CN110296668A - A kind of circular raster sensor angle error modification method based on BP neural network - Google Patents
A kind of circular raster sensor angle error modification method based on BP neural network Download PDFInfo
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
- G01B11/00—Measuring arrangements characterised by the use of optical techniques
- G01B11/26—Measuring arrangements characterised by the use of optical techniques for measuring angles or tapers; for testing the alignment of axes
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06N—COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06N—COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
- G06N3/00—Computing arrangements based on biological models
- G06N3/02—Neural networks
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Abstract
The invention belongs to measuring instrument fields, a kind of circular raster sensor angle error modification method based on BP neural network is disclosed, include the following steps, preparing experiment device, demarcate angle error value, the functional relation of angle error obtains angle α value corresponding to each angle error harmonic term order n according to functional relation；Obtain the discrete point α of angleopqAnd the difference of 2 reading heads is fourier transformed rear E21Discrete point E21opq；BP neural network is modeled and is tested, and the angle measurement difference of 2 reading heads and the relationship E of environment temperature T, harmonic order n are obtained21The relationship α (T, n) of the practical angle of (T, n) and 2 reading heads and environment temperature T, harmonic order n；The E that BP neural network algorithm is found out again21(T, n), α (T, n) bring relational expression into, obtain the F (n) under the environment temperature, and F (n) carries out inverse Fourier transform and obtains the angle error ε (θ) of the first reading head.It is remarkably improved the measurement accuracy of Circular gratings with parallel doublejointed coordinate measuring machine.
Description
Technical field
The invention belongs to measuring instrument field more particularly to a kind of circular raster sensor angle measurement mistakes based on BP neural network
Poor modification method.
Background technique
Joint type coordinate measuring machine is the important fine measuring instrument of one kind of modern manufacturing industry, is widely used in mold and adds
The fields such as work, automobile manufacture, aerospace.The measurement accuracy of the quasi-instrument is sensed by the Circular gratings installed in its rotary joint
Device angle measurement accuracy significantly affects, and the angle measurement accuracy of circular raster sensor is significantly affected by environment temperature in rotary joint.
In different industry spots, environment temperature may be up to 30 DEG C across width, if in angle error correction model not including working environment
Temperature parameter when then when the environment temperature of industry spot is demarcated with instrument, environment temperature differs larger, can cause significant
Angle error.
Problem, common side are corrected to the angle error for being mounted on circular raster sensor in rotary joint for environment temperature
Method is single reading head standardization, i.e., using the arrangement of single reading head, using polygon and autocollimator in nominal temperature
Degree takes several temperature values in section, is demarcated, establishes error correction function and Circular gratings by least square method scheduling algorithm
Sensor angles value, the functional relation of temperature, to correct angle error, but this method works as instrument due to using single reading head
Device causes operating condition to change after long-time use due to bearing wear etc., since single reading head can not carry out certainly
Amendment, therefore can not eliminate and thus cause biggish first order harmonic components in angle error ingredient, it generates biggish angle measurement and misses
Difference.Another widely used method is that more reading heads are evenly distributed with scheme, and the most commonly used is double-reading head diameters to be evenly distributed with scheme,
It takes mean value to carry out self-correction the angle measurement data summation of 2 reading heads, can theoretically eliminate in angle error harmonic components
Odd item can also eliminate operating ambient temperature variation and cause the odd item harmonic components of angle error, but work as environment temperature
Change, causes precision bearing system mechanical structure to deform, cause the change of angle value between 2 reading heads, lead to the surprise of angle error
Secondary item harmonic components cannot be completely eliminated, while this method can not eliminate even order terms harmonic components.
Summary of the invention
The purpose of the present invention is to solve this problems, provide a kind of circular raster sensor survey based on BP neural network
Angle error modification method, can effectively correct operating condition variation and rotary joint mechanical structure deforms caused angle error side
Method, ensure that Circular gratings angle measurement accuracy and joint type coordinate measuring machine for a long time industry spot use when measurement accuracy,
With great applicability.
