CN105739489B - A kind of batch process fault detection method based on ICA KNN - Google Patents
A kind of batch process fault detection method based on ICA KNN Download PDFInfo
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- 238000001514 detection method Methods 0.000 title claims abstract description 31
- 238000010923 batch production Methods 0.000 title abstract description 8
- 238000000034 method Methods 0.000 claims abstract description 60
- 239000011159 matrix material Substances 0.000 claims description 60
- 238000012545 processing Methods 0.000 claims description 13
- 238000000926 separation method Methods 0.000 claims description 13
- 230000002087 whitening effect Effects 0.000 claims description 12
- 238000004422 calculation algorithm Methods 0.000 claims description 7
- 238000010606 normalization Methods 0.000 claims description 6
- 238000009826 distribution Methods 0.000 claims description 5
- 238000012887 quadratic function Methods 0.000 claims description 5
- 238000010276 construction Methods 0.000 claims description 3
- 238000007781 pre-processing Methods 0.000 claims description 3
- 238000005070 sampling Methods 0.000 claims description 3
- 238000012549 training Methods 0.000 abstract description 5
- 238000012880 independent component analysis Methods 0.000 description 15
- 238000000513 principal component analysis Methods 0.000 description 8
- 239000004065 semiconductor Substances 0.000 description 7
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- 230000000694 effects Effects 0.000 description 3
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- XAGFODPZIPBFFR-UHFFFAOYSA-N aluminium Chemical compound [Al] XAGFODPZIPBFFR-UHFFFAOYSA-N 0.000 description 2
- 229910052782 aluminium Inorganic materials 0.000 description 2
- 238000005530 etching Methods 0.000 description 2
- 238000004088 simulation Methods 0.000 description 2
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- G05B23/00—Testing or monitoring of control systems or parts thereof
- G05B23/02—Electric testing or monitoring
- G05B23/0205—Electric testing or monitoring by means of a monitoring system capable of detecting and responding to faults
- G05B23/0218—Electric testing or monitoring by means of a monitoring system capable of detecting and responding to faults characterised by the fault detection method dealing with either existing or incipient faults
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- G05B23/00—Testing or monitoring of control systems or parts thereof
- G05B23/02—Electric testing or monitoring
- G05B23/0205—Electric testing or monitoring by means of a monitoring system capable of detecting and responding to faults
- G05B23/0218—Electric testing or monitoring by means of a monitoring system capable of detecting and responding to faults characterised by the fault detection method dealing with either existing or incipient faults
- G05B23/0224—Process history based detection method, e.g. whereby history implies the availability of large amounts of data
- G05B23/024—Quantitative history assessment, e.g. mathematical relationships between available data; Functions therefor; Principal component analysis [PCA]; Partial least square [PLS]; Statistical classifiers, e.g. Bayesian networks, linear regression or correlation analysis; Neural networks
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Abstract
The invention discloses a kind of batch process fault detection method based on ICA KNN, training dataset is handled by application ICA, less independent pivot is chosen again substitutes original high dimensional data, the main feature of initial data is extracted at the same time, afterwards, corresponding Statisti-cal control is asked for using KNN methods in independent principal component space to limit the use of in fault detect.So make the nonlinear batch production process of non-gaussian that there is higher fault detect rate, while computation complexity is also reduced compared to KICA.
Description
Technical Field
The invention belongs to the technical field of intermittent processes, and particularly relates to an ICA-KNN-based intermittent process fault detection method.
Background
A batch process is also referred to as a batch process. Due to the flexible operation, the method is widely applied to the production of small-batch and high-value-added products. Nowadays, the intermittent process becomes a main production mode in industries such as fine chemical industry, biological pharmacy, agricultural product deep processing and the like. The characteristics of unequal batch lengths, process center drift, variable nonlinearity, multiple working conditions and the like exist in the semiconductor batch production process, and the fault detection method becomes a key subject for reducing the rejection rate in the semiconductor wafer generation process.
