CN110262393A - Gray theory segmented with lag data processing weights thermal error modeling method - Google Patents
Gray theory segmented with lag data processing weights thermal error modeling method Download PDFInfo
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Abstract
The invention discloses a kind of gray theory segmenteds of band lag data processing to weight thermal error modeling method, gray model preprocessing module is formed by the gray model that processing capacity of the Grey Model to temperature and thermal error data establishes multiple and different sequence lengths, input by the output of preprocessing module as distributed lag model post-processing module, lag model is established as post-processing module after determining model lag order, forms the hierarchal model that gray model and distributed lag model combine；Based on hierarchal model, the GM-DL compensation model under different initial temperatures is established, adjacent two heat error compensation models are selected according to test sample original ambient temperature and final thermal error data completion modeling is calculated by way of sectionally weighting.The present invention extracts useful information in data to greatest extent, and model is made to have very strong tendency and adaptability, improves model to the adaptability in each season and period, finally substantially increases the machining accuracy of lathe.
Description
Technical field
The invention belongs to machine tool thermal error compensation technique fields, and in particular to a kind of gray theory of band lag data processing
Segmented weights thermal error modeling method.
Background technique
A large amount of experimental study shows that Thermal Error is the principal element for influencing Numerical Control Machine Tool Machining Error, wrong in institute
Accounting example can achieve 40%~70% in poor source, higher for more accurate machine tool thermal error accounting.And Thermal Error be by
Caused by heat source, and heat source is certainly existed in lathe operation, thus it is inevitable the problem of machine tool thermal error, therefore seek to reduce
Thermal Error method is only the key for improving processing precision of precise numerical control machine.For the Thermal Error problem of lathe, Thermal Error prevention
Method and heat error compensation method are two kinds of basic skills for reducing Thermal Error and improving machine finish.Wherein Thermal Error preventive treatment is
Hard technology mainly improves the production precision of lathe to meet the machining accuracy of workpiece, with Thermal Error in the stage that designs and manufactures
Penalty method compares, and it is very big to improve the cost of same machining accuracy economically, and precision raising is limited, so heat is accidentally
Poor penalty method is the current main method for reducing Thermal Error.Heat error compensation method is mainly by establishing thermo-responsive point and thermal deformation pair
The mathematical model that should be related in actual processing, infers the size of thermal deformation by the temperature value of thermo-responsive point, to pass through machine
The origin offset functions of bed digital control system realize the compensation of Thermal Error, improve machine finish.
There are many kinds of heat error compensation models, according to the gray model (GM) of gray theory foundation and according to time series original
The distributed lag model (DL) that reason is established is common method.Gray system theory is by the stochastic variable in system as variation
Grey colo(u)r specification, random process is as the Grey Sets for generating variation in a certain range.Before establishing model, to irregular or have
The initial data of weaker rule is pre-processed, so that it becomes the new data with certain rule, the model to there is Given information,
There is the system modelling effect of unknown message preferable again simultaneously, there is stronger tendency.But what it is due to temperature sensor measurement is
Material surface somewhere temperature, which, which does not consider to model brought by hysteresis quality of the material deformation relative to temperature, influences, especially
When being in the case of operating condition is more complicated, numerically-controlled machine tool heat source switches more frequent, sensor measured temperature and material internal
The deformation as caused by temperature change has larger hysteresis quality, ignores hysteresis quality Direct Modeling to a certain extent and will affect model and is pre-
Survey precision.The distributed lag model established for time series principle is by the value of dependent variable and current independent variable and multiple lag
Independent variable connects, and has for then indicating the current thermal error value of lathe in thermal error modeling not only with multiple current temperature values
Relationship and there is relationship with several temperature hysteresis values, just reduction hysteresis quality bring significantly influences the model being built such that, mentions
High precision of prediction.But due to the complexity of the inexactness of measurement and lathe, temperature data and heat for thermal error modeling are accidentally
Difference data inevitably includes " grey information ", and in the processing for " grey information ", distributed lag model does not have
Advantage.
In addition, lathe is typically placed in factory, workshop isoperibol is kept to expend huge, so around general lathe
Environment temperature changes with Four seasons change, and by the document of a large amount of thermal error modeling and compensation, our summaries obtain rule, environment
Temperature has important influence in machine tool thermal error modeling.When the sample data and test data original ambient temperature phase of modeling
When difference is little, the model compensation effect of test sample is preferable；At the beginning of the training data of modeling and with the test data of Thermal Error
When beginning environment temperature difference is larger, compensation effect is often very poor.Such as Thermal Error model is established to compensate the summer with the data in winter
Often there is biggish deviation in the Thermal Error that the Thermal Error model compensation morning that the Thermal Error or the data at high noon in season are established surveys.
