CN110046412B - Circular grating angle measurement error correction method based on optimized BP neural network - Google Patents

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, comprising the following steps. It can be used normally; step 2, calibrate the angle measurement error value, and repeat the experiment for many times; step 3, analyze the harmonic terms, perform Fourier transform on the multiple sets of experimental data at the set temperature, and analyze each harmonic term The amplitude and phase are determined, and the harmonic term with the relative error less than 10% is determined, and the subsequent correction is carried out; Step 4, adjust the temperature of the temperature control box, and perform the operations from the above steps 2 to 3; Step 5, use genetic algorithm to optimize the BP neural network. The network method is used to establish the relationship between the amplitude and phase of each harmonic item to be corrected and the temperature, and verify the correction model to complete the correction of the angle measurement error of the circular grating. It can significantly improve the measurement accuracy of the parallel double-joint coordinate measuring machine.

Description

An error correction method for circular grating angle measurement based on optimized BP neural network

technical field

The invention belongs to the field of measuring instruments, in particular to a circular grating angle measurement error correction method based on an optimized BP neural network.

Background technique

Joint coordinate measuring machine is a precision measuring instrument widely used in modern manufacturing, mainly used in automobile manufacturing, aerospace, mold processing and other fields. This type of instrument adopts a tandem structure and is composed of multiple precision shaft systems and connecting rod structures. Therefore, the measurement accuracy of the instrument is significantly affected by the angle measurement accuracy of the precision shaft system. However, the angle measurement accuracy of the circular grating in the precision shaft system is affected by the environment. significant effect of temperature. In different industrial sites, the variation range of the ambient temperature may reach 30°C. If the ambient temperature parameter is not included in the angle measurement error model of the circular grating, when the ambient temperature of the industrial site and the instrument are more than 20°C during calibration When it is large, it will cause a significant angle measurement error of the circular grating, which will lead to a significant decrease in the measurement accuracy of the instrument.

In view of the decrease of measurement accuracy of the current joint coordinate measuring machine due to the change of ambient temperature, the method adopted is the whole machine calibration method, that is, a temperature sensor is installed on the joint coordinate measuring machine, and the whole instrument is placed in a large temperature control box. When the temperature of the instrument is high, use standard parts such as quartz rods to calibrate the instrument to obtain the structural parameters such as the length of the connecting rod of the instrument, and make a table and enter it into the upper computer system. This method can correct the measurement error to a certain extent, but There is no correction for the angle measurement error of the circular grating caused by the temperature change, and the instrument measurement error caused by it. At present, there is no method for correcting the angle measurement error of the circular grating caused by the change of the ambient temperature. There is only a method for correcting the geometric structure and motion errors caused by the grating disc engraving error, the grating disc installation eccentricity, and the shaking of the rotating shaft, that is, by using self-alignment. A straight meter, a polygonal prism or a high-precision circular grating sensor is used as a standard quantity to obtain the discrete value of the angle measurement error of the circular grating to be corrected, and a correction function is established using algorithms such as the least squares method.

SUMMARY OF THE INVENTION

The purpose of the present invention is to solve this problem, to provide a circular grating angle measurement error correction method based on an optimized BP neural network. The angle measurement error caused by the circular grating is used to improve the measurement accuracy of the joint coordinate measuring machine when it is used in the industrial field.

In order to realize the above-mentioned purpose of the invention, the technical scheme of the present invention is:

A circular grating angle measurement error correction method based on an optimized BP neural network is characterized in that, comprising the following steps:

Step 1, prepare the experimental device, install a single reading head on the precision shaft system, fix the rotation axis in the precision shaft system with the 23-face prism through the fixture, adjust the position of the autocollimator and the precision shaft system and fix it to achieve a possible normal use state;

Step 2, calibrate the angle measurement error value, at the set temperature, calibrate the discrete angle measurement error value of the circular grating, and repeat the experiment many times;

Step 3, analyze harmonic term, carry out Fourier transform to many groups of experimental data under this setting temperature, analyze the amplitude and phase of each harmonic term, determine the relative error of harmonic term composition, carry out follow-up correction;

Step 4, adjust the temperature of the temperature control box, carry out the operations of above-mentioned steps 2 to 3 respectively at every 5°C of the set temperature range;

Step 5: Use the genetic algorithm to optimize the BP neural network method, establish the functional relationship between the amplitude and phase of each harmonic term to be corrected and the temperature, and verify the correction model to complete the correction of the angle measurement error of the circular grating.

Preferably, in step 2, the experiment is repeated three times.

Preferably, in step 3, the number of experimental data is the same as the number of repeated experiments.

Preferably, in step 5, the genetic algorithm optimizes the BP neural network method, and the steps are as follows: 1) constructing the BP neural network, 2) training the BP neural network, first normalizing the training data, then optimizing the initial parameters by the genetic algorithm, and finally BP Neural network training.

