CN101403923A - Course monitoring method based on non-gauss component extraction and support vector description - Google Patents

Course monitoring method based on non-gauss component extraction and support vector description Download PDF

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CN101403923A
CN101403923A CNA200810122086XA CN200810122086A CN101403923A CN 101403923 A CN101403923 A CN 101403923A CN A200810122086X A CNA200810122086X A CN A200810122086XA CN 200810122086 A CN200810122086 A CN 200810122086A CN 101403923 A CN101403923 A CN 101403923A
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gauss
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许仙珍
谢磊
王树青
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Zhejiang University ZJU
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Abstract

The invention discloses a process monitoring method which is based on non-Gaussian component extraction and support vector description. The method comprises the following steps: read-in of training data and data to be diagnosed, data preprocessing, establishment of a principal component analysis model, particle swarm optimization algorithm, non-Gaussian projection calculation, support vector data description, residual analysis, principal component estimation, fault detection and the model updating. By the method, the non-Gaussian components can be automatically extracted from operating data of an industrial process, thus avoiding the disadvantage that the conventional statistical process monitoring method assumes that data is subject to normal distribution, and the non-Gaussian projection algorithm based on the particle swarm optimization algorithm ensures the maximization of the non-Gaussian properties of the extracted independent components, and avoids the problem that the independent component analysis method is easy to be involved in the locally optimal solution. Compared with the conventional statistical process monitoring method, the method can find abnormity in time, effectively reduce the rate of false alarm, and obtain better monitoring effect.

Description

Course monitoring method based on non-gauss component extraction and support vector description
Technical field
The present invention relates to the industrial process fault diagnosis field, especially, relate to a kind of based on the non-Gaussian statistics monitoring of non-gauss component extraction and support vector description and the method for fault detect.
Background technology
Along with developing rapidly of modern industry and science and technology, characteristics such as modern process industry presents that scale is big, strong coupling between the complex structure, productive unit, investment are big.Meanwhile, the possibility that breaks down of production run also increases thereupon.In a single day this type systematic breaks down, and not only can cause the massive losses of personnel and property, and also will cause irremediable influence to ecologic environment.In order to improve the security of industrial processes and control system, improve simultaneously product quality, reduce production costs, process monitoring and fault diagnosis have become a part indispensable in the IT application in enterprises.
In recent years, multivariate statistical analysis is applied to process monitoring and fault diagnosis has obtained broad research.Traditional multivariate statistics method for supervising adopts pivot analysis (PCA:Principal Component Analysis) more, minimum partially binary is analysed methods such as (PLS:Partial Least Square), these methods are in the hypothesis independent identically distributed while of variable, also require the variable Normal Distribution, and utilization only is second-order statistic information.In industrial real process, the reasons such as fluctuation owing to measuring interference, production status can cause no longer Normal Distribution of variable, T usually 2Do not satisfying F distribution and x with the Q statistic yet 2Distribute.Therefore,, often be difficult to obtain monitoring effect preferably, fail to report, rate of false alarm is higher, and can't note abnormalities timely and effectively if only adopt traditional Multivariable Statistical Methods to monitor to this type of industrial process.
Independent pca method (ICA:Independent Component Analysis) is a kind of analytical approach based on signal higher order statistical characteristic, can be used for extracting non-gauss component.The purpose of this method is that observable data are carried out certain linear decomposition, utilizes the independence and the non-Gauss of source signal, it is resolved into add up independently composition.Use it for the process data analyzing and processing of process industry, the probabilistic statistical characteristics of energy more efficient use variable, can under the meaning observational variable be decomposed adding up independently, obtain the activation bit source of process inherence, thus more essential description process feature.The FastICA algorithm is an algorithms most in use of monitoring at present work based on ICA, and its weak point is that separating resulting depends on initial solution, can't guarantee global optimum's property of separating also to lack effective standard of selecting the pivot number in addition.