For this problem, often first is that being that the data in summer in winter is used to build simultaneously as sample data by the method for increasing sample size
Mould, second is that the strong Thermal Error model such as support vector regression model of selection generalization ability, but by forefathers' compensation effect I
Find, compensation effect increases but effect is limited.
Summary of the invention
In view of the above-mentioned deficiencies in the prior art, the technical problem to be solved by the present invention is that providing a kind of band lag number
Thermal error modeling method is weighted according to the gray theory segmented of processing, Thermal Error predictive ability is can be improved and finally improves lathe
Machining accuracy.
The invention adopts the following technical scheme:
Gray theory segmented with lag data processing weights thermal error modeling method, by Grey Model to temperature
The processing capacity of degree and thermal error data establishes the gray model GM of n different sequence lengths1(1,N),GM2(1,N),...,GMn
(1, N) gray model preprocessing module is formed, by the output of preprocessing module as the defeated of distributed lag model post-processing module
Enter, establishes lag model as post-processing module after determining model lag order, form gray model and distributed lag model phase
In conjunction with hierarchal model；Based on hierarchal model, the GM-DL compensation model under different initial temperatures is established, according to test specimens
This original ambient temperature selects adjacent two heat error compensation models and final heat is calculated by way of sectionally weighting
Error information completes modeling.
Specifically, data sequence length is n1,n2,...,nn, gray model is trained with data sequence respectively, together
When sequence length adjusted according to the comparison of trained precision Yu expected precision, new samples are pre-processed by n gray model
After obtain n*m group thermal error value, m is thermo-responsive points, pretreatment values and measured value as the trained distributed lag model of new samples,
Establish GM-DL model.
Further, ifFor the sequence of Thermal Error,For the temperature sequence of key temperatures sensitive spot, wherein i=2,
3 ... .N, i.e. model have chosen N-1 temperature point altogether, and n is the sequence length chosen, and carry out to temperature and thermal error data
One-accumulate sequence establishes GM (1, N) model, then calculates thermal error data and temperature data structure by one-accumulate processing
At matrix, finally calculates and restore to obtain GM (1, N) model to the predicted value of Thermal Error by a regressive, repeat above method and obtain
To the preprocessing module of n GM (1, N) model composition Thermal Error.
Further, the one-accumulate sequence of temperature and thermal error data are as follows:
The thermal error data and temperature data handled by one-accumulate constitutes matrix are as follows:
It restores to obtain GM (1, N) model by a regressive as follows to the predicted value of Thermal Error:
Wherein, k=2,3 ..., n.
Further, it takesThe equal value sequence of adjacent two generations in sequence establishes GM (1, N) model are as follows:
Wherein, a is model development coefficient；biFor drive factor.
Further, the mathematic(al) representation of lag model is established:
Wherein, εt~IID (0, σ2)；N is the maximum lag period；α0For constant term；U is thermo-responsive number, ytFinal heat is accidentally
Difference.
Specifically, setting machine tool environment temperature as 0~40 DEG C, establishing initial temperature respectively every 5 DEG C of selection training samples is 0
DEG C, 5 DEG C, 10 DEG C, 15 DEG C, 20 DEG C, 25 DEG C, 30 DEG C, 35 DEG C, 40 DEG C of GM-DL Thermal Error model, row is at different initial environment temperature
The GM-DL Thermal Error model library of degree.
Further, it is assumed that the initial temperature of test data is t, and system calculates separately node temperature difference between t
Absolute value, the sequence being incremented by by absolute value choose the smallest two groups of data of absolute value, two groups of data difference to above-mentioned sequence permutation
Corresponding temperature nodes are corresponded to, two GM-DL models that two corresponding temperature nodes are established are the model chosen.
Further, after model selects between T1 DEG C and T2 DEG C of temperature nodes, wherein T1 < t < T2, it will
It is respectively y1 and y2 that test sample, which brings into and obtains Thermal Error in the GM-DL model that original ambient temperature is T1 DEG C and T2 DEG C, preceding
On the basis of phase establishes segmented model library, by model selection and two step of weighted calculation, complete to be directed to different initial environments
At a temperature of Thermal Error calculate.
