CN115415851A - Cutter health monitoring method based on functional data principal component analysis - Google Patents
Cutter health monitoring method based on functional data principal component analysis Download PDFInfo
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- 238000003754 machining Methods 0.000 claims abstract description 32
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- 238000012847 principal component analysis method Methods 0.000 claims abstract description 5
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- 238000005299 abrasion Methods 0.000 abstract description 3
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Abstract
The invention provides a cutter health monitoring method based on functional data principal component analysis, which comprises the following steps: acquiring a time domain monitoring signal of a sensor in the cutter processing process, inputting sensor data selection and data preprocessing, and then performing time-frequency domain transformation to obtain a frequency domain signal; (II) converting the frequency domain signal into a functional signal by using a function basis according to the frequency and the amplitude of the corresponding frequency; (III) extracting principal components and calculating the scores of the principal components of the frequency domain signals converted into the functional signals by adopting a functional data principal component analysis method; (IV) determining a main component serving as a health index, and constructing the health index; and (V) monitoring the health state of the cutter according to the health indexes. The invention realizes non-contact monitoring of the abrasion condition and the health condition of the cutter in the machining process of the numerical control machine tool, and ensures the machining quality and the machining efficiency.
Description
Technical Field
The invention belongs to the technical field of numerical control machines, and relates to a cutter health monitoring method based on functional data principal component analysis.
Background
The manufacturing industry is the foundation of national economy, and numerical control machine tools are used as the core of basic manufacturing capability, and the unexpected condition of key components can directly reduce the machining efficiency of the machine tools, so that the real-time state monitoring and performance evaluation of the key components are particularly critical. The tool is one of the key parts of the numerical control machine tool, the abrasion degradation of the tool is an inevitable process in the machining process, the surface of the tool which is excessively abraded is torn, the anti-fatigue capability is reduced, and the machined product and even the machine tool are easily damaged.
According to statistics of relevant data, the cost of the cutter accounts for 2.5% -4% of the total manufacturing cost, wherein the cost is about four times of the cost of the cutter due to indirect costs related to procedures such as cutter management, grinding and detection. The wear condition and the health condition of the cutter are accurately monitored, and the cutter can be repaired or replaced in a machining gap in time, so that the production efficiency is improved, and the method has great significance for maintaining the machining precision of the cutter. However, in the machining process, the machining process needs to be frequently paused when the abrasion condition of the tool is directly measured on line, and the measurement adopts instruments such as a microscope, so that the time cost and the labor cost are high.
The non-contact health state monitoring problem of the cutter can be regarded as a design problem of a health index, and a mapping relation between sensor monitoring data of a numerical control machine tool and the wear condition and the health condition of the cutter needs to be established. In the training stage, a training set is constructed according to historical monitoring data in the machining process of the machine tool and wear data measured by a traditional contact type measuring method after the cutter is machined, and the analysis and verification of the mapping relation are completed, so that health indexes capable of reflecting the wear condition and the health condition of the cutter are designed according to the mapping relation. And then in the monitoring process, obtaining a tool health index value according to the sensor monitoring data in the processing process of the data machine tool, judging the health condition of the tool after the processing is finished according to the value, and arranging a grinding and replacing plan of the tool. The process needs to comprehensively apply various sensor data and various signal processing technologies, establish a monotonous mapping relation related to the tool wear by utilizing the existing high-dimensional high-frequency data, excavate the state information of the tool wear, and timely and effectively monitor the health condition of the machining tool, which is a significant but very challenging task for guaranteeing the machining quality and reducing the manufacturing cost.
Disclosure of Invention
Aiming at the defects in the prior art, the invention aims to provide a tool health monitoring method based on functional data principal component analysis, which realizes non-contact monitoring of the wear condition and health condition of a tool in the machining process of a numerical control machine tool, guarantees the machining quality and the machining efficiency, analyzes and processes multi-source state sensor information acquired in real time by utilizing online monitoring data of vibration, spindle current, working conditions and the like in the machining process, indirectly predicts the wear condition of the tool by unsupervised design of health index values, can accurately monitor the health condition of the tool without influencing normal machining operation of the machine tool, and provides technical support for tool management, maintenance and replacement of the machine tool.
