CN108459579A - Semiconductor run-to-run process failure diagnosis method based on time series models coefficient - Google Patents
Semiconductor run-to-run process failure diagnosis method based on time series models coefficient Download PDFInfo
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- G05B23/0254—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 model based detection method, e.g. first-principles knowledge model based on a quantitative model, e.g. mathematical relationships between inputs and outputs; functions: observer, Kalman filter, residual calculation, Neural Networks
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Abstract
The invention discloses a kind of semiconductor run-to-run process failure diagnosis method based on time series models, including：Settling time series model y (t)=θ0*h0(t 1), θ0=[φ0, δ, ρ],The output data y (t) for obtaining semiconductor run-to-run process, by high-order autoregression model and experience threshold values υ, whenIt obtainsThen by model andObtain coefficient θ0(t), grader then is established to handle the corresponding coefficient θ of output data y (t) of semiconductor run-to-run process using support vector machines0(t) and fault category, wherein fault category is configured to label vector f (t) and is hereafter only needed the corresponding coefficient θ of the output data y (t) of the online semiconductor run-to-run process obtained instantly after grader is established0(t) grader is inputted, by comparing grader output valve and label vector f (t), obtains the fault category of semiconductor run-to-run process.It is used to diagnose semiconductor run-to-run procedure fault.
Description
Technical field
The invention belongs to the fault diagnosis technology fields for control system, and in particular to one kind being based on time series models
The semiconductor run-to-run process failure diagnosis method of coefficient, the accuracy rate for improving semiconductor run-to-run process failure diagnosis.
Background technology
Batch controls (Run-to-run control are abbreviated as R2R control), also known as criticizes to batch control, is anti-
The one kind for presenting control has many similar places with iterative learning control and Repetitive controller.It passes through the history batch number to process
According to statistical analysis change the process scheme (Recip) of next batch, solve in batch process due to a lack of on-line measurement means
And the problem of causing to be difficult to carry out real time planning, to reduce the quality difference of batch products.
Publication date is that the Chinese patent literature CN1592873A on March 9th, 2005 discloses one kind with state and model
The semiconductor run-to-run control system of parameter Estimation is used and is combined in the estimation R2R control applications of Model Predictive Control (MPC) principle
State and parameter.
MSPC is a kind of fault diagnosis technology based on data-driven, has been applied successfully to batch process in recent years
On-line monitoring, especially in semiconductor run-to-run process.Many documents all only considered system when being monitored using MSPC
Inputoutput data.The introducing of automatic process control can weaken influence of the external disturbance to system output, and different inputs can
Almost the same output can be obtained, therefore the inputoutput data of closed-loop system provides the information in relation to system dynamic characteristic and compares
It is few.When failure is in early stage or smaller amplitude, a relatively good feedback controller can ensure the output of system
It is consistent with original stable state.In this case, traditional SPC can only be detected in limited window and is out of order,
Result in higher rate of failing to report.
In order to solve this problem, Zheng et al. proposes the fault monitoring method based on time series models coefficient
(Zheng Y,Wang Y,Wong D.S.H,et al.A time series model coefficients monitoring
approach for controlled processes[J].Chemical Engineering Research and
Design, 2015,1 0 0:228–236.).The coefficient of time series models is the function of some process variables, they include
The information of process variable.When system encounters external interference, and the input/output relation of process changes, time series models
Coefficient can also change.
However, the emphasis point of the studies above concentrates on the malfunction monitoring aspect of semiconductor run-to-run process, seldom consider partly to lead
The fault diagnosis of body batch process.
Support vector machines (SVM) is a kind of novel machine learning algorithm, it is basically independent on the mathematical modulo of system
Type is relatively more suitable for the system with uncertain and nonlinearity, and has stronger adaptation and learning ability.
Invention content
In order to improve the low problem of existing semiconductor run-to-run fault diagnosis accuracy rate, SVM is introduced into the time by inventor
In the fault diagnosis of series model coefficient, the fault diagnosis model based on time series models coefficient is proposed, and apply it to
In semiconductor run-to-run process failure diagnosis, to improve the accuracy rate in semiconductor run-to-run process failure diagnosis.
The technical problem to be solved in the present invention is to provide a kind of semiconductor run-to-run processes based on time series models coefficient
Method for diagnosing faults, to improve the accuracy rate in semiconductor run-to-run process failure diagnosis.
