Lagrangian functions of formula (2) are
Wherein α=(α1,α2,…,αl)T;α is Lagrange multiplier;
(4.3) obtained by formula (3)
I.e.
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Wherein, N is number of samples, and l is sample dimension,Y=[y1,y2,…,yl]T,ξ=(ξ1,ξ2,…,ξl)T, α=(α1,α2,…,αl)T;
Known by formula (5)Eliminate w, ξiObtain system of linear equations:
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Know with reference to Mercer conditions:
Kernel function k () take gaussian kernel function exp (- | | xi-xj||2/(2σ2));
(4.4) A ≡ Ω+γ are remembered-1I, formula (5) are converted into formula (8)
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Tried to achieve by formula (9)The curvilinear function to be then fitted is
6. city rail vehicle wheel according to claim 1 is to curve-fitting method, it is characterised in that the calculating described in step 5
Wheelset profile parameter, it is specially:On the basis of tread matched curve is obtained, rule is defined according to tread datum mark, extracts benchmark
Point coordinates, wheel is obtained to parameter.
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Cited By (2)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
CN110239588A (en) * | 2019-06-12 | 2019-09-17 | 中国神华能源股份有限公司 | Wheel tread wear determines method and apparatus |
CN115031640A (en) * | 2022-08-12 | 2022-09-09 | 广州运达智能科技有限公司 | Train wheel set online detection method, system, equipment and storage medium |
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