CN110705180B

CN110705180B - Nonlinear autoregressive neural network machine tool thermal error modeling method with external input

Info

Publication number: CN110705180B
Application number: CN201910946714.4A
Authority: CN
Inventors: 张成新; 孔凡红; 崔敏
Original assignee: Qufu Normal University
Current assignee: Qufu Normal University
Priority date: 2019-10-07
Filing date: 2019-10-07
Publication date: 2024-06-14
Anticipated expiration: 2039-10-07
Also published as: CN110705180A

Abstract

The invention discloses a numerical control machine tool thermal error modeling method, which comprises the following steps: step 1, testing temperature and thermal error data of a machine tool; step 2, selecting key temperature measuring points as input of a thermal error model by adopting an information entropy algorithm; step 3: NARX model training; and 4, calculating a real-time thermal error compensation value of the machine tool through the model. According to the method, the temperature measuring point most relevant to the thermal error can be found by adopting the algorithm of the relative information entropy; the NARX model can overcome the hysteresis characteristic of temperature-thermal error, and has the advantages of high prediction precision and strong adaptability.

Description

Nonlinear autoregressive neural network machine tool thermal error modeling method with external input

Technical Field

The invention belongs to the technical field of thermal error compensation of precision numerical control machine tools, and relates to a machine tool thermal error modeling method with an external input nonlinear autoregressive neural network NARX (Nonlinear AutoRegressive with eXternal input neural network).

Background

In the working process of the machine tool, the thermal deformation of each part of the machine tool can be caused by the factors of main shaft heating, friction heating of moving parts, cutting heat, environmental temperature change and the like, so that the ideal positions of the cutting tool and a workpiece are changed to cause machining errors. At present, due to the improvement of the machining manufacturing technology, the geometric error of a precision machine tool is small, and the thermal error becomes the most important factor affecting the precision of the precision machine tool. Related researches show that the thermal error can account for about 70% of the machining error of the precision machine tool, so that the thermal error compensation of the precision numerical control machine tool becomes a key task for improving the machining precision of the precision numerical control machine tool.

Since the industry recognizes that thermal errors have a significant impact on machine tool accuracy, there has been a great deal of research to reduce or eliminate thermal errors in machine tools. At present, common methods for modeling thermal errors include a linear regression model, a support vector machine model, a neural network model, a gray prediction model and the like. One common problem with these models is that they do not take into account the hysteresis or multivalue characteristics of thermal error variations, and when used in a complex environment, the models cannot adapt to the strong nonlinearity of thermal error variations, resulting in low prediction accuracy and even failure.

The hysteresis characteristic of temperature-thermal error refers to that when the temperature rises and then falls, the thermal error curves in the temperature rising and falling stages are not coincident, and one temperature value corresponding to two or more thermal error values is generated, as shown in fig. 1. Because of this property of temperature-thermal errors, it is difficult to build accurate thermal error prediction models.

Disclosure of Invention

The invention aims to solve the technical problem of establishing a prediction model capable of overcoming the temperature-thermal error hysteresis characteristic and providing a high-precision thermal error prediction method.

The technical scheme of the invention is as follows: a nonlinear autoregressive neural network model with external input is introduced to establish a thermal error model, and a neural network model suitable for thermal error prediction is constructed aiming at hysteresis characteristics of temperature-thermal error, and the method specifically comprises the following implementation steps:

step 1: testing machine tool thermal error and each point temperature

Arranging a large number of temperature sensors on a machine tool, and measuring temperature data required by modeling; an eddy current sensor is placed at the end of the spindle to measure the thermal error of the machine tool. Due to hysteresis characteristics of temperature-thermal errors, the collected temperature and thermal error data must have a plurality of temperature rise and fall periods, so that the collected signals contain enough information to ensure adaptability and prediction accuracy of the prediction model.