In order to achieve the purpose, the invention adopts the following technical scheme:
the invention provides a cutter health monitoring method based on functional data principal component analysis, which comprises the following steps:
acquiring a time domain monitoring signal of a sensor in the machining process of a numerical control machine tool cutter, inputting sensor data for selection, preprocessing the data, and performing time-frequency domain transformation on the time domain monitoring signal to obtain a frequency domain signal;
(II) converting the frequency domain signal into a functional signal by using a function base according to the frequency in the step (I) and the amplitude of the corresponding frequency;
(III) adopting a functional data principal component analysis method to extract principal components and calculate the score of the principal components of the frequency domain signals converted into functional signals;
(IV) determining a main component serving as a health index based on the result of the main component analysis of the functional signal in the step (III), and constructing the health index;
(V) acquiring actual time domain monitoring signals in the machining process of the numerical control machine tool cutter in real time, sequentially carrying out preprocessing and time-frequency domain transformation, and monitoring the health state of the cutter according to the health indexes in the step (IV).
As a preferred technical solution of the present invention, in the step (i), the input data selection and data preprocessing specifically include the following steps:
s101, selecting and determining variables in a tool health state monitoring model in the machining process of a numerical control machine tool;
s102, inputting sensor data, constructing a data matrix, and realizing variable initialization;
s103, according to the sampling frequency of the sensor data, the sensor data in each processing process is subjected to time-frequency domain transformation by utilizing fast Fourier transformation, and the time-domain monitoring signals are converted into frequency-domain signals.
As a preferred embodiment of the present invention, in step (i), the sensor includes any one of a current sensor, a voltage sensor, a vibration sensor, a noise sensor, or an acoustic emission sensor, or a combination of at least two of them.
As a preferred technical solution of the present invention, in the step (ii), the converting into the functional signal specifically includes the following steps:
s201, selecting proper function base types and function numbers;
s202, determining a regular term and a regular term coefficient to perform noise reduction processing to obtain training data, as shown in the following formula:
, wherein ,
s203, solving the optimization problem, and performing functional data transformation:
wherein ,
is a frequency signal;
is a functional signal; λ is a regular term coefficient;
is a regular term;
in order to process the number of times,
；
is a sensor, and is characterized in that,
；
is a functional group; q is the number of functions;
is the frequency amplitude;
is the coefficient term of the corresponding function base.
In a preferred embodiment of the present invention, in the step (ii), the function base includes any one of a trigonometric function base, a spline function base, and a polynomial function base.
As a preferred technical solution of the present invention, in the step (iii), the principal component extraction and the calculation of the score of the principal component specifically include the steps of:
s301, constructing a functional data principal component analysis model;
s302, solving an optimization problem to obtain main components and main component values of functional data;
s303 determines the principal component data that needs to be retained.
As a preferred technical solution of the present invention, in step S301, the constructing a functional data principal component analysis model specifically includes:
is provided with
Is defined in the interval [0,W]Random process of
Respectively calculate independent and identically distributed data of
Mean and variance of (c):
wherein ,
is a functional data model;
is composed of
The mean value of (a);
is composed of
The variance of (a);
decomposing the variance function according to the Karhunen-Loeve theorem to obtain an expression:
wherein ,
is a coefficient of a regular term and is,
is an ordered non-negative characteristic value;
is a functional principal component;
is a functional group; q is the number of functions;
is the coefficient term of the corresponding function base.
As a preferred technical solution of the present invention, in step S302, the expression of the principal component of the functional data is as follows;
the expression of the principal component score is as follows;
wherein ,
is a functional principal component;
is composed of
The mean value of (a);
a principal component score that is a functional principal component;
is a functional principal component.
As a preferred technical solution of the present invention, in the step (iv), the constructing of the health index includes: and comparing the correlation relationship between the principal component scores and the tool wear value, and selecting a plurality of principal component scores with the maximum correlation as health indexes.
In the step (IV), aiming at a plurality of sensor data sets, different principal component scores are analyzed, a plurality of principal components which can best reflect the health condition are determined, the principal component scores are fused, and a health index is constructed.
