CN110046412B - Circular grating angle measurement error correction method based on optimized BP neural network - Google Patents
Circular grating angle measurement error correction method based on optimized BP neural network Download PDFInfo
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Abstract
The invention belongs to the field of measuring instruments, and discloses a circular grating angle measurement error correction method based on an optimized BP neural network, which comprises the following steps of firstly, preparing an experimental device, adjusting and fixing the positions of an autocollimator and a precision shafting to achieve a normal use state; calibrating the angle measurement error value, and repeating the experiment for multiple times; analyzing harmonic terms, performing Fourier transform on a plurality of groups of experimental data at the set temperature, analyzing the amplitude and the phase of each harmonic term, determining the harmonic term with the relative error of less than 10%, and performing subsequent correction; step four, adjusting the temperature of the temperature control box, and performing the operations of the step two to the step three; and fifthly, optimizing a BP neural network method by using a genetic algorithm, establishing the relation between the amplitude and the phase of each harmonic item to be corrected and the same temperature, verifying a correction model, and finishing the correction of the angle measurement error of the circular grating. The measurement precision of 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 angle measurement error correction method based on an optimized BP neural network.
Background
The joint coordinate measuring machine is a precision measuring instrument widely applied to modern manufacturing industry, and is mainly applied to the fields of automobile manufacturing, aerospace, mold processing and the like. The instrument adopts a series structure and consists of a plurality of precision shafting and connecting rod structures, so that the measurement precision of the instrument is obviously influenced by the angle measurement precision of the precision shafting, while the angle measurement precision of the circular grating in the precision shafting is obviously influenced by the ambient temperature. In different industrial fields, the variation range of the environmental temperature can reach 30 ℃, if the environmental temperature parameter is not included in the circular grating angle measurement error model, when the difference between the environmental temperature of the industrial field and the instrument in the calibration (usually 20 ℃) is too large, a remarkable circular grating angle measurement error can be caused, and the measurement accuracy of the instrument is remarkably reduced.
Aiming at the problem that the measurement accuracy of the conventional joint coordinate measuring machine is reduced due to the change of environmental temperature, the adopted method is a complete machine calibration method, namely a temperature sensor is arranged on the joint coordinate measuring machine, the complete machine of the instrument is placed in a large temperature control box, under the condition of different temperatures, the complete machine calibration is carried out on the instrument by using standard components such as quartz rods and the like, structural parameters such as the length of a connecting rod of the instrument are obtained, a table is made and is input into an upper computer system, and the method can correct the measurement error to a certain extent, but does not relate to the correction of the angle measurement error of the circular grating caused by the temperature change and the instrument measurement error caused by the angle measurement error. At present, no method for correcting the angle measurement error of the circular grating caused by the change of the environmental temperature exists, and only a method for correcting geometric structures and motion errors caused by groove errors of a grating disc, installation eccentricity of the grating disc, shaking of a rotating shaft and the like is used, namely, an autocollimator, a polygon or a circular grating sensor with higher precision is used as a standard quantity to obtain a discrete value of the angle measurement error of the circular grating to be corrected, and a correction function is established by using algorithms such as a least square method and the like.
Disclosure of Invention
The invention aims to solve the problem and provides a circular grating angle measurement error correction method based on an optimized BP neural network.
In order to achieve the purpose, the technical scheme of the invention is as follows:
a circular grating angle measurement error correction method based on an optimized BP neural network is characterized by comprising the following steps,
preparing an experimental device, installing a single reading head on a precision shaft system, fixing a rotating shaft in the precision shaft system and a 23-face prism through a clamp, and adjusting and fixing the positions of an autocollimator and the precision shaft system to achieve a normal use state;
calibrating the angle measurement error value, calibrating the discrete angle measurement error value of the circular grating at a set temperature, and performing repeated experiments for multiple times;
analyzing harmonic terms, performing Fourier transform on a plurality of groups of experimental data at the set temperature, analyzing the amplitude and the phase of each harmonic term, determining the relative error of harmonic term components, and performing subsequent correction;
step four, adjusting the temperature of the temperature control box, and respectively performing the operations of the step two to the step three at intervals of 5 ℃ within a set temperature range;
and fifthly, optimizing a BP neural network method by using a genetic algorithm, establishing the function relation between the amplitude of each harmonic item to be corrected and the phase and the same temperature, verifying a correction model, and finishing the correction of the angle measurement error of the circular grating.
Preferably, step 2, the experiment is repeated 3 times.
Preferably, in step 3, the number of experimental data is the same as the number of repeated experiments.
Preferably, in step 5, the method for optimizing the BP neural network by the genetic algorithm comprises the following steps of 1) constructing the BP neural network, 2) training the BP neural network, firstly training data normalization, then optimizing initial parameters by the genetic algorithm, and finally training the BP neural network.