For achieving the above object, the technical scheme is that
A kind of circular raster sensor angle error modification method based on BP neural network, includes the following steps,
Step 1, preparing experiment device, precision bearing system is fixed in insulating box, and two readings are installed on precision bearing system
23 face rib bodies are fixed in the rotary shaft of precision bearing system by head by fixture, adjust the position of autocollimator and precision bearing system,
It can work normally；
Step 2, demarcate angle error value, setting at a temperature of, the angle measurement numerical value H of 2 reading heads of synchronous recording1k,
H2k, k=1,2,23 and autocollimator horizontal direction indicating value γXk, demarcate angle error discrete value ε (θk)；
Step 3, the functional relation of angle error, the angle error discrete value of the first reading head carry out Fourier transformation and obtain
To F (n), the difference of the second reading head and the first reading head carries out Fourier transformation again, obtains discrete with the first reading head angle measurement
It is worth the functional relation of error；
Step 4 obtains angle α value corresponding to each angle error harmonic components order n according to functional relation；
Step 5 repeats above-mentioned steps more than two to four times every 5 DEG C within the scope of set temperature respectively, obtains angle
Discrete point αopqAnd the difference of 2 reading heads is fourier transformed rear E21Discrete point E21opq；
Step 6, by the angle measurement difference discrete point E of 2 reading heads21opq, angle discrete point αopq, experimental group number of repetition o,
Temperature value p and angle error order value q bring BP neural network into and are modeled and tested in insulating box, obtain 2 reading heads
The relationship E of angle measurement difference and environment temperature T and harmonic order n21The practical angle of (T, n) and 2 reading heads and environment temperature
Spend the relationship α (T, n) of T and harmonic order n；
Step 7, then the E that BP neural network algorithm is found out21(T, n), α (T, n) bring relational expression into, obtain the environment temperature
F (n) under degree, F (n) carry out inverse Fourier transform and obtain the angle error ε (θ) of the first reading head, i.e., Circular gratings to be modified pass
The angle error ε (θ) of sensor.
Preferably, step 1, angle α is 144 ± 0.5 ° between 2 reading heads.
Preferably, step 2, angle error discrete value is
Preferably, step 5, number of repetition is 3 times.
Preferably, the BP neural network algorithm, steps are as follows, and 1) building BP neural network, 2) training BP nerve net
Network, first BP neural network initialization, BP neural network training are tested in BP neural network.
Compared with prior art, the beneficial effects of the present invention are:
The modification method is based on the transmission function in Fourier transformation, in combination with the circular raster sensor of BP neural network
Angle error amendment, including environment temperature change caused by angle error including angle error ingredient, can effectively correct by
The variation of the operating condition caused by the reasons such as bearing wear and the rotary joint mechanical structure deformation for eliminating variation of ambient temperature initiation
Caused angle error method, the angle measurement accuracy that ensure that Circular gratings and joint type coordinate measuring machine are for a long time in industry spot
Measurement accuracy when use has great applicability.
Detailed description of the invention
The drawings herein are incorporated into the specification and forms part of this specification, and shows and meets implementation of the invention
Example, and be used to explain the principle of the present invention together with specification.
Fig. 1 is that the present invention is based on the joint type measurement of coordinates of the Circular gratings angle error modification method of Optimized BP Neural Network
Machine rotary joint schematic diagram.
Fig. 2 is that the present invention is based on the BP neural network structures of the Circular gratings angle error modification method of Optimized BP Neural Network
Figure.
Fig. 3 is that the present invention is based on the genetic algorithm optimization BPs of the Circular gratings angle error modification method of Optimized BP Neural Network
The flow chart of neural network algorithm.
Specific embodiment
Below in conjunction with attached drawing, technical scheme in the embodiment of the invention is clearly and completely described.
The present invention establishes 2 readings by the transmission function and BP neural network in Fourier transformation using double-reading head
The angle of head and the relationship α (T, n) of environment temperature T and harmonic order n, acquire circular raster sensor by inverse Fourier transform
Angle error ε (θ).
As shown in Figure 1, a kind of circular raster sensor angle error modification method based on BP neural network, is closed for correcting
The angle error for saving circular raster sensor in rotary joint in class coordinate measuring machine, improves angle-measurement accuracy, specifically include as
Lower step:
Precision bearing system is fixed in temperature control box 3 by step 1, preparing experiment device, on the reading head bracket of precision bearing system
First, second reading head is installed, the design value α of angle is 144 (± 0.5) ° between 2 reading heads, in precision bearing system reading
Installs fixture in rotary shaft 1 fixes 23 face rib bodies 2, and 23 face rib bodies are fixed in the rotary shaft of precision bearing system by fixture,
The position for adjusting autocollimator 5 and precision bearing system makes its optical path vertically inject the work of 23 face rib bodies by the aperture 4 of temperature control box
Make face, can work normally.Unscrew the nut for fixing 23 face rib bodies and fixture, the position of 23 face rib bodies is adjusted, so that working as Circular gratings
When No. 1 reading head indicating value of sensor is close to 0 ° (less than 0.01 °), the 1st working face of 23 face rib bodies is perpendicular to autocollimator light
Nut is tightened on road, shuts insulating box chamber door.
