CN113344395A - Machining quality monitoring method based on dynamic PCA-SVM - Google Patents

Machining quality monitoring method based on dynamic PCA-SVM Download PDF

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CN113344395A
CN113344395A CN202110657758.2A CN202110657758A CN113344395A CN 113344395 A CN113344395 A CN 113344395A CN 202110657758 A CN202110657758 A CN 202110657758A CN 113344395 A CN113344395 A CN 113344395A
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周竞涛
李恩明
蒋腾远
王明微
张乐毅
马玉亮
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Abstract

The invention discloses a processing quality monitoring method based on dynamic PCA-SVM, aiming at the time sequence correlation existing between non-uniformly sampled processing process data and quality data, extracting the time sequence dynamic relation between the processing process data and the quality data by utilizing a dynamic time window, and further combining a PCA method to carry out preprocessing and characteristic extraction such as denoising, dimension reduction, correlation elimination and the like on related processing process variables, thereby improving the quality monitoring efficiency; aiming at poor quality monitoring accuracy caused by nonlinear and high-dimensional complex association relation between the processing process and the quality, false alarm and missing report occur, the main component characteristics of the processing process and the quality data extracted by dynamic PCA are used as samples, an SVM classifier is trained, SVM model test is carried out by using the test samples, and finally a processing process quality monitoring model with strong generalization is obtained. The method reduces the noise in the original process data, and further improves the accuracy and the calculation efficiency of the quality monitoring model.