Further, practical Thermal Error y are as follows:
Compared with prior art, the present invention at least has the advantages that
The method of the present invention to the outstanding processing capacity of " grey information " and utilizes the outstanding of " a small number of evidences " using gray model
Modeling ability extracts useful information in data to greatest extent, so that model is had very strong tendency and adaptability, then utilizes
Distributed lag model solves the problems, such as the hysteresis quality of temperature and deformation on lathe, and model is made to influence more serious feelings for hysteresis quality
There has also been very strong predictability for condition, carry out sectionally weighting modeling to Thermal Error using original ambient temperature, improve model to each
The adaptability in season and period finally substantially increases the machining accuracy of lathe.
Further, combined using the ability that the data-handling capacity of gray model and distributed lag model solve hysteresis quality
Modeling, solves the problems, such as that single model is insurmountable, improves the predictability of Thermal Error.
Further, the pre-processing to " grey information " using gray model preprocessing module is extracted in model
Useful information makes model have very strong tendency and adaptability.
Further, temperature sensor observed temperature and the machine tool deformation as caused by temperature have lag in data acquisition
Property, so that model is can solve hysteresis quality influences modeling bring, and there has also been very strong in the case of hysteresis quality influences more serious
It is predictive.
Further, model library provides the model of different heat error compensations, we can be according to different initial temperatures
The suitable model of optimum selecting is modeled, and is laid the foundation for weighted modeling.
Further, sectionally weighting modeling is carried out to Thermal Error using original ambient temperature, can make full use of in model
Information, improve model to the adaptability in each season and period.
In conclusion the present invention to the outstanding processing capacity of " grey information " and is utilized " a small number of evidences " using gray model
Outstanding modeling ability extracts useful information in data to greatest extent, so that model is had very strong tendency and adaptability, then
It solves the problems, such as the hysteresis quality of temperature and deformation on lathe using distributed lag model, influences model for hysteresis quality more serious
The case where there has also been very strong predictability, sectionally weighting modeling is carried out to Thermal Error using original ambient temperature, improves model pair
The adaptability in each season and period finally substantially increases the machining accuracy of lathe.
Below by drawings and examples, technical scheme of the present invention will be described in further detail.
Detailed description of the invention
Fig. 1 is GM-DL model structure；
Fig. 2 is sectionally weighting heat error compensation model.
Specific embodiment
The present invention provides a kind of gray theory segmenteds of band lag data processing to weight thermal error modeling method, utilizes
Grey Model is to the outstanding processing capacity of " grey information " and utilizes the outstanding modeling ability of " a small number of evidences ", to Thermal Error into
Gone pretreatment, then carried out analysis and modeling using hysteresis quality problem of the distributed lag model to deformation in lathe, row at
GM-DL hierarchal model.The different sample data of original ambient temperature is chosen, the GM-DL heat under different original ambient temperatures is established
Error model library is chosen positive and negative most similar GM-DL Thermal Error model in library according to test sample original ambient temperature and is counted respectively
Thermal Error is calculated, and final Thermal Error is finally obtained according to initial temperature part weight.
Fig. 1 and Fig. 2 are please referred to, a kind of gray theory segmented of band lag data processing of the present invention weights thermal error modeling
Method, comprising the following steps:
S1, the gray model GM for establishing n different sequence lengths1(1,N),GM2(1,N),...,GMn(1, N), data sequence
Column length is respectively n1,n2,...,nn, model is trained with these data sequences respectively, while can be according to trained precision
Comparison with expected precision adjusts sequence length；
S2, new samples are obtained to n*m group (m is thermo-responsive points) thermal error value after n gray model pre-processes, it should
Pretreatment values and measured value finally establish GM-DL model as new samples training distributed lag model；
S3, machine tool environment temperature are 0~40 DEG C, and establishing initial temperature respectively every 5 DEG C of selection training samples is 0 DEG C, 5
DEG C, 10 DEG C, 15 DEG C, 20 DEG C, 25 DEG C, 30 DEG C, 35 DEG C, 40 DEG C of GM-DL Thermal Error model, row is at different original ambient temperatures
GM-DL Thermal Error model library；
S4, initial temperature in GM-DL Thermal Error model library is chosen according to test sample original ambient temperature and it is most close
Two groups of GM-DL Thermal Error models and calculate separately Thermal Error；
S5, to calculate it according to test sample initial temperature in step S4 big with the absolute difference of two group model initial temperatures
It is small and by inverse correlation be arranged weight, obtain final thermal error value.
In order to make the object, technical scheme and advantages of the embodiment of the invention clearer, below in conjunction with the embodiment of the present invention
In attached drawing, technical scheme in the embodiment of the invention is clearly and completely described, it is clear that described embodiment is
A part of the embodiment of the present invention, instead of all the embodiments.The present invention being described and shown in usually here in attached drawing is real
The component for applying example can be arranged and be designed by a variety of different configurations.Therefore, below to the present invention provided in the accompanying drawings
The detailed description of embodiment be not intended to limit the range of claimed invention, but be merely representative of of the invention selected
Embodiment.Based on the embodiments of the present invention, those of ordinary skill in the art are obtained without creative efforts
The every other embodiment obtained, shall fall within the protection scope of the present invention.
