CN105739489B - A kind of batch process fault detection method based on ICA KNN - Google Patents

Abstract

The present invention discloses an intermittent process fault detection method based on ICA-KNN. By applying ICA to process the training data set, select fewer independent pivots to replace the original high-dimensional data, and extract the main features of the original data at the same time. After that, In the independent pivot space, the KNN method is applied to obtain the corresponding statistical control limits for fault detection. In this way, the non-Gaussian nonlinear batch production process has a high fault detection rate, and at the same time reduces the computational complexity compared with KICA.

Description

A Fault Detection Method for Batch Process Based on ICA-KNN

technical field

The invention belongs to the field of batch process technology, and more specifically relates to an ICA-KNN-based batch process fault detection method.

Background technique

Batch process, also known as batch process. Because of its flexible operation, it is widely used in the production of small batches and high value-added products. Nowadays, the batch process has become the main production method in industries such as fine chemical industry, biopharmaceutical and deep processing of agricultural products. The semiconductor batch production process has the characteristics of batch unequal length, process center drift, variable nonlinearity and multiple working conditions. In order to reduce the scrap rate in the semiconductor wafer production process, fault detection methods have become a key topic.

Multivariate statistical analysis, such as principal component analysis (PCA) and partial least squares (PLS) and independent principal component analysis (ICA), has been widely used in the chemical industry. PCA is an important tool for multivariate statistical process monitoring, as well as an effective tool for data compression and information extraction. Since the PCA algorithm assumes that the process is linear, for a production process with strong nonlinearity, the results of online monitoring are very unreliable, and there is a phenomenon that the false alarm rate is too high. In particular, the statistic T ² used by PCA for fault detection and the assumption of multivariate Gaussian distribution are required to determine the control limit by SPE. This assumption requires that the variables in the training set conform to the multivariate Gaussian distribution. For most semiconductor batch processes, this assumption is not true. of. Different from the principal component analysis (PCA) method, the independent component analysis (ICA) does not require the observed variable data to obey the Gaussian distribution, and at the same time separate or estimate statistically independent source signals based on high-order statistical information, which has stronger statistical significance, and these The implied signal usually has actual physical meaning, or reflects the essential characteristics of the research object, so ICA has better feature extraction ability in analyzing non-Gaussian distribution process data. However, the ICA method itself is also a linear method, so the monitoring effect for the nonlinear data existing in the batch process is not satisfactory. Based on this, some scholars proposed the Kernel Independent Component Analysis (KICA) method based on the kernel function method for fault detection in batch processes, and achieved good results. The basic idea is to first project the input data to a high-dimensional feature space through a nonlinear mapping, and then apply linear ICA processing in the high-dimensional feature space. However, the KICA method needs to calculate the kernel matrix. The dimension of the kernel matrix is the square of the number of samples. When the number of samples is large, the complexity of the calculation will be increased. QPHe and J.Wang proposed a fault detection method based on the K nearest neighbor rule (FD-KNN). This method does not care whether the processed data is linear or not, and can overcome the non-linearity and multiple working conditions of semiconductor data in the fault detection process. characteristics, and achieve good results in practical applications. However, the FD-KNN method has corresponding defects. For example, when the batch process data is expanded, the variable scale will increase rapidly, causing FD-KNN to consume a lot of time for the calculation of data information, and occupy a large amount of storage space to record data. Huge The data scale makes it difficult to apply FD-KNN.

Contents of the invention

The purpose of the present invention is to overcome the deficiencies of the prior art, to provide an ICA-KNN-based intermittent process fault detection method, aiming at the semiconductor production process with the characteristics of nonlinearity and multiple working conditions, on the basis of reducing computational complexity , effectively improving the accuracy of fault detection.