In order to solve the above technical problems, the present invention adopts the following technical scheme that：
A kind of semiconductor run-to-run process failure diagnosis method based on time series models is designed, is included the following steps,
Step 1 is based on exponentially weighted moving average (EWMA) controller, establishes the time series models of semiconductor run-to-run process
In formula (1), (2), (3), y (t) be semiconductor run-to-run process output data, t indicate batch serial number, t=1,
2 ..., N,β is the gain in batch process, and b is the estimated initial value of β, and λ is discount factor, and 0≤λ≤1, δ are
Drift term, ρ are the coefficients of batch process interference model,It is the estimated value of ε (t-1),Belong to white noise
Sound sequence, σεIt is the variance of white noise sequence；
Step 2 estimates the white noise sequence of the step 1 Chinese style (3)
(1) the output data y (t) for obtaining semiconductor run-to-run process, establishes following high-order autoregression AR (n) model
Y (t)=φ1y(t-1)+φ2y(t-2)+...+φny(t-n)+ε(t) (4)
Wherein, φnIt is the coefficient of high-order AR (n) models, n is the order of model, n=10~20；
(2) coefficient θ (t)=[φ of least square method of recursion identification high-order AR (n) model is utilized1(t),φ2(t),...,
φn(t)]：
Wherein, h (t-1)=[y (t-1), y (t-2) ..., y (t-n)]T, K (t) is gain vector, and P (t) is that dimension is p
The matrix of × p, p are the numbers of variable in coefficient vector θ (t), and μ is forgetting factor, and μ ∈ [0,1], I are dimension p × p unit squares
Battle array, p=n, c >=105；
(3) estimated value of white noise is calculated
(4) compare estimated valueWith the size of experience threshold values υ, whenEnable t=t+1, this step of repetitive cycling
(2)-(4) in rapid untilWhen end loop,
Step 3, the coefficient θ of estimation time series models Chinese style (1) and formula (2)0(t)：
The white noise estimated according to step 2Construction：
The coefficient θ of estimation time series models is recognized using least square method of recursion0(t)：
Wherein K0(t) it is gain vector, P0(t) be dimension be p0×p0Matrix, p0It is coefficient vector θ0(t) variable in
Number, μ0It is forgetting factor, μ0∈ [0,1], I0For dimension p0×p0Unit matrix, c0≥105；
Step 4 defines label vector f (t) so that the value of f (t) is uniquely corresponding with fault category, and the fault category exists
Different both phase step faults are shown as during semiconductor run-to-run；
The failure output data y (t) for acquiring semiconductor run-to-run process corresponding with the failure under operation, repeats
It is described Step 2: step 3 is to obtain model coefficient θ corresponding with the failure0(t) value, composing training sample X, X include two
The data of a type：
Data prediction is carried out to the training sample X,
Wherein Xi,jIt is the arbitrary value in sample jth dimension data, maxjAnd minjIt is the maximum value and minimum of jth dimension data
Value, [a ', b '] are scaling target intervals, and N and m are the number of sample and variable in X respectively；
SVM training is carried out based on pretreated training sample X data, determines the parameter a of following graders1(t)、b1、γ
Value, and by parameter a1(t)、b1, γ value substitute into grader to update grader,
Wherein a1(t) and b1It is normal real number and a1(t)>0, Ψ (*, *) is kernel function, and γ is the parameter of kernel function, sign
It is sign function；
The output data y (t) of semiconductor run-to-run process, repeating said steps two, step are received in the current state of operation
Three couples of output data y (t) are handled to obtain the model coefficient θ of the output data0(t) value, by model coefficient θ0
(t) value is input in the grader (15) built up, comparison prediction result Δ (θ0(t)) and the value of label vector f (t), when
Δ(θ0(t)) when identical as a certain value in label vector f (t), then the sample to be tested is the corresponding fault category of the value.
The beneficial effects of the invention are as follows：Using based on time series models coefficient fault diagnosis and traditional Kernel-based methods
The fault diagnosis of data is compared, and the coefficient of time series models is introduced into the fault diagnosis of semiconductor run-to-run process, this
Method efficiently solves the problems, such as that closed-loop system process data multidate information amount is few, using first estimating white noiseIt recognizes again
Model coefficient θ0(t) two step Model Distinguish algorithms effectively have modified the not high problem of discrimination power of direct estimation model coefficient,
Improve the identification precision of model coefficient, then by SVM algorithm be introduced into model during semiconductor run-to-run failure it is online
In estimation application, the accuracy rate of inline diagnosis semiconductor run-to-run procedure fault is improved.
Description of the drawings
Fig. 1 is a kind of schematic diagram of the semiconductor run-to-run process failure diagnosis method based on time series models coefficient.
Fig. 2 is a kind of flow chart of the semiconductor run-to-run process failure diagnosis method based on time series models coefficient.
Fig. 3 is a kind of input and output number of the semiconductor run-to-run process failure diagnosis method based on time series models coefficient
According to figure.
Specific implementation mode
Illustrate the specific implementation mode of the present invention with reference to the accompanying drawings and examples, but following embodiment is used only in detail
It describes the bright present invention in detail, does not limit the scope of the invention in any way.