Summary of the invention
The objective of the invention is in order to overcome the deficiency that existing Multivariable Statistical Methods is not considered the non-Gauss of process variable, is difficult to obtain better monitoring effect, a kind of statistic processes monitoring and fault detection method based on non-gauss component extraction and Support Vector data description is provided.This method has been avoided the deficiency of conventional statistics course monitoring method tentation data Normal Distribution, the abnormal conditions that occur in the discovery procedure in time.
Technical solution of the present invention is: by PCA dimensionality reduction is carried out in the process variable data space, then principal component space and residual error space are adopted the independent component that extracts non-Gauss based on particulate group's FastICA algorithm respectively.After the non-Gauss's independent component of procurement process, utilize the support vector data to describe its distribution situation, construct new statistic, determine its statistics control limit.Concrete steps are as follows:
The data of key variables are as training sample TX when 1) reading production run and normally move;
2) training sample TX is carried out pre-service, make that the average of each variable is 0, variance is 1, obtains input matrix X ∈ R N * n, step is:
(1) computation of mean values: TX ‾ = 1 N Σ i = 1 N TX i
(2) calculate variance: σ x 2 = 1 N - 1 Σ i = 1 N ( TX i - TX ‾ ) 2
(3) albefaction is handled: X = TX - TX ‾ σ x 2
Wherein, TX is a training sample, and N is a number of training, and n is a variable number;
3) set up the pivot analysis model;
4) calculate based on the non-Gauss projection of particle swarm optimization algorithm, extract the non-gauss component in the data;
5), make up the statistical variable and the control limit of non-Gaussian signal based on Support Vector data description; Ask for the hypersphere that non-Gaussian signal distributes, find the solution following quadratic programming problem:
max &alpha; &Sigma; i &alpha; i < x i &CenterDot; x i > - &Sigma; i &Sigma; j &alpha; i &alpha; j < x i &CenterDot; x j >
s . t . &Sigma; i &alpha; i = 1 , &alpha; i &Element; [ 0 , C ] , i = 1 , &CenterDot; &CenterDot; &CenterDot; , N .
Obtain hyperspherical center a = &Sigma; i &alpha; i x i And radius: R 2 = < x k &CenterDot; x k > - 2 &Sigma; i &alpha; i < x k &CenterDot; x i > + &Sigma; i &Sigma; j &alpha; i &alpha; j < x i &CenterDot; x j > , x i, x jBe the sample point of non-gauss component, x kBe the borderline support vector of hypersphere;
6) pivot is estimated: the T that makes up the pivot gaussian signal 2Statistic, the calculation control limit; When insolation level is α, the control limit is calculated as follows:
T &alpha; 2 = l ( N 2 - 1 ) N - l F l , N - l ; &alpha; , L is the pivot number.
7) residual analysis: make up residual error gaussian signal Q statistic, the calculation control limit;
For arbitrary input residual error e i, the Q statistic is:
Q = | | e i | | 2 = e i T e i ;
When insolation level is α, the control limit is calculated as follows:
&delta; &alpha; 2 = g&chi; h ; &alpha; 2 ,
Wherein g = &rho; 2 2 &mu; , h = 2 &mu; 2 &rho; 2 , ρ and μ are respectively the variance and the average of Q statistic.
8) read variable data up-to-date in the production run as diagnostic data VX;
9) fault detect;
10) regularly the normal point of process status is added among the training set TX, repeats 2)~7) training process so that models such as the support vector description that upgrades in time, residual analysis and pivot statistics.