As a preferred technical solution of the present invention, in the step (v), the monitoring of the health status of the tool specifically includes the following steps:
s401, reading actual sensor data needing to be input based on the composition of the principal component score of the health index, and performing data preprocessing on the actual sensor data;
s402, performing functional data transformation on actual sensor data subjected to data preprocessing to obtain actual functional data, and calculating specific principal component values according to the actual functional data;
s403, obtaining an actual health index value of the cutter based on the calculated principal component score, and judging whether to repair or replace the cutter according to the health index.
Compared with the prior art, the invention has the beneficial effects that:
the invention provides a cutter health monitoring method based on functional data principal component analysis, which aims at the problem of cutter health condition monitoring of a numerical control machine tool, realizes a non-contact health monitoring technology, does not need to stop the machine to disassemble and assemble the cutter for detection, collects sensor signals in the machining process of the numerical control machine tool by utilizing the numerical control machine tool, converts the sensor signals into functional data through a series of signal processing technologies, constructs a cutter health condition index by utilizing a functional data principal component analysis method, and indirectly knows the wear condition and the health condition of the cutter by calculating a health index value. The invention can accurately and efficiently evaluate the health condition of the cutter, does not interfere the normal processing of the numerical control machine tool, and has the advantages of simple structure, lower calculation cost, high efficiency and strong practicability.
Drawings
FIG. 1 is a flow chart of a tool health monitoring method based on functional data principal component analysis according to an embodiment of the present invention;
FIG. 2 is a timing chart of data of each sensor in one process according to example 1 of the present invention;
fig. 3 is an example of a B-spline basis function provided in embodiment 1 of the present invention (the number of functions Q = 7);
fig. 4 is a frequency domain signal diagram of time-domain-transformed time-domain data of the spindle current sensor in several processing processes provided in embodiment 1 of the present invention;
fig. 5 is a data image of a frequency domain signal of a spindle current sensor, which is recorded after several times of processing by a tool according to embodiment 1 of the present invention, after functional data transformation (in the figure, the abscissa represents a frequency range after scaling, and the ordinate represents an amplitude corresponding to a frequency);
FIG. 6 is a point line graph of the predicted tool health indicator score and the actual flank wear value of the tool provided in example 1 of the present invention.
Detailed Description
The technical scheme of the invention is further explained by the specific implementation mode in combination with the attached drawings.
In one embodiment, the invention provides a tool health monitoring method based on functional data principal component analysis, which can identify the health condition of the wear condition of a tool by using sensor monitoring data in the machining process of a numerical control machine tool under the condition of not needing to stop to check the tool, and provides technical support for tool state monitoring and tool management.
As shown in fig. 1, the tool health monitoring method based on functional data principal component analysis includes:
the method comprises the following steps: the method comprises the steps of obtaining a time domain monitoring signal of a sensor in the machining process of a numerical control machine tool cutter, inputting sensor data for selection, preprocessing the data, and then carrying out time-frequency domain transformation on the time domain monitoring signal to obtain a frequency domain signal.
Comprises the following substeps:
s101, selecting and determining variables in the tool health state monitoring model in the machining process of the numerical control machine tool.
According to the analysis of the tool degradation mechanism and the analysis of the variable correlation, the invention mainly considers the following sensor monitoring data as the input variables of the model according to the sensor types on different types of numerical control machines, and the method comprises the following steps: any one or a combination of at least two of a current sensor, a voltage sensor, a vibration sensor, a noise sensor, or an acoustic emission sensor. The correlation between sensors of the same type is generally strong, while the correlation between sensors of different types is weak. Therefore, in actual use, sensors of the same type and different positions can be added as input according to conditions, each variable is monitored respectively, and finally the health degree of the cutter is evaluated comprehensively according to the health index scores of each variable.
S102, inputting sensor data, constructing a data matrix, and realizing variable initialization.
Aiming at the initialization of variables, the invention takes the monitoring data of m sensors in the processing process of n times as the input data of a model to form a data matrix:
wherein ,
is a first
In the secondary processing
A first of the sensors
The number of the data is set to be,
，
，
。
s103, according to the sampling frequency of the sensor data, the sensor data in each processing process is subjected to time-frequency domain transformation by utilizing fast Fourier transformation, and the time-domain monitoring signals are converted into frequency-domain signals.