In order to realize the foregoing invention object, a kind of intermittent process fault detection method based on ICA-KNN of the present invention is characterized in that, comprises the following steps:

(1), data preprocessing

The three-dimensional sample matrix X(I×J×K) collected in the batch process is first expanded based on the number of batches to obtain the two-dimensional matrix X(I×KJ), and then the two-dimensional matrix X(I×KJ) in the batch Do normalization in the direction, so that the mean value of each column of the two-dimensional matrix X (I×KJ) is 0, and the variance is 1. Finally, the normalized two-dimensional matrix X (I×KJ) is vertically rearranged into a matrix X (KI×J); Among them, I represents the number of batches, J represents the number of observed variables, and K represents the number of samples;

(2) Perform ICA dimensionality reduction on the matrix X(KI×J) to obtain d independent components S _d reflecting batch process information and main part separation matrix W _d

(2.1), first carry out whitening process to matrix X (KI×J), obtain whitening vector Z;

Z=QX

Among them, Q is the whitening matrix, Q=Λ ^-1/2 U ^T , Λ=diag(λ ₁ ,…,λ _n ), λ _i (i=1,…,n) is the covariance matrix E{XX ^T } The first n eigenvalues of , U is a matrix composed of eigenvectors corresponding to n eigenvalues;

(2.2), decompose the whitening vector Z, obtain d independent components S _d and the main part separation matrix W _d reflecting the intermittent process information;

(2.2.1), construct the initial random vector value b _k , and set k=1, k∈[1,n];

b _k ＝E{Zg(b _k ^T Z)}-E{g'(b _k ^T Z)}b _k

Among them, the function g() is the first-order derivative of the selected non-quadratic function G, g'() represents the derivative of the function g(), and E{} represents expectation;

(2.2.2), iterating b _k ;

(2.2.3), carry out normalization process to b _k after the iteration, i.e. b _k =b _k /||b _k ||, wherein, ||b _k || represents seeking the norm of b _k ;

(2.2.4), judge b _k after the normalization process, if |b _k ^T b _k |=1 ± 5%, then output vector value b _k , and enter step (2.2.5); Otherwise, k=k+1, and return to step (2.2.2) to continue iteration until satisfying | b _k ^T b _k |=1 ± 5%, then enter step (2.2.5);

(2.2.5), construct matrix B=[b ₁ ,...,b _n ] ^T , use the formula S=B ^T Z to obtain the independent components, use the formula W=B ^T Q to obtain the separation matrix; then the independent components S Arranged according to the degree of non-Gaussian, select the first d as independent components S _d , and the corresponding first d as the main part separation matrix W _d ;

(3), use the KNN algorithm in the independent component S _d to obtain the statistical control limit CL

In the independent component S _d =[s ₁ ,…,s _d ], calculate the square sum distance between rows, determine the m neighbors of each row through the distance, and calculate its KNN square distance D _s ;

in, Indicates the square of the Euclidean distance between the i-th row and the j-th closest row in S _d ;

Since D _s approximately obeys the χ ² distribution, the control limits can be determined according to the significance level α is the confidence level, N is the number of rows of independent components S _d ;

(4), standardize the data x' to be detected according to step (1) to obtain the data x, and then calculate the independent components of the data x according to the main part separation matrix W _d

(5), the independent components Calculate the KNN square distance D _x according to step (3); compare D _x with the control limit CL, if D _x > CL, the sample is considered to be a fault sample, otherwise, the sample is considered to be a normal sample.

The purpose of the invention of the present invention is achieved like this:

The present invention is based on the ICA-KNN intermittent process fault detection method, by applying ICA to process the training data set, then selecting less independent pivots to replace the original high-dimensional data, and extracting the main features of the original data at the same time, after that, in the independent pivots The KNN method is applied in the space to obtain the corresponding statistical control limits for fault detection. In this way, the non-Gaussian nonlinear batch production process has a high fault detection rate, and at the same time reduces the computational complexity compared with KICA.

Description of drawings

Figure 1 is a flow chart of the intermittent process fault detection method based on ICA-KNN;

Fig. 2 is the I2 detection figure of KICA method;

Fig. 3 is the SPE detection figure of KICA method;

Figure 4 is a detection map of the KNN method;

Figure 5 is the detection map of the ICA-KNN method.

Detailed ways

Specific embodiments of the present invention will be described below in conjunction with the accompanying drawings, so that those skilled in the art can better understand the present invention. It should be noted that in the following description, when detailed descriptions of known functions and designs may dilute the main content of the present invention, these descriptions will be omitted here.