Compared with the prior art, the beneficial effects of the present invention are:

Based on a single reading, the spectrum analysis genetic algorithm is used to optimize the BP neural network's circular grating angle measurement error correction method, which is used to correct the angle measurement errors caused by ambient temperature, circular grating structure and motion errors. The error harmonic term is corrected, and the angle measurement error caused by the temperature change, the grating geometry and the error motion is corrected, which greatly improves the angle measurement accuracy of the circular grating, thereby improving the measurement accuracy of the joint coordinate measuring machine. The applicability of such instruments in industrial sites is of great significance.

Description of 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 the experimental device of the method for correcting the angle measurement error of the circular grating based on the optimized BP neural network of the present invention.

Fig. 2 is the flow chart of the genetic algorithm optimization of the BP neural network algorithm based on the optimization method of the circular grating angle measurement error correction method of the BP neural network of the present invention.

Fig. 3 is the angle measurement error correction effect diagram of the circular grating angle measurement error correction method based on the optimized BP neural network of the present invention.

FIG. 4 is a schematic diagram of a precise shaft system of the method for correcting the angle measurement error of a circular grating based on an optimized BP neural network according to the present invention.

Detailed ways

The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings.

As shown in Figure 1 and Figure 4, a method for correcting the angle measurement error of a circular grating based on an optimized BP neural network includes the following steps:

Step 1, prepare the experimental device, install a single reading head on the bracket of the reading head 7, fix the connection fixture on the rotating shaft 1 in the precision shaft system by screws, and fix the fixture with the 23-sided prism 2 through the nut. The shaft system is placed in the temperature control box 4, and the positions of the autocollimator 5 and the precision shaft system are adjusted so that the light path enters the 23-sided prism vertically through the opening 6 of the temperature control box, and the position of the 23-sided prism is adjusted. When the indication value of the circular grating 8 is close to 0°, the first working surface of the 23-sided prism is perpendicular to the optical path of the autocollimator. Tighten the nut and close the box door to achieve normal use. A ball bearing 31 and a shaft sleeve 32 in which the ball bearing is sleeved are arranged in the precision shaft system.

Step 2: Calibrate the angle measurement error value. Under a certain set ambient temperature, the rotating shaft is rotated by the motor, so that the first working face to the 23rd working face of the 23-face prism is perpendicular to the optical path of the autocollimator. That is, the cross target of the self-collimator is located in the middle of the field of view after being reflected by the working surface of the 23-sided prism;

At these 23 positions, the angle measurement values of the circular grating H _k , k=1, 2, . . . , 23 and the autocollimator horizontal direction indication γ _Xk are recorded simultaneously. The angle measurement values H _k and γ _Xk of the circular grating are processed to obtain the discrete angle measurement error value ε(θ _k ) calibrated by the 23-sided prism and the autocollimator at the current temperature:

Repeat the above step 2 to obtain 3 sets of measurement data ε _m (θ _k ) at a certain set temperature, m=1, 2, 3, k=1, 2, . . . , 23.

即对每组ε(θ_k)进 行傅里叶变换可以得到F(n)。由于使用23面棱体，实际有效的谐波项为0至11阶项，写 成三角函数形式为：According to the formula:

That is, F(n) can be obtained by performing Fourier transform on each group of ε(θ _k ). Since a 23-sided prism is used, the actual effective harmonic terms are 0 to 11th order terms, written in trigonometric form as:

为谐波相位。Among them, c ₀ , c _i are the amplitude values of each order,

is the harmonic phase.

如彼此间相对误差小 于10％的谐波项成分，即认为是稳定的测角误差项，后续进行建模修正。对经频谱分析得 到的稳定的谐波项的幅值和相位取算数平均值，得到c_j,

其中j是稳定谐波项的阶数。Step 3, analyze the harmonic term, apply 3 sets of data at this temperature, and perform Fourier transform spectrum analysis on the amplitude and phase of each harmonic. If the relative error of the amplitude and phase of a certain order harmonic term is less than 10%, that is, it is considered as a stable angle measurement error term. For example, analyze the magnitude c ₁₀ , c ₂₀ , c ₃₀ and the phase of the 1st order term

If the relative error between each other is less than 10% of the harmonic term components, it is considered as a stable angle measurement error term, and subsequent modeling correction is performed. Take the arithmetic mean of the amplitude and phase of the stable harmonic term obtained by spectrum analysis to obtain c _j ,

where j is the order of the stable harmonic term.

Step 4: Adjust the temperature of the temperature control box, and perform the above steps 2 to 4 at 10°C to 40°C at intervals of 5°C to obtain the discrete points c _Tj of the amplitude and phase of the stability error with respect to the temperature T at each temperature,

和温 度T的函数关系，并验证模型，最终完成圆光栅测角误差修正。Step 5: Since the relationship between the amplitude and phase at each temperature is complex and nonlinear, the BP neural network method optimized by the genetic algorithm is used to establish the amplitude c _j of each harmonic term to be corrected. and phase

And the functional relationship of temperature T, and verify the model, and finally complete the angle measurement error correction of the circular grating.