According to the sampling frequency of the sensor data, the invention uses Fast Fourier Transform (FFT) to perform time-frequency domain transformation on the sensor data in each processing process, and converts the time-domain signal into a frequency-domain signal, for example, the result of transforming the sensor time-domain signal of the jth sensor in the ith processing process is as follows:
step two: and converting the frequency domain signal into a functional signal by using a function basis according to the frequency of the first step and the amplitude of the corresponding frequency.
And (3) performing functional data transformation on the frequency domain signals subjected to the time-frequency domain transformation in the step (S103), and taking the frequency domain signals of the same sensor in different processing processes as a group of training data:
and then, converting the functional signal, wherein the method specifically comprises the following sub-steps:
s201, according to the periodicity of the training data and the data complexity, selecting a proper spline function base type
And number of functions
。
The commonly used function bases include any one of a trigonometric function base, a spline function base, or a polynomial function base, and the more complex the training data, the greater the number of functions required.
S202, determining a regular term and a regular term coefficient to perform noise reduction processing.
After S203 determines the relevant modules in step S201 and step S202, the training data may be written in the following form:
wherein ,
is the corresponding error term.
Then solving the optimization problem, and carrying out functional data transformation:
wherein ,
is a frequency signal;
is a functional signal; λ is a regular term coefficient;
is a regular term;
is a functional group; q is the number of functions;
is the frequency amplitude;
is the coefficient item corresponding to the function base.
The training data usually contains some noise data, and in order to make the subsequent calculation more accurate, a regular term is usually added in the conversion process to smooth the final result, so as to achieve the purpose of noise reduction, and therefore, a proper regular term needs to be determined
And a regular term coefficient λ.
Step three: and performing principal component extraction and principal component score calculation on the frequency domain signals converted into the functional signals by adopting a functional data principal component analysis method.
After the second step, the original frequency domain signal is processed
Converted into a smoothed functional signal
And step three, performing Principal component extraction and Principal component score calculation on the frequency domain model converted into the Functional signal by using a Functional Principal Components Analysis (FPCA), specifically including the following sub-steps:
s301, a functional data principal component analysis model is constructed.
Is provided with
Is defined in the interval [0,W]Random process on
Respectively calculating independent and equally distributed data
Mean and variance of (c):
wherein ,
is a functional signal;
is composed of
The mean value of (a);
is composed of
The variance of (a);
decomposing the variance function according to the Karhunen-Loeve theorem to obtain an expression:
wherein ,
in the case of the regular term coefficients,
is an ordered non-negative characteristic value;
the eigenvectors corresponding to the eigenvalues, called Functional Principal Components (FPCs), can also be written as a weighted sum of basis functions in the function base;
is a functional group; q is the number of functions;
is the coefficient item corresponding to the function base.
S302, an optimization problem is solved, and the principal component score of the functional data are obtained.
Functional data
Expressed as FPCs:
wherein ,
is a functional principal component;
is composed of
The mean value of (a);
is the principal component score of the functional principal component,
is independent of
And are and
the random variable that is not correlated is,
, and 
；
is a functional principal component.
It should be noted that Karhunen-Loeve's theorem, well known to those skilled in the art, refers to a transformation that decomposes a signal into linear combinations of uncorrelated basis functions, and is an optimal transformation in the sense of least mean square error.
S303 determines the principal component data that needs to be retained.
Functional data from the analysis
Can be expressed as the sum of an infinite number of functional principal components, but usually only a few eigenvalues are significantly non-zero, and for the eigenvalues that are near zero, the corresponding FPCs score is also near zero, so that usually only a few functional principal components with the largest eigenvalues are of interest.
Step four: and determining principal components serving as health indexes based on the results of principal component analysis of the function type signals in the second step and the third step, analyzing different principal component scores aiming at a plurality of sensor data sets, comparing correlation relations between the principal component scores and the tool wear values, and selecting a plurality of principal component scores with the maximum correlation as the health indexes.
The actual wear value of the cutter can be measured in a microscope, and the more serious the cutter is worn, the worse the health condition is.