The described pivot analysis model step of setting up:
(1) covariance matrix of calculating X is designated as ∑ x;
(2) ∑ x is carried out svd, obtain characteristic root λ 1, λ 2..., λ n, λ wherein 1〉=λ 2〉=... 〉=λ n, the characteristic of correspondence vector matrix is U;
(3) calculate population variance and each eigenwert corresponding variance contribution rate, adding up from big to small by the variance contribution ratio of each eigenwert reaches set-point up to total variance contribution ratio, and it is r that note is chosen number;
(4) the preceding r row of selected characteristic vector matrix U constitute principal component space P ∈ R N * r, remaining columns constitutes the residual error space P ~ &Element; R n &times; ( n - r ) ;
(5) calculate respectively that PCA keeps variation per minute Z=XP and remain variation per minute Z ~ = X P ~ ; The described step of calculating based on the non-Gauss projection of particle swarm optimization algorithm:
(1) makes Z (1)=Z ', i=1 asks for the strongest pairing separating vector b of non-Gauss's independent component of following formula by adopting the particle swarm optimization algorithm 1:
b ~ 1 = arg max a J ( a T Z ( 1 ) / | | a | | )
b 1 = b ~ 1 / | | b ~ 1 | |
Wherein J () is non-Gauss's metric function, its functional form be J (y) ≈ [E{G (y) }-E{G (v) }] 2, in the formula, v is zero-mean, unit variance gaussian variable, and G () is a non-quadratic function, and first independent component is s 1 = b 1 T Z ( 1 ) .
(2) check s iGauss; Calculate non-Gauss and measure J (s i) significance degree is the confidence limit J of α αIf J is (s i)≤J α, s then iBe gaussian signal, non-Gaussian signal is counted m=i-1, forwards (5) to, otherwise continues;
(3)i=i+1, Z ( i ) = ( I r , r - b i - 1 b i - 1 T ) Z ( i - 1 ) = ( I r , r - &Sigma; j = 1 i - 1 b j - 1 b j - 1 T ) Z ( 1 ) , R in the formula is the dimension of input sample point;
(4) adopt the PSO algorithm to ask for the separating vector of i non-gauss component:
b ~ i = arg max a J ( a T M T Z ( i ) / | | Ma | | )
b i = M b ~ i / | | M b ~ i | |
In the formula, M = ( I r , r - &Sigma; j = 1 i - 1 b j - 1 b j - 1 T ) . By the projection of M battle array, guaranteed the orthogonality between the separating vector.I independent component is s i = b i T Z ( i ) , Return (2);
(5) output separation matrix B=(b 1, b 2..., b m), finish;
Described particle swarm optimization algorithm steps:
(1) initialization a group particulate comprises granule amount, particulate random site and speed;
(2) estimate the fitness of each particulate;
(3) to each particulate, if adaptive value is greater than its desired positions, then with it as current desired positions; If adaptive value is then reset call number greater than full group's desired positions;
(4) as not reaching termination condition, then revise i particle's velocity and position, return (2) by following formula; Otherwise, finish
v i d &OverBar; k + 1 = wv i d &OverBar; k + c 1 r 1 ( p i d &OverBar; k - a ~ i d &OverBar; k ) + c 2 r 2 ( p g d &OverBar; k - a ~ i d &OverBar; k ) a ~ i d &OverBar; k + 1 = a ~ i d &OverBar; k + v i d &OverBar; k + 1 d &OverBar; = 1,2 , &CenterDot; &CenterDot; &CenterDot; , r &OverBar;
In the formula, a ~ i = [ a ~ i 1 , a ~ i 2 , . . . , a ~ ir ] Represent i particulate, V i=[V I1, V I2..., V Ir] be the speed of particulate, p i=[p I1, p I2..., p Ir] be the optimum position of this particulate experience, p g=[p G1, p G2..., p Gr] be the desired positions of all particulate experience in the colony, r is equal to dimension to be found the solution; W represents inertia weight, c 1And c 2Be positive acceleration constant, r 1, r 2Be the random number that is evenly distributed on interval [0,1].
Described fault detect:
To data to be tested VX with when training the TX and the σ that obtain x 2Carry out albefaction and handle, and with the input of the data after the albefaction as the pivot analysis model, the P that obtains with training with It is divided into principal component space and residual error residual error space, matrix is input to non-Gauss projection module respectively after the conversion, obtain non-gauss component, the gauss component of principal component space, non-gauss component and gauss component with the residual error space, non-gauss component calculates corresponding statistic by support vector description, and gauss component calculates corresponding T by the pivot analysis of routine 2Statistic and Q statistic are if all less than control limit separately, judge that then this sample point is normal; Otherwise, think that the sample point statistics is unusual, the process object may break down.