Multivariate statistical analysis, such as Principal Component Analysis (PCA) and Partial Least Squares (PLS) and independent principal component analysis (ICA), is widely used in the chemical industry. PCA is an important tool for monitoring a multivariate statistical process and is also an effective tool for data compression and information extraction. Because the PCA algorithm assumes that the process is linear, the online monitoring result is very unreliable for the production process with strong nonlinearity, and the phenomenon of overhigh false alarm rate exists. Statistic T used in particular when PCA performs fault detection2And the assumption that the SPE needs to perform multivariate Gaussian distribution when determining the control time limit requires that the variables in the training set conform to the multivariate Gaussian distribution, which is not true for most semiconductor batch processes. Unlike Principal Component Analysis (PCA) methods, Independent Component Analysis (ICA) does not require observed variable data to be gaussian distributed, while separating or estimating statistically independent source signals based on higher-order statistical information is more statistically significant, and these implicit signals are usually of actual physical significance, or are essentially characteristic reflections of the object under study, so ICA has more of a problem in analyzing non-gaussian distributed process dataGood feature extraction capability. However, the ICA method itself is a linear method, and thus the monitoring effect on the non-linear data existing in the intermittent process is not satisfactory. Based on this, researchers have proposed a Kernel Independent Component Analysis (KICA) method based on a kernel function method for intermittent process fault detection and have achieved a good effect. The basic idea is to first project the input data through a non-linear mapping to a high-dimensional feature space and then apply linear ICA processing to the high-dimensional feature space. However, the kira method requires calculation of a kernel matrix, the dimension of which is the square of the number of samples, and when the number of samples is large, the complexity of calculation is increased. Q.P.He and J.Wang propose a fault detection method (FD-KNN) based on K neighbor rule, which is not dependent on the linearity of processed data, can overcome the characteristics of semiconductor data nonlinearity and multiple working conditions in the fault detection process, and has better effect in practical application. However, the FD-KNN method has corresponding drawbacks, such as rapid increase of variable scale after development of batch process data, which results in that FD-KNN consumes a lot of time for calculation of data information and occupies a large storage space for recording data, and the application of FD-KNN is difficult due to the huge data scale.
Disclosure of Invention
The invention aims to overcome the defects of the prior art and provide an ICA-KNN-based intermittent process fault detection method, aiming at effectively improving the accuracy of fault detection on the basis of reducing the calculation complexity in the semiconductor production process with the characteristics of nonlinearity, multiple working conditions and the like.
In order to achieve the above object, the present invention provides an ICA-KNN based intermittent process fault detection method, which is characterized by comprising the following steps:
(1) data preprocessing
Expanding a three-dimensional sample matrix X (I multiplied by J multiplied by K) acquired in an intermittent process based on the number of batches to obtain a two-dimensional matrix X (I multiplied by KJ), standardizing the two-dimensional matrix X (I multiplied by KJ) in the batch direction to enable the mean value of each row of the two-dimensional matrix X (I multiplied by KJ) to be 0 and the variance to be 1, and finally longitudinally rearranging the standardized two-dimensional matrix X (I multiplied by KJ) into a matrix X (KI multiplied by J); wherein I represents the number of batches, J represents the number of observation variables, and K represents the sampling times;
(2) ICA dimension reduction processing is carried out on the matrix X (KI multiplied by J) to obtain d independent components S reflecting intermittent process informationdAnd a main part separation matrix Wd
(2.1) whitening the matrix X (KI multiplied by J) to obtain a whitening vector Z;
Z＝QX
wherein Q is a whitening matrix, Q ═ Λ-1/2UT，Λ＝diag(λ1,…,λn)，λi(i ═ 1, …, n) is the covariance matrix E { XXTThe first n eigenvalues of the matrix are obtained, and U is a matrix formed by eigenvectors corresponding to the n eigenvalues;
(2.2) decomposing the whitening vector Z to obtain d independent components S reflecting the information of the intermittent processdAnd a main part separation matrix Wd；
(2.2.1) constructing an initial random vector value bkAnd let k equal to 1, k ∈ [1, n ]]；