As shown in Figure 2, the system block diagram of the BP neural network method optimized by the genetic algorithm, the steps are as follows:

1. Build BP neural network

Using a single hidden layer structure, the input layer has 1 node, corresponding to the temperature T, the hidden layer uses 17 nodes, and the layer has 2N nodes, where N is the number of stable harmonic terms.

The transfer function of the hidden layer is the tangent sigmoid transfer function tansig:

The transfer function of the output layer is a linear transfer function purelin: g(x)=x.

Let the threshold of the qth neuron in the output layer be θ _j ,

The threshold of the hth hidden layer neuron is γ _h ,

The weight between the ith node of the input layer and the hth node of the hidden layer is v _ih ,

The weight of the hth node of the hidden layer and the qth node of the output layer is w _hq ,

The input received by the hth neuron in the hidden layer is α _h = v _h T,

The output of the hth neuron in the hidden layer is b _h =f(α _h -γ _h ),

The input received by the qth neuron in the output layer is

The output of the qth neuron in the output layer is y _q =g(β _q -θ _q ).

Among them, y _q is c _q , and y _q+1 is

2. Training BP neural network

2.1 Normalization of training data

Use the obtained data as network training data, and normalize the training. The normalization method is as follows:

x _k =(x _k -x _min )/(x _max -x _min ) (3)

In the formula, x _min is the minimum number in the data sequence, and x _max is the maximum number in the sequence. Configure the network parameters, set the number of iterations, learning rate and target.

2.2 Genetic algorithm to optimize initial parameters

The initial parameters of the neural network are random numbers in [0,1], and the genetic algorithm is used to optimize the initial weights and thresholds of the BP neural network, so that the optimized BP neural network can better predict the function output. The method mainly includes fitness function, selection operation, crossover operation and mutation operation.

Use the training data to train the BP neural network to predict the system output, take the absolute value of the error between the predicted output and the expected output and E as the individual fitness value F, and use the selection roulette method to perform the selection operation. Since the individual is encoded by real numbers, so The crossover operation method uses the real number crossover method. The crossover operation method of the kth chromosome a _k and the lth chromosome a _l at the j position is as follows:

where b is a random number between [0,1]. Set the population size to 10, the evolution times to 40, the crossover probability to be 0.3, and the mutation probability to be 0.2. After optimization by genetic algorithm, the initial value of neural network algorithm is obtained.

2.3 BP neural network training

其中

对于训练数据集中的 单个数据其误差

采用梯度下降法根据误差对神经网络中的参数进行反 馈学习，采用Levenberg-Marquardt算法对神经网络进行训练，提高网络的收敛速度，减少 训练误差，提高网络性能。The output of the neural network is

in

For a single data in the training data set its error

Gradient descent method is used for feedback learning of the parameters in the neural network according to the error, and the Levenberg-Marquardt algorithm is used to train the neural network, which improves the convergence speed of the network, reduces the training error and improves the network performance.

带入修正模型，得到：In other ambient temperatures, for example, when the temperature control box is 28°C, the operation described in step 2 is performed to obtain a discrete angle measurement error value ε(θ _k ), which is used to verify the effect of the algorithm. The relationship between the amplitude and phase of the harmonic term of the stable angle measurement error obtained by the BP neural network method optimized by the genetic algorithm c _j (T),

Bringing in the corrected model, we get:

如果|Δθ|≤1.5″即认 为满足指标要求。如果没有达到要住，则再次进行神经网络训练。Bring the 23 angle values θ _k into the above equation, and calculate |Δθ _k |, where

If |Δθ|≤1.5″, it is considered that the index requirements are met. If it does not meet the requirements, the neural network training is performed again.

As shown in Figure 3, the maximum residual error amplitude of the error correction effect is 1.3", which meets the requirements.

The experimental data of repeated experiments at various temperatures are shown in Table 1-Table 7:

Table 1 The calibration value of the angle measurement error of the circular grating when the incubator is 10 °C

Table 2 The calibration value of the angle measurement error of the circular grating when the incubator is 15 ℃

Table 3 The calibration value of the angle measurement error of the circular grating when the incubator is 20 ℃

Table 4 The calibration value of the angle measurement error of the circular grating when the incubator is 25 ℃

Table 5 The calibration value of the angle measurement error of the circular grating when the incubator is 30 ℃

Table 6 The calibration value of the angle measurement error of the circular grating when the incubator is 35 ℃

Table 7 The calibration value of the angle measurement error of the circular grating when the incubator is 40 ℃

和温度T的函数关系c_j(T)、

Bring the data in the table according to the above method, and calculate the amplitude c _j and phase

and the functional relationship of temperature T c _j (T),

The above-described embodiments are only a part of the embodiments of the present invention, but not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative work, all belong to 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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