Example

For the convenience of description, the relevant technical terms appearing in the specific implementation are explained first:

ICA (Independent Component Analysis) independent component analysis;

KNN (K-Nearest Neighbor) K nearest neighbor;

FD-KNN (Fault Detection based on K-Nearest Neighbor) is a fault detection method based on K-nearest neighbors;

KICA (Kernel Independent Component Analysis) nuclear independent component analysis;

Figure 1 is a flow chart of the fault detection method for intermittent processes based on ICA-KNN.

In the present embodiment, as shown in Figure 1, a kind of intermittent process fault detection method based on ICA-KNN of the present invention comprises the following steps:

S1. Data preprocessing

The three-dimensional sample matrix X(I×J×K) collected in the batch process is first expanded based on the number of batches to obtain the two-dimensional matrix X(I×KJ), so as to eliminate the influence of dimension; then the two-dimensional matrix X( I×KJ) is standardized in the batch direction, so that the mean value of each column of the two-dimensional matrix X(I×KJ) is 0 and the variance is 1, so that the average running track of all batches is removed; finally, the normalized The processed two-dimensional matrix X (I×KJ) is vertically rearranged into a matrix X(KI×J); where I represents the number of batches, J represents the number of observed variables, and K represents the number of samples.

In this embodiment, the semiconductor aluminum etching reaction performed on Lam 9600 contains 107 batches of normal data and 20 batches of fault data. Take 82 batches of normal data as training samples, 25 batches of normal data as test samples, and finally detect 20 batches of faulty data to see if the 20 batches of faulty data can be detected in time.

Let the final batch data of all training samples be a three-dimensional sample matrix of (82×18×90), expand based on the number of batches, and obtain a two-dimensional sample matrix (82×1620), and then subtract the mean value from the two-dimensional sample matrix The standard deviation is used for standardization, and finally the normalized sample matrix (82×1620) is vertically rearranged into a two-dimensional matrix (7380×18) for subsequent ICA dimension reduction.

S2. Carry out ICA dimension reduction processing on matrix X(KI×J), and obtain d independent components S _d reflecting batch process information and main part separation matrix W _d

S2.1. In order to remove the correlation between sample data and simplify the independent component extraction process, it is necessary to

The matrix X (KI×J) is whitened to obtain the whitening vector Z;

Z=QX

Among them, Q is the whitening matrix, Q=Λ ^-1/2 U ^T , Λ=diag(λ ₁ ,…,λ _n ), λ _i (i=1,…,n) is the covariance matrix E{XX ^T } The first n eigenvalues of , U is a matrix composed of eigenvectors corresponding to n eigenvalues;

S2.2. Decompose the whitening vector Z to obtain d independent components S _d reflecting the information of the batch process and the main part separation matrix W _d ;

S2.2.1. Construct the initial random vector value b _k ,k∈[1,n];

b _k ＝E{Zg(b _k ^T Z)}-E{g'(b _k ^T Z)}b _k

Among them, the function g() is the first-order derivative of the selected non-quadratic function G, g'() represents the derivative of the function g(), and E{} represents expectation;

In this embodiment, the non-quadratic function G can be selected in various forms, such as:

Among them, 1≤a ₁ ≤2, a ₂ =1; cosh() indicates a function used to return the hyperbolic cosine value of the parameter

S2.2.2, starting to iterate b _k from k=1;

S2.2.3. Perform normalization processing on the iterated b _k , that is, b _k = b _k /||b _k ||, where ||b _k || represents seeking the norm of b _k ;

S2.2.4. Judge b _k after normalization processing, if |b _k ^T b _k |=1±5%, then output vector value b _k and enter step S2.2.5; otherwise, k=k+ 1, and return to step S2.2.2 to continue iterating until |b _k ^T b _k |=1±5% is satisfied, then enter step S2.2.5;

S2.2.5. Construct matrix B=[b ₁ ,...,b _n ] ^T , use formula S=B ^T Z to obtain independent components, use formula W=B ^T Q to obtain separation matrix; Arrangement of Gaussian degree, select the first d as the independent components S _d , and the corresponding first d as the main part separation matrix W _d ;