bk＝E{Zg(bk TZ)}-E{g'(bk TZ)}bk
Wherein, the function G () is the first derivative of the selected non-quadratic function G, G' () represents the derivative of the function G (), E { } represents the expectation;
(2.2.2) to bkCarrying out iteration;
(2.2.3) for b after iterationkPerforming a normalization process, i.e. bk＝bk/||bkI, wherein i bkI represents solving bkNorm of (d);
(2.2.4) normalization of bkMaking a judgment if | bk Tbk1 +/-5%, then outputting vector value bkAnd entering step (2.2.5); otherwise, k is k +1 and returns to step (2.2.2) to continue the iteration until | b is satisfiedk TbkIf | ═ 1 ± 5%, then go to step (2.2.5);
(2.2.5) construction matrix B ═ B1,…,bn]TUsing the formula S ═ BTZ is the independent component, and the formula W is BTQ, solving a separation matrix; then arranging the independent components S according to the non-Gaussian degree, and selecting the first d as the independent components SdThe first d corresponding to it as main part separation matrix Wd；
(3) In the independent component SdIn the method, a KNN algorithm is used to obtain a statistical control limit CL
In the independent component Sd＝[s1,…,sd]Calculating the square sum distance between rows, determining m neighbors of each row according to the distance, and calculating the KNN square distance Ds；
Wherein,denotes SdThe square of the euclidean distance between the ith row and the row closest to it;
due to DsApproximate compliance chi2Distribution, from which a control limit can be determinedα confidence level, N is independent component SdA number of rows;
(4) carrying out standardization processing on the data x' to be detected according to the step (1) to obtain data x, and then separating the matrix W according to the main partdCalculating the independent components of the data x
(5) The independent componentsCalculating the KNN squared distance D according to the step (3)x(ii) a Will DxCompared with the control limit CL, if DxIf the sample is more than CL, the sample is considered to be a fault sample, otherwise, the sample is considered to be a normal sample.
The invention aims to realize the following steps:
according to the ICA-KNN-based intermittent process fault detection method, an ICA is applied to process a training data set, then fewer independent principal elements are selected to replace original high-dimensional data, main characteristics of the original data are extracted at the same time, and then a KNN method is applied to an independent principal element space to obtain corresponding statistical control limits for fault detection. This allows a non-gaussian non-linear intermittent production process with a higher failure detection rate while reducing computational complexity compared to KICA.
Drawings
FIG. 1 is a flow chart of an ICA-KNN based intermittent process fault detection method;
FIG. 2 is an I2 detection map of the KICA method;
FIG. 3 is a SPE detection diagram of the KICA method;
FIG. 4 is a detection diagram of the KNN method;
FIG. 5 is a detection diagram of the ICA-KNN method.
Detailed Description
The following description of the embodiments of the present invention is provided in order to better understand the present invention for those skilled in the art with reference to the accompanying drawings. It is to be expressly noted that in the following description, a detailed description of known functions and designs will be omitted when it may obscure the subject matter of the present invention.
Examples
For convenience of description, the related terms appearing in the detailed description are explained:
ICA (independent Component analysis);
KNN (K-Nearest Neighbor) K Nearest Neighbor;
FD-KNN (Fault Detection based on K-Nearest Neighbor) Fault Detection method based on K Neighbor;
(iii) a KICA (Kernel Independent Component analysis) nuclear Independent Component analysis;
FIG. 1 is a flow chart of an ICA-KNN based intermittent process fault detection method.
In this embodiment, as shown in fig. 1, the present invention relates to an ICA-KNN based intermittent process fault detection method, which includes the following steps:
s1, preprocessing data
The three-dimensional sample matrix X (I multiplied by J multiplied by K) acquired in the intermittent process is firstly expanded based on the number of batches to obtain a two-dimensional matrix X (I multiplied by KJ), so that the influence of dimension is eliminated; then, the two-dimensional matrix X (I multiplied by KJ) is standardized in the batch direction, so that the mean value of each row of the two-dimensional matrix X (I multiplied by KJ) is 0, and the variance is 1, and the average running track of all batches is removed; finally, the two-dimensional matrix X (I multiplied by KJ) after the standardization processing is longitudinally rearranged into a matrix X (KI multiplied by J); wherein, I represents the number of batches, J represents the number of observation variables, and K represents the sampling times.