Description

Machining quality monitoring method based on dynamic PCA-SVM
Technical Field
The invention belongs to the technical field of machining, and particularly relates to a machining quality monitoring method.
Background
The processing quality of complex mechanical products is generally determined by a plurality of quality characteristic factors with certain correlation, and under the condition of multi-variable manufacturing process environment with influence on the processing quality, the correlation exists between a plurality of complicated quality related data, so that the traditional process quality monitoring or analysis method with mutually independent assumed variables is difficult to work. The literature 'monitoring and optimizing of processing quality of process products, science and technology and engineering, 2017, Vol17(18), p 277-281' discloses a method for monitoring and optimizing of processing quality of process products. The method comprises the steps that before a product processing quality monitoring optimization model is trained, Principal Component Analysis (PCA) algorithm is adopted to preprocess data, so that data dimension is reduced and data characteristic information is extracted; and then, optimizing parameters of a Support Vector Machine (SVM) by using an improved grid algorithm to finally obtain an optimized SVM model, and better solving the problems that the quality characteristics of the processing process are more, the characteristics have coupling property, and the processing quality of the product is difficult to accurately monitor. The method disclosed by the literature highlights the clustering characteristics by performing dimensionality reduction on the quality data, and then establishes the high-performance SVM quality monitoring. However, for a complex dynamic processing process, processing process data and quality data are sampled asynchronously, time sequence correlation exists between different processing process data and quality data, a time sequence dynamic relation between the processing process data and the quality data is difficult to extract by directly adopting variance maximization criterion principal component analysis, and the quality analysis and monitoring of the complex dynamic processing process are poor in accuracy and low in efficiency.
Disclosure of Invention
Aiming at the time sequence correlation between non-uniformly sampled processing process data and quality data, the invention extracts the time sequence dynamic relation between the processing process data and the quality data by utilizing a dynamic time window, and further combines a PCA method to carry out pretreatment and feature extraction such as denoising, dimensionality reduction, correlation elimination and the like on related processing process variables, thereby improving the quality monitoring efficiency; aiming at poor quality monitoring accuracy caused by nonlinear and high-dimensional complex association relation between the processing process and the quality, false alarm and missing report occur, the main component characteristics of the processing process and the quality data extracted by dynamic PCA are used as samples, an SVM classifier is trained, SVM model test is carried out by using the test samples, and finally a processing process quality monitoring model with strong generalization is obtained. The method reduces the noise in the original process data, and further improves the accuracy and the calculation efficiency of the quality monitoring model.
The technical scheme adopted by the invention for solving the technical problem comprises the following steps:
step 1: the process data and the non-uniform quality data are expressed as follows:
Figure BDA0003113989720000021
Figure BDA0003113989720000022
wherein X ∈ Rn×mRepresenting n sample process data matrices containing m process variables, Yun∈Rn ×pRepresenting a non-uniform quality data matrix comprising p process quality variables, nyA number of samples representing a quality variable; t represents the sampling period of the machining process data;
constructing dynamic time windows as in equation (3) for non-uniform process data XunCollecting:
Figure BDA0003113989720000023
Figure BDA0003113989720000024
in the formula (I), the compound is shown in the specification,
Figure BDA0003113989720000025
is the dynamic time window length for each variable i;
step 2: for uneven quality data YunAnd non-uniform machining process data XunAnd respectively carrying out principal component analysis, and calculating the adjacent and corresponding load matrixes of the principal component variances of the two:
Figure BDA0003113989720000026
in the formula, TxAnd TyRespectively, data X of non-uniform working processesunAnd non-uniform quality data YunScore matrix of (1), XreAnd YreRespectively, data X of non-uniform working processesunAnd non-uniform quality data YunThe residual error of (a) is calculated,
Figure BDA0003113989720000027
and
Figure BDA0003113989720000028
respectively, data X of non-uniform working processesunAnd non-uniform quality data YunThe load matrix of (a); data X of non-uniform machining processunAnd non-uniform quality data YunIf the number of the reserved main components is r, the following components are present:
Figure BDA0003113989720000029
Figure BDA00031139897200000210
and step 3: using principal component vectors of the uneven processing process data and uneven processing quality data extracted by the principal components as training sample sets to train an SVM classifier;
firstly, constructing a sample set:
Figure BDA0003113989720000031
to pair
Figure BDA0003113989720000032
Performing normalization to
Figure BDA0003113989720000033
Class p to which the sample in (1) belongsyiE { -1, +1}, and under constraint
Figure BDA0003113989720000034
(0≤aiC is less than or equal to C; 1, 2.. n), the optimal objective function is:
Figure BDA0003113989720000035
the corresponding classification decision function is:
Figure BDA0003113989720000036
in the formula (I), the compound is shown in the specification,
Figure BDA0003113989720000037
is a support vector, b is a classification threshold, aiAnd ajAre Lagrange multipliers;
k (.) is a gaussian radial basis function of the form:
K(px,pxi)＝exp(-||px-pxi||/2σ2),σ>0 (11)
and 4, step 4: after an SVM classification model is established, classifying the machining process data detection samples by adopting a voting method, and finally obtaining a machining process quality monitoring model.
The invention has the following beneficial effects:
the invention adopts a dynamic time window to dynamically correlate processing process data and non-uniform processing quality data, combines Principal Component Analysis (PCA) to reduce dimension, eliminate correlation and extract features of processing process variables, trains obtained principal component feature vectors by adopting an SVM method to obtain an optimal classification function, and realizes monitoring of processing quality by classifying the processing process feature vectors; in the stage of extracting the principal component feature vectors of the processing process variables, the dynamic relation between the process data and the quality data is effectively captured by using the dynamic time window and the PCA, the noise in the original process data is reduced, and the accuracy and the calculation efficiency of the quality monitoring model are improved.
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FIG. 1 is a schematic flow chart of the dynamic PCA-SVM-based processing quality monitoring method of the present invention.
Detailed Description
The invention is further illustrated with reference to the following figures and examples.
In order to solve the problems of poor accuracy and low efficiency of the conventional machining quality monitoring method for the machining process quality of complex products with dynamic and time sequence correlation, the invention provides the machining process quality monitoring method which is suitable for irregularly sampling machining process data and machining quality data in the machining process and has time sequence correlation.
Step 1: the process data and the non-uniform quality data are expressed as follows:
Figure BDA0003113989720000041
Figure BDA0003113989720000042
wherein X ∈ Rn×mRepresenting n sample process data matrices containing m process variables, Yun∈Rn ×pRepresenting a non-uniform quality data matrix comprising p process quality variables, nyA number of samples representing a quality variable; t represents process dataSampling period;
constructing dynamic time windows as in equation (3) for non-uniform process data XunCollecting:
Figure BDA0003113989720000043
Figure BDA0003113989720000044
in the formula (I), the compound is shown in the specification,
Figure BDA0003113989720000045
is the dynamic time window length for each variable i;
step 2: for uneven quality data YunAnd non-uniform machining process data XunAnd respectively carrying out principal component analysis, and calculating the adjacent and corresponding load matrixes of the principal component variances of the two:
Figure BDA0003113989720000046
in the formula, TxAnd TyRespectively, data X of non-uniform working processesunAnd non-uniform quality data YunScore matrix of (1), XreAnd YreRespectively, data X of non-uniform working processesunAnd non-uniform quality data YunThe residual error of (a) is calculated,
Figure BDA0003113989720000047
and
Figure BDA0003113989720000048
respectively, data X of non-uniform working processesunAnd non-uniform quality data YunThe load matrix of (a); data X of non-uniform machining processunAnd non-uniform quality data YunIf the number of the reserved main components is r, the following components are present:
Figure BDA0003113989720000049
Figure BDA0003113989720000051
the changes of the process data matrix X and the quality data matrix Y are mainly reflected in the direction of the foremost load vectors, the projections on the rearmost load vectors are very small, mainly caused by measurement noise, the number of the preserved principal elements in principal element analysis is calculated by adopting a variance cumulative contribution rate method, and the number of the preserved principal elements with the contribution rate of more than 85 percent is reserved:
Figure BDA0003113989720000052
after the number k of the principal elements is determined, selecting the eigenvectors corresponding to the first k eigenvalues as the most extracted features, wherein the process data matrix X and the quality data matrix Y after the principal element analysis are as follows:
Figure BDA0003113989720000053
Figure BDA0003113989720000054
in the formula, E is an error matrix and is mainly caused by measurement errors, and neglecting E plays a role in eliminating measurement noise without causing obvious loss of useful information; the characteristic vector P of the processing process data matrix and the quality data matrix corresponding to the first k preserved principal elementsx＝[px1,px2,...,pxk]And Py＝[py1,py2,...,pyk]；
And step 3: using principal component vectors of the uneven processing process data and uneven processing quality data extracted by the principal components as training sample sets to train an SVM classifier;
firstly, constructing a sample set:
Figure BDA0003113989720000055
to pair
Figure BDA0003113989720000056
Performing normalization to
Figure BDA0003113989720000057
Class p to which the sample in (1) belongsyiE { -1, +1}, and under constraint
Figure BDA0003113989720000058
(0≤aiC is less than or equal to C; 1, 2.. n), the optimal objective function is:
Figure BDA0003113989720000059
regarding m-class classification problems, regarding one class as a positive class and regarding the rest m-1 as a negative class, solving a decision function by using corresponding two classes of support vector machines, wherein the corresponding classification decision function is as follows:
the corresponding classification decision function is:
Figure BDA00031139897200000510
in the formula (I), the compound is shown in the specification,
Figure BDA00031139897200000511
is a support vector, b is a classification threshold, aiAnd ajAre Lagrange multipliers;
k (.) is a gaussian radial basis function of the form:
K(px,pxi)＝exp(-||px-pxi||/2σ2),σ>0 (11)
and 4, step 4: after m (m-1)/2 SVM are established, a voting method is adopted to treat a detection sampleThis pxClassifying when the SVM of the i-th class and the j-th classijJudgment of pxIf the ticket belongs to the ith category, the number of the ith category is added with 1, otherwise, the number of the jth category is added with 1; when all SVMijAfter the judgment is finished, inputting pxThe class with the most votes is obtained, namely the class with the largest number of votes in the classification decision function of the formula (10); and finally, obtaining a machining process quality monitoring model.

