CN110296668B - Angle measurement error correction method of circular grating sensor based on BP neural network - Google Patents
Angle measurement error correction method of circular grating sensor 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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Abstract
The invention belongs to the field of measuring instruments, and discloses a method for correcting angle measurement errors of a circular grating sensor based on a BP neural network, which comprises the following steps of preparing an experimental device, calibrating angle measurement error values and the functional relation of the angle measurement errors, and obtaining included angle alpha values corresponding to harmonic order numbers n of all the angle measurement errors according to the functional relation; obtain the discrete point alpha of the included angleopqAnd the difference values of the 2 reading heads are Fourier transformed E21Discrete point E of21opq(ii) a Modeling and testing the BP neural network to obtain the relation E between the angle measurement difference values of the 2 reading heads and the ambient temperature T and the harmonic order n21(T, n), and the relation alpha (T, n) of the actual included angle of the 2 reading heads with the ambient temperature T and the harmonic order n; e calculated by BP neural network algorithm21And substituting the (T, n) and the alpha (T, n) into a relational expression to obtain F (n) at the ambient temperature, and performing inverse Fourier transform on the F (n) to obtain an angle measurement error epsilon (theta) of the first reading head. The measuring precision of the circular grating and the parallel double-joint coordinate measuring machine can be obviously improved.
Description
Technical Field
The invention belongs to the field of measuring instruments, and particularly relates to a circular grating sensor angle measurement error correction method based on a BP neural network.
Background
The joint coordinate measuring machine is an important precision measuring instrument in modern manufacturing industry, and is widely applied to the fields of die processing, automobile manufacturing, aerospace and the like. The measuring precision of the instrument is obviously influenced by the angle measuring precision of a circular grating sensor arranged in a rotary joint of the instrument, and the angle measuring precision of the circular grating sensor in the rotary joint is obviously influenced by the ambient temperature. In different industrial fields, the ambient temperature span may be as high as 30 ℃, and if the angle measurement error correction model does not contain a working ambient temperature parameter, a significant angle measurement error may be caused when the ambient temperature of the industrial field is greatly different from the ambient temperature when the instrument performs calibration.
Aiming at the problem of correcting the angle measurement error of a circular grating sensor installed in a rotary joint by ambient temperature, a common method is a single reading head calibration method, namely, an arrangement scheme of a single reading head is adopted, a polygon and an autocollimator are used for taking a plurality of temperature values in a nominal temperature range for calibration, and a function relation between an error correction function and the angle value and the temperature of the circular grating sensor is established by an algorithm such as a least square method, so that the angle measurement error is corrected. The other widely applied method is a multi-reading-head uniform distribution scheme, a dual-reading-head radial uniform distribution scheme is commonly used, the sum and the mean of the angle measurement data of 2 reading heads are subjected to self-correction, the odd-order term in the angle measurement error harmonic component can be eliminated theoretically, the odd-order harmonic component of the angle measurement error caused by the change of the working environment temperature can also be eliminated, when the environment temperature changes, the mechanical structure of a precise shaft system is deformed, the included angle value between the 2 reading heads is changed, the odd-order harmonic component of the angle measurement error cannot be completely eliminated, and meanwhile, the method cannot eliminate the even-order harmonic component.
Disclosure of Invention
The invention aims to solve the problem and provides a method for correcting angle measurement errors of a circular grating sensor based on a BP neural network, which can effectively correct angle measurement errors caused by working condition changes and mechanical structure deformation of a rotary joint, ensures the angle measurement accuracy of the circular grating and the measurement accuracy of a joint coordinate measuring machine used in an industrial field for a long time and has great applicability.