Embodiment 1：
A kind of semiconductor run-to-run process failure diagnosis method based on time series models coefficient, referring to Fig. 1-2, including with
Lower step：
Step 1 is based on exponentially weighted moving average (EWMA) (EWMA) controller, establishes the time series of semiconductor run-to-run process
Model：
Wherein, y (t) be semiconductor run-to-run process output data, t indicate batch serial number, t=1,2 ..., 200, β=
2.5 be the gain in batch process, and b=3 is the estimated initial value of β, and λ=0.6 is discount factor, and δ=0.05 is drift term, ε
(t)~N (0,0.01) belongs to white noise sequence, and ρ=0.5 is the coefficient of batch process interference model.
Enable θ0=[φ0, δ, ρ],Then formula (17) is：
Y (t)=θ0*h0(t-1) (18)
WhereinIt is the estimated value of ε (t-1).
Step 2：Estimate the white noise sequence of time series models (18)
(1) the output data y (t) for obtaining semiconductor run-to-run process, establishes following high-order autoregression AR (n) model：
Y (t)=φ1y(t-1)+φ2y(t-2)+...+φny(t-n)+ε(t) (19)
Wherein φnIt is the coefficient of high-order AR (n) models, n is the order of model, takes n=10.
(2) coefficient θ (t)=[φ of least square method of recursion identification high-order AR (n) model is utilized1(t),φ2(t),...,
φn(t)]：
Wherein h (t-1)=[y (t-1), y (t-2) ..., y (t-10)]T, K (t) is gain vector, and P (t) is that dimension is
10 × 10 matrix, μ=0.99 are forgetting factors, and I is 10 × 10 unit matrix of dimension, and c is prodigious real number, takes c=105。
(3) estimated value of white noise is calculated
(4) compare estimated valueWith experience threshold values υ=0.01, whenEnable t=t+1, this step of repetitive cycling
(2)-(4) in rapid untilWhen end loop,Experience threshold values υ is rich by experience
Rich engineer's setting.
Step 3, the coefficient θ of estimation time series models Chinese style (18)0(t)：
The white noise estimated according to step 2Construction：
The coefficient θ of estimation time series models is recognized using least square method of recursion0(t)：
Wherein K0(t) it is gain vector, P0(t) be dimension be 3 × 3 matrix, μ0=0.2 is forgetting factor, I0For dimension
3 × 3 unit matrixs, c0For prodigious real number, c is taken0=105。
Step 4, it is { 1, -1 } to define label vector f (t), wherein f (t)=1 corresponds to failure A, f (t)=- 1 correspondence
Different both phase step faults are shown as during semiconductor run-to-run in failure B, failure A, failure B；Referring to Fig. 1-2,
Two difference both phase step fault β (β → β+0.5) in batch process, ρ=0.5 → ρ=1 pair are acquired under operation
The failure output data y (t) for the semiconductor run-to-run process answered is repeated Step 2: step 3 is corresponding with two failures to obtain
Model coefficient θ0(t) value, composing training sample X, X include the data of two types：
Data prediction is carried out to the training sample X：
Wherein Xi,jIt is the arbitrary value in sample jth dimension data, maxjAnd minjIt is the maximum value and minimum of jth dimension data
Value, [a ', b '] are scaling target intervals, and it is sample and variable in X respectively generally to take [- 1,1] and [0,1], N=200 and m=3
Number.
SVM training is carried out based on pretreated training sample X data, determines the parameter a of following graders1(t)、b1、γ
Value, and by parameter a1(t)、b1, γ value substitute into grader to update grader：
Wherein a1(t) and b1It is normal real number and a1(t)>0, Ψ (*, *) is kernel function, and γ is the parameter of kernel function, sign
It is sign function.The foundation of formula (30) grader can pass through Libsvm (http://www.csie.ntu.edu.tw/~
Cjlin/ easy.py functions in) are realized.
The step of output data y (t) of reception semiconductor run-to-run process in the current state of operation, repetition embodiment 1 two,
Step 3 is handled the output data to obtain the model coefficient θ of the output data0(t) value, by model coefficient θ0
(t) value is input in the grader (30) built up, and will be projected in data space, by prediction result Δ (θ0(t))
It is compared one by one with the value in label vector f (t), as Δ (θ0(t)) when=1, i.e., the fault type of sample to be tested is failure A, when
Δ(θ0(t)) when=- 1, i.e., the fault type of sample to be tested is failure B.
It is tested through analog simulation, inventor obtains following data, is shown in Table 1.