A kind of gray theory segmented of band lag data processing of the present invention weights thermal error modeling method specifically:
Establish GM-DL model
1) gray model preprocessing module
IfFor the sequence of Thermal Error,For the temperature sequence of key temperatures sensitive spot, wherein i=2,3 ... .N,
I.e. model has chosen N-1 temperature point altogether, and n is the sequence length chosen.
The one-accumulate sequence of temperature and thermal error data are as follows:
In formula, k=1,2 ..., n, n are data sequence length.
It takesThe equal value sequence of adjacent two generations in sequence are as follows:
Wherein, k=2,3 ..., n establish GM (1, N) model based on the variation of above data sequence
Wherein, k=2,3 ..., n, a are model development coefficient；biFor drive factor (or grey actuating quantity).
If coefficient a and b in formula (1)iConstitute coefficient vector
PN=(a, b2,b3,...,bN)T
It is by the column vector that n-1 thermal error datas are constituted
The thermal error data and temperature data handled by one-accumulate constitutes following matrix:
Then formula (1) can be expressed as Matrix division
YN=BPN
According to Least square-fit, the coefficient vector of model can be found out
PN=(BTB)-1BTYN (2)
According to gray theory it is found that the time proximity of GM (1, N) accordingly can be expressed as
GM (1, N) model is just obtained to the predicted value of Thermal Error by a regressive reduction:
Different sequence length n is set1,n2,...,nn, repeat the above method and obtain n GM (1, N) model composition heat accidentally
The preprocessing module of difference, as shown in Figure 1.
2) distributed lag model post-processing module
In post-processing module, the mathematic(al) representation of lag model is established:
In formula, εt~IID (0, σ2)；N is the maximum lag period；α0For constant term；U is thermo-responsive number, ytFinal heat is accidentally
Difference.
N*m group (m is thermo-responsive points) thermal error value that n gray model is pre-processed is as distributed lag model
Input be distributed according to Least Square Method stagnant using the error measured value in new samples as the output of distributed lag model
Model coefficient afterwards completes the modeling of post-processing module
4.2 segmented weighted modelings
GM-DL hierarchal model is the basis of segmented modeling.According to the long-term ambient temperature situations of lathe, it is assumed herein that being
0~40 DEG C, model is established every fixed temperature, it is assumed herein that 5 DEG C of interval selection, therefore the initial temperature node of modeling data point
It Wei not be 0 DEG C, 5 DEG C, 10 DEG C, 15 DEG C, 20 DEG C, 25 DEG C, 30 DEG C, 35 DEG C, 40 DEG C.By the experimental data of measurement, not equality of temperature is established
GM-DL model at node is spent, the model library of segmented is obtained with this, as shown in Figure 2.
1) GM-DL model is chosen
Assuming that the initial temperature of test data is t, system calculates separately the absolute value of node temperature difference between t, i.e.,
|-t|、|5-t|、|10-t|、|15-t|、|20-t|、|25-t|、|30-t|、|35-t|、|40-t|
The sequence being incremented by by absolute value chooses the smallest two groups of data of absolute value, two groups of data point to above-mentioned sequence permutation
Corresponding temperature nodes are not corresponded to, then two GM-DL models that two corresponding temperature nodes are established are that we will select
The model taken.
2) weighted calculation:
Assuming that test sample original ambient temperature is t, after model selects between temperature nodes T1 and T2 DEG C,
In, T1 < t < T2, bringing test sample into original ambient temperature is that Thermal Error difference is obtained in T1 and T2 DEG C of GM-DL model
For y1 and y2, then according to following weight calculation rule, practical Thermal Error y are as follows:
On the basis of establishing to segmented model library early period, by model selection and two step of weighted calculation, needle is completed
Thermal Error under different original ambient temperatures is calculated.
The above content is merely illustrative of the invention's technical idea, and this does not limit the scope of protection of the present invention, all to press
According to technical idea proposed by the present invention, any changes made on the basis of the technical scheme each falls within claims of the present invention
Protection scope within.