In order to achieve the purpose, the technical scheme of the invention is as follows:
a method for correcting angle measurement error of a circular grating sensor based on a BP neural network comprises the following steps,
preparing an experimental device, fixing a precision shaft system in a thermostat, mounting two reading heads on the precision shaft system, fixing a 23-surface prism on a rotating shaft of the precision shaft system through a clamp, and adjusting the positions of an autocollimator and the precision shaft system to enable the precision shaft system to work normally;
calibrating the error value of the angle measurement, and synchronously recording the angle measurement numerical values H of the 2 reading heads at the set temperature1k,H2kK 1,2, 23 and the horizontal indication γ of the autocollimatorXkCalibrating the discrete value epsilon (theta) of angle measurement errork)；
Step three, carrying out Fourier transform on the angle measurement error discrete value of the first reading head to obtain F (n), and carrying out Fourier transform on the difference value of the second reading head and the first reading head to obtain a functional relation with the angle measurement discrete value error of the first reading head;
step four, obtaining an included angle alpha value corresponding to each angle measurement error harmonic component order n according to the function relation;
step five, repeating the steps two to four times at intervals of 5 ℃ within a set temperature range to obtain discrete points alpha of included anglesopqAnd the difference values of the 2 reading heads are Fourier transformed E21Discrete point E of21opq；
Step six, dispersing the angle measurement difference values of 2 reading heads to obtain a point E21opqIncluded angle discrete point alphaopqThe repetition times o of the experimental group, the temperature value p in the constant temperature box and the angle measurement error order value q are brought into a BP neural network for modeling and testing to obtain the relation E between the angle measurement difference value of 2 reading heads and the environmental temperature T and the harmonic order n21(T, n), and the relation alpha (T, n) of the actual included angle of the 2 reading heads to the ambient temperature T and the harmonic order n;
step seven, calculating E by using BP neural network algorithm21Substituting (T, n) and alpha (T, n) into a relational expression to obtain F (n) at the ambient temperature, and performing inverse Fourier transform on the F (n) to obtain an angle measurement error epsilon (theta) of the first reading head, namely the angle measurement of the circular grating sensor to be correctedError e (theta).
Preferably, the included angle alpha between the 1 and 2 reading heads is 144 +/-0.5 degrees.
Preferably, step 2, the angular error dispersion value is
Preferably, step 5 is repeated 3 times.
Preferably, the BP neural network algorithm comprises the following steps of 1) constructing a BP neural network, 2) training the BP neural network, initializing the BP neural network, training the BP neural network, and testing the BP neural network.
Compared with the prior art, the invention has the beneficial effects that:
the correction method is based on a transfer function in Fourier transform, and is combined with angle measurement error correction of a circular grating sensor of a BP neural network, the angle measurement error including an angle measurement error component caused by environment temperature change can effectively correct working condition change caused by bearing abrasion and the like and eliminate the angle measurement error method caused by mechanical structure deformation of a rotary joint caused by environment temperature change, the angle measurement precision of the circular grating and the measurement precision of a joint coordinate measuring machine in long-term use in an industrial field are ensured, and the correction method has great applicability.
Drawings
The accompanying drawings, which are incorporated in and constitute a part of this specification, illustrate embodiments consistent with the invention and together with the description, serve to explain the principles of the invention.
FIG. 1 is a schematic view of a rotary joint of a joint coordinate measuring machine based on a circular grating angle measurement error correction method of an optimized BP neural network.
Fig. 2 is a BP neural network structure diagram of the circular grating angle measurement error correction method based on the optimized BP neural network of the present invention.
FIG. 3 is a flow chart of the algorithm of the genetic algorithm optimized BP neural network based on the correction method of the circular grating angle measurement error of the optimized BP neural network.
Detailed Description
The technical solution in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings.
The invention uses double reading heads, establishes the relation alpha (T, n) between the included angle of 2 reading heads and the ambient temperature T and the harmonic order n through the transfer function in Fourier transform and BP neural network, and obtains the angle measurement error epsilon (theta) of the circular grating sensor through inverse Fourier transform.
As shown in fig. 1, a method for correcting angle measurement errors of a circular grating sensor based on a BP neural network is used for correcting angle measurement errors of the circular grating sensor in a rotary joint in a joint coordinate measuring machine, and improving angle measurement accuracy, and specifically includes the following steps:
firstly, preparing an experimental device, fixing a precision shaft system in a temperature control box 3, installing a first reading head and a second reading head on a reading head bracket of the precision shaft system, wherein the design value alpha of an included angle between 2 reading heads is 144 (+ -0.5) DEG, installing a clamp on a rotating shaft 1 during reading of the precision shaft system, fixing 23 prisms 2, fixing the 23 prisms on the rotating shaft of the precision shaft system through the clamp, and adjusting the positions of an autocollimator 5 and the precision shaft system to enable the light path of the light path to vertically enter a working surface of the 23 prisms through an opening 4 of the temperature control box, so that the light path can normally work. The nut of the fixed 23 face arriss bodies and anchor clamps is unscrewed, the position of the 23 face arriss bodies is adjusted for when reading head indicating value of circular grating sensor No. 1 is close 0 (less than 0.01 °), the 1 st working face perpendicular to autocollimator light path of the 23 face arriss bodies screws up the nut, closes the oven door.