Step 2, demarcate angle error value, a certain setting at a temperature of, the angle measurement numerical value of 2 reading heads of synchronous recording
H1k,H2k, k=1,2,23 and autocollimator horizontal direction indicating value γXk, demarcate angle error discrete value ε (θk)；
A certain setting at a temperature of, by motor, rotary shaft is driven, so that 23 face rib bodies are from the 1st working face to the 23rd
Successively perpendicular to autocollimator optical path, the cross drone for showing as autocollimator goes out working face after rib body running face reflects
The center of present visual field.At this 23 uniformly distributed positions, the angle measurement numerical value H of 2 reading heads of synchronous recording1k,H2k, k=1,
2,23 and autocollimator horizontal direction indicating value γXk, enabling the angle measurement difference of 2 reading heads is δk, δk=H2k-
H1k。
Step 3, the functional relation of angle error, the angle error discrete value of the first reading head carry out Fourier transformation and obtain
To F (n), the difference of the second reading head and the first reading head carries out Fourier transformation again, obtains discrete with the first reading head angle measurement
It is worth the functional relation of error；
To the first reading head (reference count head) angle measurement numerical value H1kAnd γXkIt is handled, is obtained under Current Temperatures through 23 faces
The angle error discrete value ε (θ that rib body and autocollimator calibratek):
According to formula:Wherein ε (θ) is that the angle measurement of No. 1 reading head (reference count head) misses
Difference is launched into Fourier space, wherein0≤n≤22, i.e., to ε (θk) carry out Fourier transformation
Available F (n).
Step 4 obtains angle α value corresponding to each angle error harmonic components order n according to functional relation；
According to formula: H1(θ)=θ+ε (θ), H2(θ)=θ+ε (θ+α), wherein θ is the rotational angle of rotary shaft, and ε (θ) is
The angle error of No. 1 reading head (reference count head), δ (θ)=H2(θ)-H1(θ)=ε (θ+α)-ε (θ) carries out in Fu δ (θ)
The available E of leaf transformation21(n),
E21(n)=(einα- 1) F (n)=W21(n)F(n)。
According to formula:Each angle error harmonic components at a temperature of the calibration are calculated
α value corresponding to order n.
Step 5 repeats above-mentioned steps more than two to four times every 5 DEG C within the scope of set temperature respectively, obtains angle
Discrete point αopqAnd the difference of 2 reading heads is fourier transformed rear E21Discrete point E21opq；
Respectively at 10 DEG C to 40 DEG C every 5 DEG C of progress above-mentioned steps two to step 6, weighed three times at each temperature
Multiple experiment, obtains discrete point α of the angle α about temperature T and order nopq, o=1,2,3p=10,15,20,25,30,35,
40q=1,2, the difference of 11 and 2 reading heads is fourier transformed rear E21About the discrete of temperature T and order n
Point E21opq。
Step 6, by the angle measurement difference discrete point E of 2 reading heads21opq, angle discrete point αopq, experimental group number of repetition o,
Temperature value p and angle error order value q bring BP neural network into and are modeled and tested in insulating box, obtain 2 reading heads
The relationship E of angle measurement difference and environment temperature T and harmonic order n21The practical angle of (T, n) and 2 reading heads and environment temperature
Spend the relationship α (T, n) of T and harmonic order n；
As shown in Figure 2 and Figure 3, the BP neural network algorithm steps are as follows:
1, BP neural network constructs
Using single hidden layer structure, input layer has 2 nodes, respectively corresponds environment temperature T and harmonic order n, implies
Layer has 10 nodes, and output layer has 2 nodes, respectively corresponds E21And α.
The transmission function of hidden layer is tangent S type transmission function tansig:
The transmission function of output layer is linear transfer function purelin:g (x)=x.
Enabling j-th of neuron threshold value of output layer is θj,
H-th of hidden layer neuron threshold value is γh,
Weight between h-th of node of i-th of node of input layer and hidden layer is vih,
The weight of h-th of node of hidden layer and j-th of node of output layer is whj,
The input that h-th of neuron of hidden layer receives is
The output of h-th of neuron of hidden layer is bh=f (αh-γh),
The input that j-th of neuron of output layer receives is
The output of j-th of neuron of output layer is yj=g (βj-θj)。
Wherein, x1For temperature T, x2For order n, y1For E21, y2For α.
2, the training of BP neural network
(1) BP neural network initializes
According to (11 × 7 × 3=) obtained by calibrating 231 groups of inputoutput datas, 200 groups of data conducts are therefrom randomly selected
Network training data, 31 groups of data are normalized training data as network testing data, are returned using following
One changes method:
xk=(xk-xmin)/(xmax-xmin)
In formula, xminFor the minimum number in data sequence, xmaxFor the maximum number in sequence.Configuration network parameter, setting change
Generation number, learning rate and target.