In this example, the semiconductor aluminum etching reaction performed on Lam 9600 contained 107 batches of normal data and 20 batches of failure data. And taking 82 batches of normal data as training samples and 25 batches of normal data as test samples, and finally detecting 20 batches of fault data to see whether 20 batches of fault data can be detected in time.
And finally, expanding a three-dimensional sample matrix with the batch data of all the training samples being (82 × 18 × 90) based on the number of batches to obtain a two-dimensional sample matrix (82 × 1620), then performing normalization processing on the two-dimensional sample matrix by subtracting the mean value and dividing the standard deviation, and finally longitudinally rearranging the normalized sample matrix (82 × 1620) into a two-dimensional matrix (7380 × 18) for subsequent ICA dimension reduction processing.
S2, carrying out ICA dimension reduction processing on the matrix X (KI multiplied by J) to obtain d independent components S reflecting intermittent process informationdAnd a main part separation matrix Wd
S2.1, in order to remove the correlation among sample data and simplify the independent component extraction process, the method needs to be applied to
Carrying out whitening processing on the matrix X (KI multiplied by J) to obtain a whitening vector Z;
Z＝QX
wherein Q is a whitening matrix, Q ═ Λ-1/2UT，Λ＝diag(λ1,…,λn)，λi(i ═ 1, …, n) is the covariance matrix E { XXTThe first n eigenvalues of the matrix are obtained, and U is a matrix formed by eigenvectors corresponding to the n eigenvalues;
s2.2, decomposing the whitening vector Z to obtain d independent components S reflecting intermittent process informationdAnd a main part separation matrix Wd；
S2.2.1, constructing an initial random vector value bk,k∈[1,n]；
bk＝E{Zg(bk TZ)}-E{g'(bk TZ)}bk
Wherein, the function G () is the first derivative of the selected non-quadratic function G, G' () represents the derivative of the function G (), E { } represents the expectation;
in this embodiment, the non-quadratic function G can be selected from various forms, such as:
wherein, 1 is more than or equal to a1≤2，a21 is ═ 1; cosh () represents a hyperbolic cosine value used by a function to return a parameter
S2.2.2, starting from k equal to 1 and starting from bkCarrying out iteration;
s2.2.3, for b after iterationkPerforming a normalization process, i.e. bk＝bk/||bkI, wherein i bkI represents solving bkNorm of (d);
s2.2.4, normalizing bkMaking a judgment if | bk Tbk1 +/-5%, then outputting vector value bkAnd proceeds to step S2.2.5; otherwise, k is k +1 and returns to step S2.2.2 to continue the iteration until | b is satisfiedk TbkWhen | ═ 1. + -. 5%Then go to step S2.2.5;
s2.2.5, construction matrix B ═ B1,…,bn]TUsing the formula S ═ BTZ is the independent component, and the formula W is BTQ, solving a separation matrix; then arranging the independent components S according to the non-Gaussian degree, and selecting the first d as the independent components SdThe first d corresponding to it as main part separation matrix Wd；
S3, in the independent component SdIn the method, a KNN algorithm is used to obtain a statistical control limit CL
In the independent component Sd＝[s1,…,sd]Calculating the square sum distance between rows, determining m neighbors of each row according to the distance, and calculating the KNN square distance Ds；
Wherein,denotes SdThe square of the euclidean distance between the ith row and the row closest to it;
in the present embodiment, it is preferred that,the sum of squares distance between row 1 and row 2 is then:
(1-1)2+(1-2)2+(1-1)21, the squares and distances between the 1 st and other rows are, similarly: 1,1,1,3, 12; in this embodiment, m is equal to 3, and the KNN squared distance D of each row is obtaineds；
Due to DsApproximate compliance chi2Distribution, from which a control limit can be determinedα confidence level, N is independent component SdA number of rows;
s4, carrying out standardization processing on the data x' to be detected according to the step S1 to obtain data x, and then carrying out standardization processing according to the main part separation matrix WdCalculating the independent components of the data x
S5, mixing the independent componentsCalculating the KNN squared distance D according to the step S3x(ii) a Will DxCompared with the control limit CL, if DxIf the sample is more than CL, the sample is considered to be a fault sample, otherwise, the sample is considered to be a normal sample.