S3. Use the KNN algorithm in the independent component S _d to obtain the statistical control limit CL

In the independent component S _d =[s ₁ ,…,s _d ], calculate the square sum distance between rows, determine the m neighbors of each row through the distance, and calculate its KNN square distance D _s ;

in, Indicates the square of the Euclidean distance between the i-th row and the j-th closest row in S _d ;

In this example, Then the sum of squares distance between row 1 and row 2 is:

(1-1) ² +(1-2) ² +(1-1) ² ＝1, similarly the square sum distances between the first row and other rows are: 1,1,1,3,12; In this embodiment, take m=3, and then calculate the KNN square distance D _s of each row;

Since D _s approximately obeys the χ ² distribution, the control limits can be determined according to the significance level α is the confidence level, N is the number of rows of independent components S _d ;

S4. Standardize the data x' to be detected according to step S1 to obtain the data x, and then calculate the independent components of the data x according to the main part separation matrix W _d

S5, the independent components Calculate the KNN square distance D _x according to step S3; compare D _x with the control limit CL, if D _x > CL, the sample is considered to be a faulty sample, otherwise, the sample is considered to be a normal sample.

In order to verify the effectiveness of the proposed method, we used the data of the aluminum stack etching process in semiconductor production to simulate, and compared it with KICA and FD-KNN methods. Fig. 2 is the I ² statistical line detection diagram of KICA; Fig. 3 is the SPE detection diagram of KICA; Fig. 4 is the KNN detection diagram; Fig. 5 is the ICA-KNN detection diagram. By comparison, it can be seen that the ICA-KNN method has a higher fault detection rate, and there is little difference between the several methods in terms of false alarm rate. From the comparison of algorithm time, ICA-KNN algorithm can effectively reduce the complexity compared with FD-KNN algorithm and KICA algorithm, which shows the superiority of this method. The simulation experiment shows that the ICA-KNN method is simple and effective, and has a good application prospect.

Although the illustrative specific embodiments of the present invention have been described above, so that those skilled in the art can understand the present invention, it should be clear that the present invention is not limited to the scope of the specific embodiments. For those of ordinary skill in the art, As long as various changes are within the spirit and scope of the present invention defined and determined by the appended claims, these changes are obvious, and all inventions and creations using the concept of the present invention are included in the protection list.

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 information_dAnd a main part separation matrix W_d

(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^-1/2U^T，Λ＝diag(λ₁,…,λ_n)，λ_i(i ═ 1, …, n) is the covariance matrix E { XX^TThe 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 process_dAnd a main part separation matrix W_d；

(2.2.1) constructing an initial random vector value b_k，k∈[1,n]；

b_k＝E{Zg(b_kTZ)}-E{g'(b_k ^TZ)}b_k

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 b_kCarrying 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>&amp;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 iteration_kPerforming a normalization process, i.e. b_k＝b_k/||b_kI, wherein i b_kI represents solving b_kNorm of (d);

(2.2.4) normalization of b_kMaking a judgment if | b_k ^Tb_k1 +/-5%, then outputting vector value b_kAnd entering step (2.2.5); otherwise, k is k +1 and returns to step (2.2.2) to continue the iteration until | b is satisfied_k ^Tb_kIf | ═ 1 ± 5%, then go to step (2.2.5);

(2.2.5) construction matrix B ═ B₁,…,b_n]^TUsing the formula S ═ B^TZ is the independent component, and the formula W is B^TQ, 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 S_dThe first d corresponding to it as main part separation matrix W_d；

(3) In the independent component S_dIn the method, a KNN algorithm is used to obtain a statistical control limit CL

In the independent component S_d＝[s₁,…,s_d]Calculating square distance between rows, determining m neighbor of each row according to distance, and calculating KNN square distance D_s；

<mrow> <msub> <mi>D</mi> <mi>s</mi> </msub> <mo>=</mo> <munderover> <mo>&amp;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 S_dThe square of the euclidean distance between the ith row and the row closest to it;

due to D_sApproximate compliance chi²Distribution, from which a control limit can be determinedα confidence level, N is independent component S_dA 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 part_dCalculating 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 D_xCompared with the control limit CL, if D_xIf 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.