Compared with the prior art, the invention has the beneficial effects that:
based on single reading, the circular grating angle measurement error correction method for optimizing the BP neural network by using the spectrum analysis genetic algorithm is used for correcting angle measurement errors caused by environmental temperature, a circular grating structure, motion errors and the like, stable error harmonic terms are determined through repeated experiments and corrected, the angle measurement errors caused by temperature change, a grating geometric structure and error motion are corrected, and the angle measurement accuracy of the circular grating is greatly improved, so that the measurement accuracy of the joint coordinate measuring machine is improved, the applicability of the instrument in an industrial field is enhanced, and the method has great significance.
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 diagram of an experimental device of the circular grating angle measurement error correction method based on the optimized BP neural network.
FIG. 2 is a flow chart of optimization of the BP neural network algorithm by the genetic algorithm based on the circular grating angle measurement error correction method for optimizing the BP neural network.
Fig. 3 is a diagram showing the angle measurement error correction effect of the circular grating angle measurement error correction method based on the optimized BP neural network.
FIG. 4 is a schematic diagram of a precision shafting of the circular grating angle measurement error correction method based on 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.
As shown in fig. 1 and 4, a circular grating angle measurement error correction method based on an optimized BP neural network includes the following steps:
the method comprises the steps of firstly, preparing an experimental device, installing a single reading head on a reading head 7 support, fixedly connecting a clamp on a rotating shaft 1 in a precision shaft system through a screw, fixedly clamping a 23-face prism 2 on the clamp through a nut, placing the precision shaft system in a temperature control box 4, adjusting the positions of an autocollimator 5 and the precision shaft system to enable a light path of the autocollimator to vertically penetrate into the 23-face prism through an opening 6 of the temperature control box, adjusting the position of the 23-face prism, screwing the nut when the indication value of a circular grating 8 is close to 0 degree, enabling a 1 st working face of the 23-face prism to be perpendicular to the light path of the autocollimator, closing a box door, and achieving a normal use state. The precision shafting is internally provided with a ball bearing 31 and a shaft sleeve 32 sleeved by the ball bearing.
Calibrating an angle measurement error value, and rotating a rotating shaft through a motor at a certain set environmental temperature to enable the 1 st working surface to the 23 rd working surface of the 23-surface prism to be sequentially vertical to the light path of the autocollimator, namely, a cross target of the autocollimator is positioned in the middle of a view field after being reflected by the 23-surface prism working surface;
at these 23 bitsSynchronously recording angle measurement value H of the circular grating k K =1,2, …,23 and autocollimator horizontal direction indication γ Xk . Angle measuring value H for circular grating k And gamma Xk Processing to obtain a discrete angle measurement error value epsilon (theta) calibrated by the 23-surface prism and the self-collimator at the current temperature k )：
Repeating the second step to obtain 3 sets of measurement data epsilon at a certain set temperature m (θ k ),m＝1,2,3,k＝1,2,…,23。
According to the formula:
i.e. for each group of epsilon (theta) k ) F (n) can be obtained by Fourier transformation. Due to the use of 23-sided prisms, the actual effective harmonic terms are 0 to 11 order terms, written as trigonometric functions:
wherein, c 0 ,c i For each of the order of magnitude values,
is the harmonic phase.
And step three, analyzing a harmonic term, applying the 3 groups of data at the temperature, performing Fourier transform spectrum analysis on the amplitude and the phase of each harmonic, and if the relative error of the amplitude and the phase of a certain harmonic term is less than 10%, determining that the harmonic term is a stable angle measurement error term. For example analysing the amplitude c of the 1 st order term 10 ,c 20 ,c 30 And phase
Harmonic term components with a relative error of less than 10% with respect to each other, i.e. considered as stable angle error terms, and subsequentlyAnd carrying out modeling correction. Taking the arithmetic mean value of the amplitude and the phase of the stable harmonic term obtained by the frequency spectrum analysis to obtain c j ,
Where j is the order of the stationary harmonic term.
Step four, adjusting the temperature of the temperature control box, and respectively carrying out the steps two to four at the temperature of 10-40 ℃ and every 5 ℃ to obtain discrete points c of the amplitude and the phase of the stable error at each temperature relative to the temperature T Tj ,
Step five, because the relation of the amplitude and the phase at each temperature and the temperature is relatively complex and nonlinear, the amplitude c of each harmonic term to be corrected is established by using a BP neural network method optimized by a genetic algorithm j And phase
And the function relation with the temperature T, and verifying the model, and finally finishing the correction of the angle measurement error of the circular grating.
As shown in fig. 2, the system block diagram of the genetic algorithm optimized BP neural network method includes the following steps:
1. building BP neural network
A single hidden layer structure is adopted, 1 node is arranged on an input layer, corresponding to the temperature T, 2N nodes are arranged on 17 node layers used by the hidden layer, and N is the number of stable terms of harmonic terms.