In order to verify the effectiveness of the method, data of the aluminum stack etching process in semiconductor production are adopted for simulation, and comparison with a KICA method and an FD-KNN method is carried out. FIG. 2 shows the formula I of KICA2Counting a line detection graph; FIG. 3 is a SPE detection map of KICA; FIG. 4 is a KNN detection map; FIG. 5 is an ICA-KNN detection chart. By contrast, it can be seen that the ICA-KNN method has a higher failure detection rate, and the several methods have little difference in terms of false alarm rate. Compared with the FD-KNN algorithm and the KICA algorithm, the ICA-KNN algorithm can effectively reduce the complexity, and the superiority of the method is shown. Simulation experiments show that the ICA-KNN method is simple and effective and has good application prospect.
Although illustrative embodiments of the present invention have been described above to facilitate the understanding of the present invention by those skilled in the art, it should be understood that the present invention is not limited to the scope of the embodiments, and various changes may be made apparent to those skilled in the art as long as they are within the spirit and scope of the present invention as defined and defined by the appended claims, and all matters of the invention which utilize the inventive concepts are protected.
Claims (2)
1. An ICA-KNN-based intermittent process fault detection method is characterized by comprising the following steps:
(1) data preprocessing
Expanding a three-dimensional sample matrix X (I multiplied by J multiplied by K) acquired in an intermittent process based on the number of batches to obtain a two-dimensional matrix X (I multiplied by KJ), standardizing the two-dimensional matrix X (I multiplied by KJ) in the batch direction to enable the mean value of each row of the two-dimensional matrix X (I multiplied by KJ) to be 0 and the variance to be 1, and finally longitudinally rearranging the standardized two-dimensional matrix X (I multiplied by KJ) into a matrix X (KI multiplied by J); wherein I represents the number of batches, J represents the number of observation variables, and K represents the sampling times;
(2) ICA dimension reduction processing is carried out on the matrix X (KI multiplied by J) to obtain d independent components S reflecting intermittent process informationdAnd a main part separation matrix Wd
(2.1) whitening the matrix X (KI multiplied by J) to obtain a whitening vector Z;
Z＝QX
wherein Q is a whitening matrix, Q ═ Λ-1/2UT，Λ＝diag(λ1,…,λn)，λi(i ═ 1, …, n) is the covariance matrix E { XXTThe first n eigenvalues of the matrix are obtained, and U is a matrix formed by eigenvectors corresponding to the n eigenvalues;
(2.2) decomposing the whitening vector Z to obtain d independent components S reflecting the information of the intermittent processdAnd a main part separation matrix Wd；
(2.2.1) constructing an initial random vector value bk，k∈[1,n]；
bk＝E{Zg(bkTZ)}-E{g'(bk TZ)}bk
Wherein, the function G () is the first derivative of the selected non-quadratic function G, G' () represents the derivative of the function G (), E { } represents the expectation;
(2.2.2) let k equal 1, pair bkCarrying out iteration;
<mrow> <msub> <mi>b</mi> <mi>k</mi> </msub> <mo>=</mo> <msub> <mi>b</mi> <mi>k</mi> </msub> <mo>-</mo> <munderover> <mo>&Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </munderover> <mrow> <mo>(</mo> <msup> <msub> <mi>b</mi> <mi>k</mi> </msub> <mi>T</mi> </msup> <msub> <mi>b</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> <msub> <mi>b</mi> <mi>i</mi> </msub> </mrow>
(2.2.3) for b after iterationkPerforming a normalization process, i.e. bk＝bk/||bkI, wherein i bkI represents solving bkNorm of (d);
(2.2.4) normalization of bkMaking a judgment if | bk Tbk1 +/-5%, then outputting vector value bkAnd entering step (2.2.5); otherwise, k is k +1 and returns to step (2.2.2) to continue the iteration until | b is satisfiedk TbkIf | ═ 1 ± 5%, then go to step (2.2.5);