Calibrating the error value of the angle measurement, and synchronously recording the angle measurement numerical values H of the 2 reading heads at a certain set temperature1k,H2kK 1,2, 23 and the horizontal indication γ of the autocollimatorXkCalibrating the discrete value epsilon (theta) of angle measurement errork)；
Under a certain set temperature, the motor drives the rotating shaft to enable the 23-surface prism to be sequentially vertical to the light path of the autocollimator from the 1 st working surface to the 23 rd working surface, and the cross target of the autocollimator is reflected by the prism working surface and then appears in the center of a view field. At the 23 equispaced positions, the same asStep recording angle measurement values H of 2 reading heads1k,H2kK 1,2, 23 and an indication γ of the autocollimator in the horizontal directionXkLet the angular difference of 2 reading heads be deltak， δk＝H2k-H1k。
Step three, carrying out Fourier transform on the angle measurement error discrete value of the first reading head to obtain F (n), and carrying out Fourier transform on the difference value of the second reading head and the first reading head to obtain a functional relation with the angle measurement discrete value error of the first reading head;
measuring the angle value H of the first reading head (reference reading head)1kAnd gammaXkProcessing to obtain the angle measurement error discrete value epsilon (theta) calibrated by the prism with 23 surfaces and the autocollimator at the current temperaturek)：
According to the formula:
where ε (θ) is the angle measurement error of reading head number 1 (reference reading head), and is expanded into a Fourier series where
N is more than or equal to 0 and less than or equal to 22, i.e. for epsilon (theta)k) Fourier transform is performed to obtain F (n).
Step four, obtaining an included angle alpha value corresponding to each angle measurement error harmonic component order n according to the function relation;
according to the formula: h1(θ)＝θ+ε(θ),H2(θ) ═ θ + e (θ + α), where θ is the rotation angle of the rotation shaft, e (θ) is the angle error of the reading head No. 1 (reference reading head), and δ (θ) ═ H2(θ)-H1E can be obtained by fourier transforming δ (θ) by (θ) ═ E (θ + α) -E (θ)21(n)，
E21(n)＝(einα-1)F(n)＝W21(n)F(n)。
According to the formula:
and calculating to obtain alpha values corresponding to the harmonic component orders n of each angle measurement error at the calibration temperature.
Step five, repeating the steps two to four times at intervals of 5 ℃ within a set temperature range to obtain discrete points alpha of included anglesopqAnd the difference values of the 2 reading heads are Fourier transformed E21Discrete point E of21opq；
Respectively carrying out the second step to the sixth step at the temperature of 10-40 ℃ every 5 ℃, and carrying out repeated experiments for three times at each temperature to obtain a discrete point alpha of an included angle alpha relative to the temperature T and the order nopqThe difference between o-1, 2,3 p-10, 15,20,25,30,35,40 q-1, 2, 11 and 2 readheads is fourier transformed E21Discrete points E for temperature T and order n21opq。
Step six, dispersing the angle measurement difference values of 2 reading heads to obtain a point E21opqIncluded angle discrete point alphaopqThe repetition times o of the experimental group, the temperature value p in the constant temperature box and the angle measurement error order value q are brought into a BP neural network for modeling and testing to obtain the relation E between the angle measurement difference value of 2 reading heads and the environmental temperature T and the harmonic order n21(T, n), and the relation alpha (T, n) of the actual included angle of the 2 reading heads to the ambient temperature T and the harmonic order n;
as shown in fig. 2 and fig. 3, the BP neural network algorithm comprises the following steps:
1. BP neural network construction
Adopting a single hidden layer structure, the input layer has 2 nodes respectively corresponding to the ambient temperature T and the harmonic order n, the hidden layer has 10 nodes, the output layer has 2 nodes respectively corresponding to E21And alpha.
The transfer function of the hidden layer is a tangent sigmoid transfer function tansig:
the transfer function of the output layer is a linear transfer function purelin: g (x) x.
Let the jth neuron threshold of the output layer be thetaj，
The h hidden layer neuron threshold is gammah，
The weight between the ith node of the input layer and the h node of the hidden layer is vih，
The weight of the h node of the hidden layer and the j node of the output layer is whj，
The h-th neuron in the hidden layer receives as input
The output of the h-th neuron of the hidden layer is bh＝f(αh-γh)，
The j-th neuron of the output layer receives as input
The output of the jth neuron of the output layer is yj＝g(βj-θj)。
Wherein x is1Is the temperature T, x2Is an order n, y1Is E21，y2Is alpha.
2. Training of BP neural networks
(1) BP neural network initialization
According to 231 sets of input and output data obtained by calibration, (11 × 7 × 3 ═ is), 200 sets of data are randomly selected as network training data, 31 sets of data are selected as network test data, and the training data are normalized by using the following normalization method:
xk＝(xk-xmin)/(xmax-xmin)
in the formula, xminIs the smallest number, x, in the data sequencemaxIs the maximum number in the sequence. Configuring network parameters, and setting iteration times, learning rate and target.