Claims (1)

1. A machining quality monitoring method based on a dynamic PCA-SVM is characterized by comprising the following steps:
step 1: the process data and the non-uniform quality data are expressed as follows:
Figure FDA0003113989710000011
Figure FDA0003113989710000012
wherein X ∈ Rn×mRepresenting n sample process data matrices containing m process variables, Yun∈Rn×pRepresenting a non-uniform quality data matrix comprising p process quality variables, nyA number of samples representing a quality variable; t represents the sampling period of the machining process data;
constructing dynamic time windows as in equation (3) for non-uniform process data XunCollecting:
Xun＝[X1 un X2 un ... Xm un] (3)
Figure FDA0003113989710000013
in the formula (I), the compound is shown in the specification,
Figure FDA0003113989710000014
Figure FDA0003113989710000015
is the dynamic time window length for each variable i;
step 2: for uneven quality data YunAnd non-uniform machining process data XunAnd respectively carrying out principal component analysis, and calculating the adjacent and corresponding load matrixes of the principal component variances of the two:
Figure FDA0003113989710000016
in the formula, TxAnd TyRespectively, data X of non-uniform working processesunAnd non-uniform quality data YunScore matrix of (1), XreAnd YreRespectively, data X of non-uniform working processesunAnd non-uniform quality data YunThe residual error of (a) is calculated,
Figure FDA0003113989710000017
and
Figure FDA0003113989710000018
respectively, data X of non-uniform working processesunAnd non-uniform quality data YunThe load matrix of (a); data X of non-uniform machining processunAnd non-uniform quality data YunIf the number of the reserved main components is r, the following components are present:
Figure FDA0003113989710000019
Figure FDA0003113989710000021
and step 3: using principal component vectors of the uneven processing process data and uneven processing quality data extracted by the principal components as training sample sets to train an SVM classifier;
firstly, constructing a sample set:
Figure FDA0003113989710000022
to pair
Figure FDA0003113989710000023
Performing normalization to
Figure FDA0003113989710000024
Class p to which the sample in (1) belongsyiE { -1, +1}, and under constraint
Figure FDA0003113989710000025
(0≤aiC is less than or equal to C; 1, 2.. n), the optimal objective function is:
Figure FDA0003113989710000026
the corresponding classification decision function is:
Figure FDA0003113989710000027
in the formula (I), the compound is shown in the specification,
Figure FDA0003113989710000028
is a support vector, b is a classification threshold, aiAnd ajAre Lagrange multipliers;
k (.) is a gaussian radial basis function of the form:
K(px,pxi)＝exp(-||px-pxi||/2σ2),σ>0 (11)
and 4, step 4: after an SVM classification model is established, classifying the machining process data detection samples by adopting a voting method, and finally obtaining a machining process quality monitoring model.
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