Step 2: selecting key temperature measurement points as inputs to a thermal error model

And selecting a temperature variable most relevant to the thermal error as a model input through an algorithm of relative information entropy.

The calculation process of the relative information entropy is as follows: normalizing the collected temperature and thermal error data; dividing the amplitude into N equal parts, sorting each group of data according to the amplitude, and calculating the data number of each interval according to the number of divided intervals, wherein the data number of each interval is divided by the total data number to obtain the data distribution frequency of each interval. After the distribution frequency of each group of data is obtained, the relative entropy of each group of temperature data and thermal error can be calculated according to a relative entropy calculation formula, and a temperature point with minimum entropy is selected. The smaller entropy represents the closer the temperature distribution is to the thermal error distribution.

And storing the selected optimal temperature measurement point data into an array u= [ u ₁,u₂,…,u_m ] and storing the thermal error into an array y= [ y ₁,y₂,…,y_m ], wherein m represents the data sampling number.

Step 3: NARX model training

The NARX model is a neural network model based on time series, and the functional relationship is a nonlinear function and can be expressed by the following formula.

y(t)＝f[y(t-1),y(t-2),…,y(t-n),u(t),u(t-1),u(t-2),…,u(t-n)]

Wherein: u (t), y (t) is an input value and an output value at the current time, u (t-n), y (t-n) is an input and output value at the first n times, n is a delay order, and f () is a nonlinear function.

And constructing a training parameter matrix for the selected temperature data u and the thermal error data y, and then training the NARX model by adopting a LEVENGERG-Marquardt algorithm.

Step 4: obtaining the thermal error compensation value of the machine tool

And (3) during compensation, the real-time temperature data of the temperature measuring points obtained in the step (2) are sequentially input into the NARX model obtained in the step (3), so that the thermal error value to be compensated by the machine tool can be calculated.

The beneficial effects of the invention are as follows:

1) By adopting a relative information entropy method to find the optimal temperature measuring point, the temperature variable with the highest matching degree with the thermal error information can be found, and the modeling precision is improved.

2) By adopting the nonlinear autoregressive neural network model with external input, the hysteresis characteristic of temperature-thermal error can be overcome, and the prediction precision and the adaptability of the model are improved.

Drawings

FIG. 1 is a schematic diagram of a principal axis temperature-thermal error hysteresis characteristic curve

FIG. 2 is a block diagram of a nonlinear neural network model with external inputs

FIG. 3 shows temperature change curves at various measuring points

FIG. 4 thermal error variation curve of an embodiment

FIG. 5 example temperature test data

FIG. 6 embodiment thermal error test data

FIG. 7 NARX prediction effect diagram

Detailed Description

The invention is described in further detail below with reference to the drawings and examples.

Step 1: test data

As shown in FIG. 1, since the spindle temperature-thermal error signal has hysteresis characteristics, a plurality of temperature rise and fall periods are required when the modeling signal is acquired, so that the acquired signal contains enough information to ensure the adaptability and the prediction accuracy of the prediction model.

And storing the temperature data and the thermal error data obtained by the test into an array.

Step 2: and carrying out normalization processing on the measured temperature data and the thermal error data, wherein a normalization formula is shown as follows:

X _i normalized data, X _i i th raw sample data, X _max,x_min are the maximum and minimum values in the set of data.

Step 3: searching for the optimal temperature measuring point.

1. The best temperature measuring point is found by calculating the relative information entropy of the temperature variable and the thermal error variable, and the smaller the entropy is, the closer the temperature variable and the thermal error variable are.

2. Taking N=50, calculating the number of data in the interval that i is less than or equal to X and less than i+0.02 in each group of data, wherein i= 0,0.02,0.04, … and 1. Temperature data is represented by UP _i and thermal error is represented by YP _i.

3. Calculating the occurrence frequency of each section data in each group of temperature data U and thermal error data Y: Substituting the relative entropy calculation formula to obtain relative entropy:

Where n=50.