(2.2.5) construction matrix B ═ B1,…,bn]TUsing the formula S ═ BTZ is the independent component, and the formula W is BTQ, solving a separation matrix; then arranging the independent components S according to the non-Gaussian degree, and selecting the first d as the independent components SdThe first d corresponding to it as main part separation matrix Wd；
(3) In the independent component SdIn the method, a KNN algorithm is used to obtain a statistical control limit CL
In the independent component Sd＝[s1,…,sd]Calculating square distance between rows, determining m neighbor of each row according to distance, and calculating KNN square distance Ds；
<mrow> <msub> <mi>D</mi> <mi>s</mi> </msub> <mo>=</mo> <munderover> <mo>&Sigma;</mo> <mrow> <mi>j</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>m</mi> </munderover> <msubsup> <mi>d</mi> <mrow> <mi>i</mi> <mi>j</mi> </mrow> <mn>2</mn> </msubsup> </mrow>
Wherein,denotes SdThe square of the euclidean distance between the ith row and the row closest to it;
due to DsApproximate compliance chi2Distribution, from which a control limit can be determinedα confidence level, N is independent component SdA number of rows;
(4) carrying out standardization processing on the data x' to be detected according to the step (1) to obtain data x, and then separating the matrix W according to the main partdCalculating the independent components of the data x
(5) The independent componentsCalculating the KNN squared distance D according to the step (3)x(ii) a Will DxCompared with the control limit CL, if DxIf the sample is more than CL, the sample is considered to be a fault sample, otherwise, the sample is considered to be a normal sample.
2. The ICA-KNN based intermittent process fault detection method of claim 1, wherein the non-quadratic function G can be selected from two forms:
G(x)＝logcosh(a1x)/a1or g (x) -exp (-a)2x2/2)/a2
Wherein, a1、a2Being constant, cosh () represents a hyperbolic cosine value that a function uses to return arguments.
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| CN107704863B (en) * | 2017-05-22 | 2021-06-15 | 上海海事大学 | PCA principal component rearrangement fault feature representation method |
| CN107065843B (en) * | 2017-06-09 | 2019-04-05 | 东北大学 | Multi-direction KICA batch process fault monitoring method based on Independent subspace |
| CN107357275B (en) * | 2017-07-27 | 2019-08-27 | 中南大学 | Non-gaussian industrial process fault detection method and system |
| CN107831662B (en) * | 2017-11-13 | 2022-01-04 | 辽宁石油化工大学 | Design method of random 2D controller for intermittent process with actuator fault |
| CN108255656B (en) * | 2018-02-28 | 2020-12-22 | 湖州师范学院 | Fault detection method applied to intermittent process |
| CN108759745B (en) * | 2018-06-05 | 2020-02-18 | 上汽大众汽车有限公司 | Body-in-white fault detection method and device based on multivariate statistical analysis |
| CN109116834B (en) * | 2018-09-04 | 2021-02-19 | 湖州师范学院 | Intermittent process fault detection method based on deep learning |
| CN109669412B (en) * | 2018-12-13 | 2021-03-26 | 宁波大学 | non-Gaussian process monitoring method based on novel dynamic independent component analysis |
| CN111898313B (en) * | 2020-06-30 | 2022-05-20 | 电子科技大学 | Fault detection method based on ICA and SVM integrated learning |
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| CN105425779A (en) * | 2015-12-24 | 2016-03-23 | 江南大学 | ICA-PCA multi-working condition fault diagnosis method based on local neighborhood standardization and Bayesian inference |
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| US6952657B2 (en) * | 2003-09-10 | 2005-10-04 | Peak Sensor Systems Llc | Industrial process fault detection using principal component analysis |
| CN101403923A (en) * | 2008-10-31 | 2009-04-08 | 浙江大学 | Course monitoring method based on non-gauss component extraction and support vector description |
| CN103488091A (en) * | 2013-09-27 | 2014-01-01 | 上海交通大学 | Data-driving control process monitoring method based on dynamic component analysis |
| CN104062968A (en) * | 2014-06-10 | 2014-09-24 | 华东理工大学 | Continuous chemical process fault detection method |
| CN105425779A (en) * | 2015-12-24 | 2016-03-23 | 江南大学 | ICA-PCA multi-working condition fault diagnosis method based on local neighborhood standardization and Bayesian inference |
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