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 q-th neuron threshold of output layer be theta j ，
The h hidden layer neuron threshold is gamma h ，
The weight between the ith node of the input layer and the h node of the hidden layer is v ih ，
The weight of the h node of the hidden layer and the q node of the output layer is w hq ，
The input received by the h-th neuron of the hidden layer is alpha h ＝v h T，
The output of the h-th neuron of the hidden layer is b h ＝f(α h -γ h )，
The q-th neuron of the output layer receives as input
The output of the q-th neuron of the output layer is y q ＝g(β q -θ q )。
Wherein, y q Is c q ，y q+1 Is composed of
2. Training BP neural network
2.1 training data normalization
Using the obtained data as network training data to carry out normalization processing on training, wherein the normalization method comprises the following steps:
x k ＝(x k -x min )/(x max -x min ) (3)
in the formula, x min Is the smallest number, x, in the data sequence max Is the maximum number in the sequence. Configuring network parameters, and setting iteration times, learning rate and target.
2.2 genetic Algorithm optimization of initial parameters
The initial parameters of the neural network are random numbers in [0,1], and the initial weight and the threshold of the BP neural network are optimized by using a genetic algorithm, so that the optimized BP neural network can better predict function output. The method mainly comprises a fitness function, a selection operation, a cross operation and a mutation operation.
Training BP nerves using training dataThe output of the prediction system after the network takes the absolute value sum E of the error between the predicted output and the expected output as an individual fitness value F, and the selection operation is carried out by using a selective roulette method k And the l-th chromosome a l The operation method of interleaving at j bit is as follows:
wherein b is a random number between [0,1 ]. The population scale is set to be 10, the evolution times are set to be 40, the cross probability is 0.3, and the variation probability is 0.2. And obtaining an initial value of the neural network algorithm after genetic algorithm optimization.
2.3BP neural network training
The output through the neural network is
Wherein
Error for individual data in training data set
And performing feedback learning on parameters in the neural network according to errors by adopting a gradient descent method, and training the neural network by adopting a Levenberg-Marquardt algorithm, so that the convergence speed of the network is increased, the training errors are reduced, and the network performance is improved.
In other environment temperature, for example, at 28 deg.C, the operation described in step two is carried out to obtain discrete angle error value epsilon (theta) k ) And the algorithm is used for verifying the effect of the algorithm. The relation c of the amplitude value and the phase of the stable angle measurement error harmonic wave term obtained by the BP neural network method optimized by the genetic algorithm and the temperature j (T)、
Carry-in repairA positive model, yielding:
the angle value theta of 23 is measured k Substituting the above equation and calculating | Δ θ k L, wherein
If the absolute value of delta theta is less than or equal to 1.5', the index requirement is met. If the waiting time is not reached, the neural network training is carried out again.
As shown in FIG. 3, the residual error amplitude of the error correction effect is 1.3 ″ at most, i.e., the requirement is met.
The experimental data for the repeated experiments at each temperature are shown in tables 1-7:
TABLE 1 calibration value of angle measurement error of circular grating at 10 deg.C in thermostat
TABLE 2 calibration value of angle measurement error of circular grating at 15 deg.C in thermostat
TABLE 3 calibration value of round grating angle measurement error at 20 deg.C in thermostat
TABLE 4 calibration value of angle measurement error of circular grating at 25 deg.C in thermostat
TABLE 5 calibration value of angle measurement error of circular grating at 30 deg.C in thermostat
TABLE 6 calibration value of angle measurement error of circular grating at 35 deg.C in thermostat
TABLE 7 calibration value of angle measurement error of circular grating at 40 ℃ in constant temperature box
The data in the table is substituted according to the method, and the amplitude c is obtained by calculation j And phase
As a function of temperature T c j (T)、 
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 circular grating angle measurement error correction method based on an optimized BP neural network is characterized by comprising the following steps,
preparing an experimental device, mounting a single reading head on a precision shaft system, fixing a rotating shaft in the precision shaft system with a 23-surface prism through a clamp, and adjusting and fixing the positions of an autocollimator and the precision shaft system to achieve a normal use state;
calibrating an angle measurement error value, calibrating a discrete angle measurement error value of the circular grating at a set temperature, and performing repeated experiments for multiple times;
analyzing harmonic terms, performing Fourier transform on a plurality of groups of experimental data at the set temperature, analyzing the amplitude and the phase of each harmonic term, determining the relative error of harmonic term components, and performing subsequent correction;
step four, adjusting the temperature of the temperature control box, and respectively performing the operations of the step two to the step three at intervals of 5 ℃ within a set temperature range;
and fifthly, optimizing a BP neural network method by using a genetic algorithm, establishing the function relationship of the amplitude and phase of each harmonic item to be corrected with the same temperature, verifying a correction model, and finishing the correction of the angle measurement error of the circular grating.
2. The circular grating angle measurement error correction method based on the optimized BP neural network according to claim 1, wherein in the second step, the experiment is repeated for 3 times.
3. The circular grating angle measurement error correction method based on the optimized BP neural network as claimed in claim 1, wherein in step three, the number of experimental data is the same as the number of repeated experiments.
4. The circular grating angle measurement error correction method based on the optimized BP neural network as claimed in claim 1, wherein the genetic algorithm optimized BP neural network method comprises the following steps of 1) constructing the BP neural network, 2) training the BP neural network, firstly training data normalization, then performing genetic algorithm optimized initial parameters, and finally training the BP neural network.
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