Claims (10)
1. the gray theory segmented with lag data processing weights thermal error modeling method, which is characterized in that managed by grey
The gray model GM of n different sequence lengths is established by processing capacity of the model to temperature and thermal error data1(1,N),GM2(1,
N),...,GMn(1, N) form gray model preprocessing module, using the output of preprocessing module as distributed lag model after
The input for managing module establishes lag model as post-processing module after determining model lag order, forms gray model and distribution
The hierarchal model that lag model combines；Based on hierarchal model, the GM-DL compensation model under different initial temperatures is established,
Adjacent two heat error compensation models are selected according to test sample original ambient temperature and are calculated by way of sectionally weighting
It obtains final thermal error data and completes modeling.
2. the gray theory segmented of band lag data processing according to claim 1 weights thermal error modeling method,
It is characterized in that, data sequence length n1,n2,...,nn, gray model is trained with data sequence respectively, while basis
The comparison of trained precision Yu expected precision adjusts sequence length, and new samples are obtained after n gray model pre-processes
N*m group thermal error value, m are thermo-responsive points, pretreatment values and measured value as new samples training distributed lag model, are established
GM-DL model.
3. the gray theory segmented of band lag data processing according to claim 1 or 2 weights thermal error modeling method,
It is characterized in that, settingFor the sequence of Thermal Error,For the temperature sequence of key temperatures sensitive spot, wherein i=2,3,
... .N, i.e. model have chosen N-1 temperature point altogether, and n is the sequence length chosen, and carry out one to temperature and thermal error data
Secondary cumulative sequence establishes GM (1, N) model, then calculates thermal error data and temperature data by one-accumulate processing and constitutes
Matrix finally calculates and restores to obtain GM (1, N) model to the predicted value of Thermal Error by a regressive, repeats above method and obtain
The preprocessing module of n GM (1, N) model composition Thermal Error.
4. the gray theory segmented of band lag data processing according to claim 3 weights thermal error modeling method,
It is characterized in that, the one-accumulate sequence of temperature and thermal error data are as follows:
The thermal error data and temperature data handled by one-accumulate constitutes matrix are as follows:
It restores to obtain GM (1, N) model by a regressive as follows to the predicted value of Thermal Error:
Wherein, k=2,3 ..., n.
5. the gray theory segmented of band lag data processing according to claim 3 weights thermal error modeling method,
It is characterized in that, takesThe equal value sequence of adjacent two generations in sequence establishes GM (1, N) model are as follows:
Wherein, a is model development coefficient；biFor drive factor.
6. the gray theory segmented of band lag data processing according to claim 1 or 2 weights thermal error modeling method,
It is characterized in that, establishing the mathematic(al) representation of lag model:
Wherein, εt~IID (0, σ2)；N is the maximum lag period；α0For constant term；U is thermo-responsive number, ytFinal Thermal Error.
7. the gray theory segmented of band lag data processing according to claim 1 weights thermal error modeling method,
It is characterized in that, if machine tool environment temperature is 0~40 DEG C, establishing initial temperature respectively every 5 DEG C of selection training samples is 0 DEG C, 5
DEG C, 10 DEG C, 15 DEG C, 20 DEG C, 25 DEG C, 30 DEG C, 35 DEG C, 40 DEG C of GM-DL Thermal Error model, row is at different original ambient temperatures
GM-DL Thermal Error model library.
8. the gray theory segmented of band lag data processing according to claim 7 weights thermal error modeling method,
It is characterized in that, it is assumed that the initial temperature of test data is t, and system calculates separately the absolute value of node temperature difference between t, presses
The incremental sequence of absolute value chooses the smallest two groups of data of absolute value to above-mentioned sequence permutation, and two groups of data respectively correspond phase
The temperature nodes answered, two GM-DL models that two corresponding temperature nodes are established are the model chosen.
9. the gray theory segmented of band lag data processing according to claim 8 weights thermal error modeling method,
It is characterized in that, after model selects between T1 DEG C and T2 DEG C of temperature nodes, wherein T1 < t < T2, by test sample band
Entering original ambient temperature to obtain Thermal Error in T1 DEG C and T2 DEG C of GM-DL model is respectively y1 and y2, in early period to segmented
On the basis of model library is established, by model selection and two step of weighted calculation, complete for heat under different original ambient temperatures accidentally
Difference calculates.
10. the gray theory segmented of band lag data processing according to claim 9 weights thermal error modeling method,
It is characterized in that, practical Thermal Error y are as follows:
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| CN114295095A (en) * | 2021-11-26 | 2022-04-08 | 广西科技大学 | Method for determining optimal measuring point number of free-form surface detection |
| CN114295095B (en) * | 2021-11-26 | 2023-07-14 | 广西科技大学 | Method for determining optimal number of measuring points for free-form surface detection |
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