Step 4: NARX model training

Fig. 2 is a block diagram of a nonlinear neural network according to the present invention. Z ^-1 in the figure represents the delay operator. By the action of a delay operator, the input signal of the neural network not only comprises the current value but also the values of the previous moments; the output signal of the neural network is also fed back to the input end through a delay operator; thus, the neural network can obtain more input information, and has extremely strong adaptability to processing time series signals.

1. Constructing NARX model, adopting 2-order delay for input and output signals, hidden layer 10, and adopting LEVENGERG-Marquardt algorithm to train neural network.

2. And obtaining training data for the optimal temperature measurement point data u and the thermal error data y determined by the relative entropy.

3. The constructed neural network is trained with the training data obtained above to obtain the NARX model.

Step 5: obtaining the thermal error compensation value of the machine tool

And (3) sequentially inputting the real-time temperature data of the temperature measuring points obtained in the step (2) into the NARX model obtained in the step (3), and then calculating the thermal error value of the machine tool at the moment.

Examples: modeling test is carried out on the axial thermal error of a spindle of a numerical control lathe, a measured modeling temperature curve is shown in fig. 3, and the thermal error is shown in fig. 4. Performing normalization processing on all measurement data according to the step 2; according to step 3, n=50 is taken during data grouping, the relative information entropy of each temperature point is calculated, the temperature measuring point 6 is selected as a modeling input point, and hysteresis curves of the temperature measuring point 6 and the thermal error are shown in fig. 5; in step 3, NARX model input/output delay is selected to be 2-order, hidden layer is 10-layer, training algorithm is LEVENGERG-Marquardt, and then model is trained. After the model is obtained, the data in fig. 5 and 6 are used for testing, and the result is shown in fig. 7, and the maximum error of the model prediction data is about 1.5 microns compared with the actual measurement data, so that the actual application requirements can be met. From the results, the NARX thermal error model can overcome the hysteresis characteristic of temperature-thermal error and provide a high-precision thermal error predicted value.

Claims

1. A nonlinear autoregressive neural network machine tool thermal error modeling method with external input is characterized by comprising the following steps:

step 1, testing machine tool temperature and thermal error data

Due to hysteresis characteristics of temperature-thermal errors, the collected temperature and thermal error data must have a plurality of temperature rise and fall periods, so that the collected signals contain enough information to ensure the adaptability and the prediction precision of the prediction model;

Selecting a temperature variable most related to the thermal error as a model input by a relative information entropy method;

The calculation process of the relative information entropy is as follows: normalizing the collected temperature and thermal error data; dividing the amplitude into N equal parts, sorting each group of data according to the amplitude, calculating the data number of each interval according to the number of divided intervals, and dividing the data number of each interval by the total data number to obtain the data distribution frequency of each interval; after the distribution frequency of each group of data is obtained, the relative entropy of each group of temperature data and thermal error can be calculated according to a relative entropy calculation formula, and a temperature point with minimum entropy is selected; the smaller entropy represents the closer the temperature distribution is to the thermal error distribution;

Storing the selected optimal temperature measurement point data into an array u= [ u ₁,u₂,…,u_m ] and storing the thermal error into an array y= [ y ₁,y₂,…,y_m ], wherein m represents the data sampling number;

step 3: NARX model training

The NARX model is a neural network model based on time sequence, and the functional relation is a nonlinear function and can be expressed by the following formula:

y(t)＝f[y(t-1),y(t-2),…,y(t-n),u(t),u(t-1),u(t-2),…,u(t-n)]

wherein: u (t), y (t) is an input value and an output value at the current moment, u (t-n), y (t-n) is an input and output value at the first n moments, n is a delay order, and f () is a nonlinear function;

Constructing a training parameter matrix for the selected temperature data u and thermal error data y, and then training an NARX model by adopting LEVENGERG-Marquardt algorithm;

Step 4: obtaining the thermal error compensation value of the machine tool