The accuracy rate of fault diagnosis under 1 different data object of table
In the prior art, the knot of generally use the output of process data y (t) or process input x (t) and output data y (t)
It builds vertical grader jointly and fault diagnosis is carried out to semiconductor batch process, in Fig. 3, x (t) is process input data, and y (t) is process
Output data；In table 1, CR (y) corresponds to carries out the accurate of fault diagnosis using the grader that the output of process data y (t) is established
Rate, CR (x, y) are corresponded to the grader established using the combination of process input x (t) and output data y (t) and carry out fault diagnosis
Accuracy rate, what CR (θ) was indicated is that the grader that model coefficient θ (t) using the present invention is established carries out the accurate of fault diagnosis
Rate.From table 1 as can be seen that when process parameter beta breaks down, when establishing grader using model coefficient, rate of accuracy reached arrives
89.17%, and model in the prior art is used, the accuracy rate according to output data or inputoutput data is respectively
45.42% and 52.5%, it is far below the former.Equally, when process parameter ρ breaks down, grader is established using model coefficient
Also obtain higher accuracy.Therefore, carrying out fault diagnosis using model coefficient has higher accuracy.
The present invention is described in detail above in conjunction with drawings and examples, still, those of skill in the art
Member is it is understood that without departing from the purpose of the present invention, can also carry out each design parameter in above-described embodiment
Change, forms multiple specific embodiments, is the common variation range of the present invention, is no longer described in detail one by one herein.
Claims (1)
1. a kind of semiconductor run-to-run process failure diagnosis method based on time series models, characterized in that include the following steps：
Step 1 is based on exponentially weighted moving average (EWMA) controller, establishes the time series models of semiconductor run-to-run process
In formula (1), (2), (3), y (t) be semiconductor run-to-run process output data, t indicate batch serial number, t=1,2 ... N,β is the gain in batch process, and b is the estimated initial value of β, and λ is discount factor, and 0≤λ≤1, δ are drift term, ρ
It is the coefficient of batch process interference model,It is the estimated value of ε (t-1),Belong to white noise sequence,
σεIt is the variance of white noise sequence；
Step 2 estimates the white noise sequence of the step 1 Chinese style (3)
(1) the output data y (t) for obtaining semiconductor run-to-run process, establishes following high-order autoregression AR (n) model
Y (t)=φ1y(t-1)+φ2y(t-2)+...+φny(t-n)+ε(t) (4)
Wherein, φnIt is the coefficient of high-order AR (n) models, n is the order of model, n=10~20；
(2) coefficient θ (t)=[φ of least square method of recursion identification high-order AR (n) model is utilized1(t),φ2(t),...,φn
(t)]：
Wherein, h (t-1)=[y (t-1), y (t-2) ..., y (t-n)]T, K (t) is gain vector, and P (t) is that dimension is p × p
Matrix, p are the numbers of variable in coefficient vector θ (t), and μ is forgetting factor, and μ ∈ [0,1], I are dimension p × p unit matrixs, p=
n,c≥105；
(3) estimated value of white noise is calculated
(4) compare estimated valueWith the size of experience threshold values υ, whenT=t+1 is enabled, in this step of repetitive cycling
(2)-(4) untilWhen end loop,
Step 3, the coefficient θ of estimation time series models Chinese style (1) and formula (2)0(t)：
The white noise estimated according to step 2Construction：
The coefficient θ of estimation time series models is recognized using least square method of recursion0(t)：
Wherein K0(t) it is gain vector, P0(t) be dimension be p0×p0Matrix, p0It is coefficient vector θ0(t) of variable in
Number, μ0It is forgetting factor, μ0∈ [0,1], I0For dimension p0×p0Unit matrix, c0≥105；
Step 4 defines label vector f (t) so that the value of f (t) is uniquely corresponding with fault category, and the fault category is partly being led
Different both phase step faults are shown as in body batch process；
Acquire the failure output data y (t) of corresponding with failure semiconductor run-to-run process under operation, repeatedly described in
Step 2: step 3 is to obtain model coefficient θ corresponding with the failure0(t) value, composing training sample X, X include two classes
The data of type：
Data prediction is carried out to the training sample X,
Wherein Xi,jIt is the arbitrary value in sample jth dimension data, maxjAnd minjIt is the maximum value and minimum value of jth dimension data,
[a ', b '] is scaling target interval, and N and m are the number of sample and variable in X respectively；
SVM training is carried out based on pretreated training sample X data, determines the parameter a of following graders1(t)、b1, γ
Value, and by parameter a1(t)、b1, γ value substitute into grader to update grader,
Wherein a1(t) and b1It is normal real number and a1(t)>0, Ψ (*, *) is kernel function, and γ is the parameter of kernel function, and sign is symbol
Number function；
The output data y (t) of semiconductor run-to-run process, repeating said steps two, step 3 pair are received in the current state of operation
The output data y (t) is handled to obtain the model coefficient θ of the output data0(t) value, by model coefficient θ0(t)
Value is input in the grader (15) built up, comparison prediction result Δ (θ0(t)) and the value of label vector f (t), as Δ (θ0
(t)) when identical as a certain value in label vector f (t), then the sample to be tested is the corresponding fault category of the value.
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