(2) BP neural network training
Training the neural network by using 200 randomly selected groups of data, wherein the initial parameter of the neural network is [0,1 ]]The output of the internal random number passing through the neural network is y% ({ y)1％,y2% }, wherein yj％＝g(βj-θj) Error for individual data in the training data set
And (3) performing feedback learning on the parameters in the neural network according to the errors by adopting a gradient descent method, wherein the formula for updating the parameters in the neural network is p ← p + delta p, and the Levenberg-Marquardt algorithm is adopted to train the neural network, so that the convergence speed of the network is improved, the training errors are reduced, and the network performance is improved.
(3) BP neural network testing
And testing the trained neural network by using 31 randomly selected groups of data, firstly normalizing the test data by using the method, predicting and outputting, and performing inverse normalization on an output result. And (3) subtracting the predicted output and the expected output of the BP neural network, when the relative error is less than 3%, determining that the requirement is met, if the relative error is not more than 3%, repeating the steps (2) to (3) until the required position is met, and obtaining the expected neural network.
Step seven, calculating E by using BP neural network algorithm21And substituting the (T, n) and the alpha (T, n) into a relational expression to obtain F (n) at the ambient temperature, and performing inverse Fourier transform on the F (n) to obtain an angle measurement error epsilon (theta) of the first reading head, namely the angle measurement error epsilon (theta) of the circular grating sensor to be corrected.
According to the formula:
wherein E21(n) is E obtained from BP neural network at certain ambient temperature21And (T, n) and alpha (T, n) are substituted into the formula to obtain F (n) at the ambient temperature, and Fourier inverse transformation is carried out on the F (n) to obtain the angle measurement error epsilon (theta) of the number 1 reading head.
The embodiments described above are only a part of the embodiments of the present invention, and not all of them. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
Claims (4)
1. A method for correcting angle measurement error of a circular grating sensor based on a BP neural network is characterized by comprising the following steps,
firstly, preparing an experimental device, fixing a precision shafting in a thermostat, mounting two reading heads on the precision shafting, fixing a 23-surface prism on a rotating shaft of the precision shafting through a clamp, and adjusting the positions of an autocollimator and the precision shafting to enable the precision shafting to work normally;
calibrating the error value of the angle measurement, and synchronously recording the angle measurement numerical values H of the 2 reading heads at the set temperature1k,H2kK-1, 2, …,23 and the horizontal direction indication γ of the autocollimatorXkCalibrating the discrete value epsilon (theta) of angle measurement errork)：
Step three, carrying out Fourier transform on the angular error discrete value of the first reading head to obtain the functional relation of the angular error
Performing Fourier transform on the difference value of the second reading head and the first reading head to obtain a functional relation with the angle measurement discrete value error of the first reading head;
step four, obtaining an included angle alpha value corresponding to each angle measurement error harmonic component order n according to the function relation;
step five, repeating the steps two to four times at intervals of 5 ℃ within a set temperature range to obtain discrete points alpha of included anglesopqAnd the difference values of the 2 reading heads are Fourier transformed E21Discrete point E of21opq；
Step six, dispersing the 2 reading heads to form a point E21opqIncluded angle discrete point alphaopqThe repetition times o of the experimental group, the temperature value p in the constant temperature box and the angle measurement error order value q are brought into a BP neural network for modeling and testing to obtain the relation E between the angle measurement difference value of the 2 reading heads and the environmental temperature T and the harmonic order n21(T, n), and the relation alpha (T, n) of the actual included angle of the 2 reading heads to the ambient temperature T and the harmonic order n;
step seven, calculating E by using BP neural network algorithm21And substituting the (T, n) and the alpha (T, n) into a relational expression to obtain F (n) at the ambient temperature, and performing inverse Fourier transform on the F (n) to obtain an angle measurement error epsilon (theta) of the first reading head.
2. The method for correcting the angle measurement error of the circular grating sensor based on the BP neural network as claimed in claim 1, wherein in the step one, the included angle between the two reading heads is 143.5-144.5 °.
3. The method for correcting the angle measurement error of the circular grating sensor based on the BP neural network as claimed in claim 1, wherein the step five is repeated for 3 times.
4. The method for correcting the angle measurement error of the circular grating sensor based on the BP neural network as claimed in claim 1, wherein the BP neural network algorithm comprises the following steps of 1) constructing the BP neural network, 2) training the BP neural network, initializing the BP neural network, training the BP neural network, and then testing the BP neural network.
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