Step five: and acquiring actual time domain monitoring signals in the machining process of the numerical control machine tool cutter in real time, preprocessing and time-frequency domain transformation, calculating corresponding principal component scores according to functional principal components of the health indexes in the step four, wherein the principal component scores can reflect the health condition of the cutter at the moment.
The method specifically comprises the following substeps:
s401, reading actual sensor data needing to be input based on the composition of the principal component score of the health index, and performing data preprocessing on the actual sensor data;
s402, performing functional data transformation on actual sensor data subjected to data preprocessing to obtain actual functional data, and calculating specific principal component values according to the actual functional data;
s403, obtaining an actual health index value of the cutter based on the calculated principal component score, and judging whether to repair or replace the cutter according to the health index.
In the fifth step, the actual time domain monitoring signals of the corresponding sensors are applied to the first step and the second step for data processing and time-frequency domain transformation.
Example 1
In the embodiment, a mathematical model is established by taking the sampling data in the operation process and the tool wear condition after operation under different operation conditions on the milling machine as objects. Three types of sensors, specifically an acoustic emission sensor, a vibration sensor and a current sensor, are used to acquire data at different positions. A total of 166 machining records of 8 cutters were included, with each record having a sample length of 9000 samples/time. Each record contains sampling data of 6 sensors, as shown in fig. 2, specifically, an alternating current spindle current sensor (smcAC), a direct current spindle current sensor (smcDC), a table vibration sensor (vib _ table), a spindle vibration sensor (vib _ spindle), a table acoustic emission sensor (AE _ table), and a spindle acoustic emission sensor (AE _ spindle). After each machining, the tool was taken out, and the flank wear Value (VB) of the tool was measured under a microscope, and it was considered that the larger VB, the more severe the tool wear, and the worse the health condition.
The model is trained by using 10 the machining data of the tool as training data, a B-spline base is selected as a function base, fig. 3 is an example of the B-spline base, and fig. 4 (case in the figure represents the tool) and fig. 5 are a result of time-frequency domain transformation and a result of function type transformation of the spindle current sensor (smcAC) data. Finally, in the present embodiment, the functional principal component with the largest spindle current sensor characteristic value is selected as the corresponding principal component of the health indicator, and the corresponding principal component score is calculated to reflect the health status of the tool, as can be seen from fig. 6 (case represents the tool in the figure), it is known that the higher the corresponding principal component score is, the larger the side wear value VB of the tool is, and this fully proves that the health indicator can reflect the wear condition and the health status of the tool.
The monitoring method provided by the invention is used for monitoring the state information such as vibration, spindle current, working conditions and the like on line in the machining process, analyzing and processing the multi-source state sensor information acquired in real time, and indirectly predicting the wear condition and health condition of the cutter.
The applicant states that the present invention is described by the above embodiments to explain the detailed structural features of the present invention, but the present invention is not limited to the above detailed structural features, that is, it is not meant to imply that the present invention must be implemented by relying on the above detailed structural features. It should be understood by those skilled in the art that any modifications, equivalent substitutions of selected elements of the present invention, additions of auxiliary elements, selection of specific forms, etc., are intended to fall within the scope and disclosure of the present invention.
The preferred embodiments of the present invention have been described in detail, however, the present invention is not limited to the specific details of the above embodiments, and various simple modifications may be made to the technical solution of the present invention within the technical idea of the present invention, and these simple modifications are within the protective scope of the present invention.
Claims (10)
1. A cutter health monitoring method based on functional data principal component analysis is characterized by comprising the following steps:
acquiring a time domain monitoring signal of a sensor in the machining process of a numerical control machine tool cutter, inputting sensor data for selection, preprocessing the data, and performing time-frequency domain transformation on the time domain monitoring signal to obtain a frequency domain signal;
(II) converting the frequency domain signal into a functional signal by using a function base according to the frequency in the step (I) and the amplitude of the corresponding frequency;
(III) extracting principal components and calculating the scores of the principal components of the frequency domain signals converted into the functional signals by adopting a functional data principal component analysis method;
(IV) determining a main component serving as a health index based on the result of the main component analysis of the functional signal in the step (III), and constructing the health index;
(V) acquiring actual time domain monitoring signals in the machining process of the numerical control machine tool cutter in real time, sequentially carrying out pretreatment and time-frequency domain transformation, and monitoring the health state of the cutter according to the health indexes in the step (IV).