(2) BP neural network training
Carry out neural metwork training using 200 groups of data randomly selecting, the initial parameter of neural network be in [0,1] with
Machine number, the output by neural network are y%={ y1%, y2% }, wherein yj%=g (βj-θj), training data is concentrated
Individual data its error
Feedback learning is carried out to the parameter in neural network according to error using gradient descent method, parameter is more in neural network
New formula is p ← p+ Δ p, is trained using Levenberg-Marquardt algorithm to neural network, improves network
Convergence rate reduces training error, improves network performance.
(3) BP neural network is tested
The neural network after trained is tested using the 31 groups of data randomly selected, uses the above method pair first
Test data is normalized, prediction output, and carries out renormalization to output result.By BP neural network prediction output and
Desired output is made the difference, and when relative error is less than 3%, that is, thinks to meet the requirements, if being unsatisfactory for requiring, repeatedly step
(2) to step (3), until meeting the requirements position to get to expected neural network.
Step 7, then the E that BP neural network algorithm is found out21(T, n), α (T, n) bring relational expression into, obtain the environment temperature
F (n) under degree, F (n) carry out inverse Fourier transform and obtain the angle error ε (θ) of the first reading head, i.e., Circular gratings to be modified pass
The angle error ε (θ) of sensor.
According to formula:Wherein E21It (n) is that will pass through BP mind under certain environment temperature
The E found out through network21(T, n), α (T, n) bring above formula into, then obtain the F (n) under the environment temperature, carry out in Fu to F (n)
Leaf inverse transformation obtains the angle error ε (θ) of No. 1 reading head.
Embodiments described above is only a part of the embodiment of the present invention, instead of all the embodiments.Based on this
Embodiment in invention, it is obtained by those of ordinary skill in the art without making creative efforts every other
Embodiment shall fall within the protection scope of the present invention.
Claims (5)
1. a kind of circular raster sensor angle error modification method based on BP neural network, which is characterized in that including walking as follows
Suddenly,
Step 1, preparing experiment device, precision bearing system is fixed in insulating box, and two readings are installed on the precision bearing system
23 face rib bodies are fixed in the rotary shaft of precision bearing system by head by fixture, are adjusted the position of autocollimator and precision bearing system, are made
It can be worked normally；
Step 2, demarcate angle error value, setting at a temperature of, the angle measurement numerical value H of 2 reading heads of synchronous recording1k,H2k, k=
1,2 ..., 23 and autocollimator horizontal direction indicating value γXk, demarcate angle error discrete value ε (θk)；
Step 3, the functional relation of angle error, the angle error discrete value of the first reading head carry out Fourier transformation and obtain F
(n), the difference of the second reading head and the first reading head carries out Fourier transformation again, obtains missing with the first reading head angle measurement discrete value
The functional relation of difference；
Step 4 obtains angle α value corresponding to each angle error harmonic components order n according to functional relation；
Step 5 repeats above-mentioned steps more than two to four times within the scope of set temperature every 5 DEG C respectively, obtain angle from
Scatterplot αopqAnd the difference of 2 reading heads is fourier transformed rear E21Discrete point E21opq；
Step 6, by 2 reading head discrete point E21opq, angle discrete point αopq, experimental group number of repetition o, temperature value in insulating box
P and angle error order value q bring BP neural network into and are modeled and tested, and obtain 2 reading head angle measurement differences and environment temperature
Spend the relationship E of T and harmonic order n21The pass of the practical angle of (T, n) and 2 reading heads and environment temperature T and harmonic order n
It is α (T, n)；
Step 7, then the E that BP neural network algorithm is found out21(T, n), α (T, n) bring relational expression into, obtain under the environment temperature
F (n), F (n) carry out inverse Fourier transform obtain, the angle error ε (θ) of the first reading head.
2. the circular raster sensor angle error modification method based on BP neural network, feature exist according to claim 1
In step 1, angle is 143.5 ° -144.5 ° between two reading heads.
3. the circular raster sensor angle error modification method based on BP neural network, feature exist according to claim 1
In step 2, angle error discrete value is
4. the circular raster sensor angle error modification method based on BP neural network, feature exist according to claim 1
In step 5, number of repetition is 3 times.
5. the circular raster sensor angle error modification method based on BP neural network, feature exist according to claim 1
In, the BP neural network algorithm, steps are as follows, and 1) building BP neural network, 2) training BP neural network, first BP neural network
Initialization, BP neural network training, then BP neural network test.
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