2. The tool health monitoring method based on functional data principal component analysis according to claim 1, wherein in step (i), the input data selection and data preprocessing specifically comprise the following steps:
s101, selecting and determining variables in a tool health state monitoring model in the machining process of the numerical control machine tool;
s102, inputting sensor data, constructing a data matrix, and realizing variable initialization;
s103, according to the sampling frequency of the sensor data, the sensor data in each processing process is subjected to time-frequency domain transformation by utilizing fast Fourier transformation, and the time-domain monitoring signals are converted into frequency-domain signals.
3. The tool health monitoring method based on principal component analysis of functional data according to claim 1 or 2, wherein in step (i), the sensor comprises any one of or a combination of at least two of a current sensor, a voltage sensor, a vibration sensor, a noise sensor or an acoustic emission sensor.
4. The tool health monitoring method based on functional data principal component analysis according to claim 1, wherein in the step (ii), the converting into the functional signal specifically comprises the steps of:
s201, selecting proper function base types and function numbers;
s202, determining a regular term and a regular term coefficient to perform noise reduction processing to obtain training data, as shown in the following formula:
，
wherein ,
s203, solving the optimization problem, and performing functional data transformation:
wherein ,
is a frequency signal;
is a functional signal; λ is a regular term coefficient;
is a regular term;
in order to process the number of times,
；
is a sensor, and is characterized in that,
；
is a functional group; q is the number of functions;
is the frequency amplitude;
is the coefficient term of the corresponding function base.
5. The tool health monitoring method based on principal component analysis of functional data according to claim 4, wherein in step (II), the function base comprises any one of a trigonometric function base, a spline function base or a polynomial function base.
6. The tool health monitoring method based on functional data principal component analysis according to claim 1, wherein in step (iii), the principal component extraction and principal component score calculation specifically comprises the following steps:
s301, constructing a functional data principal component analysis model;
s302, solving an optimization problem to obtain main components and main component values of functional data;
s303 determines the principal component data that needs to be retained.
7. The tool health monitoring method based on functional data principal component analysis according to claim 6, wherein in step S301, the constructing a functional data principal component analysis model specifically comprises:
is provided with
Is defined in the interval [0,W]Random process on
Respectively calculating independent and equally distributed data
Mean and variance of (c):
wherein ,
is a functional data model;
is composed of
The mean value of (a);
is composed of
The variance of (a);
decomposing the variance function according to the Karhunen-Loeve theorem to obtain an expression:
wherein ,
in the case of the regular term coefficients,
is an ordered non-negative characteristic value;
is a functional principal component;
is a functional group; q is the number of functions;
is the coefficient term of the corresponding function base.
8. The tool health monitoring method based on functional data principal component analysis according to claim 7, wherein in step S302, the expression of the functional data principal component is as follows;
the expression for the principal component score is as follows:
wherein ,
is a functional principal component;
is composed of
The mean value of (a);
a principal component score that is a functional principal component;
is a functional principal component.
9. The tool health monitoring method based on functional data principal component analysis according to claim 1, wherein in step (iv), the constructing of the health index comprises: comparing the correlation relationship between the principal component scores and the cutter wear value, and selecting a plurality of principal component scores with the maximum correlation as health indexes;
in the step (IV), aiming at a plurality of sensor data sets, different principal component scores are analyzed, a plurality of principal components which can best reflect the health condition are determined, the principal component scores are fused, and a health index is constructed.
10. The method for monitoring the health of a tool according to claim 1, wherein the monitoring of the health status of the tool in step (v) comprises the following steps:
s401, reading actual sensor data needing to be input based on the composition of the principal component score of the health index, and performing data preprocessing on the actual sensor data;
s402, performing functional data transformation on actual sensor data subjected to data preprocessing to obtain actual functional data, and calculating specific principal component values according to the actual functional data;
s403, obtaining an actual health index value of the cutter based on the calculated principal component score, and judging whether to repair or replace the cutter according to the health index.
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