Beneficial effect of the present invention mainly shows: 1, by non-Gauss projection, isolated the non-gauss component in the process variable, and utilize the support vector data to describe its distribution situation, construct new statistic, determine its statistics control limit, avoided the deficiency of conventional statistics course monitoring method hypothesis Normal Distribution; Gaussian signal after the separation is more suitable for the monitoring of multivariates such as pivot analysis, residual analysis, thus the abnormal conditions in time in the discovery procedure; 2, based on the non-Gauss projection algorithm of particle swarm optimization, overcome independent pivot analysis (ICA) method and easily be absorbed in the deficiency of local minimum, can guarantee the non-Gauss's maximization of independent component of extraction, and need not to set the non-gauss component number in advance.
Description of drawings
Fig. 1 is the theory diagram of course monitoring method proposed by the invention
Fig. 2 is the process flow diagram of non-Gauss projection algorithm
Fig. 3 is that synoptic diagram is carried out in on-line monitoring
Fig. 4 is traditional pca method and the inventive method monitoring effect comparison diagram
Embodiment
Below in conjunction with accompanying drawing the present invention is further described.
With reference to Fig. 1, Fig. 2 and Fig. 3, a kind of course monitoring method based on non-gauss component extraction and Support Vector data description, specific implementation method is as follows:
(1) off-line modeling
Obtain a collection of measurement data of industrial process, set up each model, obtain corresponding projection matrix, detailed process is as follows:
The data of key variables are as training sample TX when 1) reading production run and normally move N * n, wherein, N is a number of training, n is a variable number;
2) training sample TX is carried out pre-service, make that the average of each variable is 0, variance is 1, obtains input matrix X ∈ R N * n, step is:
(1) computation of mean values: TX &OverBar; = 1 N &Sigma; i = 1 N TX i
(2) calculate variance: &sigma; x 2 = 1 N - 1 &Sigma; i = 1 N ( TX i - TX &OverBar; ) 2
(3) albefaction is handled: X = TX - TX &OverBar; &sigma; x 2
3) set up the pivot analysis model;
Pivot analysis is mainly used in dimensionality reduction, extracts the pivot composition, and measurement space is decomposed into principal component space and residual error space.Pivot variance extraction ratio is generally greater than 80%, and computation process adopts the method for covariance svd, and step is as follows:
(1) covariance matrix of calculating X is designated as ∑ x;
(2) ∑ x is carried out svd, obtain characteristic root λ 1, λ 2..., λ n, λ wherein 1〉=λ 2〉=... 〉=λ n, the characteristic of correspondence vector matrix is U;
(3) calculate population variance and each eigenwert corresponding variance contribution rate, adding up from big to small by the variance contribution ratio of each eigenwert reaches set-point up to total variance contribution ratio, and it is r that note is chosen number;
(4) the preceding r row of selected characteristic vector matrix U constitute principal component space P ∈ R N * r, remaining columns constitutes the residual error space P ~ &Element; R n &times; ( n - r ) ;
(5) calculate respectively that PCA keeps variation per minute Z=XP and remain variation per minute Z ~ = X P ~ ;
Pivot analysis is lost under the minimum principle making every effort to data message, to the variable space dimensionality reduction of higher-dimension.In fact, essence is a few linear combination of research variable system, and the generalized variable that this several linear combination constituted will keep former variable information as much as possible.
4) calculate based on the non-Gauss projection of particle swarm optimization algorithm, extract the non-gauss component in the data;
It is the non-gauss component that is used to extract the input data that non-Gauss projection is calculated, and adopts based on particulate group's FastICA algorithm and realizes, can guarantee that the independent component that extracts is a global optimum, and provide the non-gauss component number automatically, need not artificial setting.Supposing will be to data set Z ∈ R N * rExtract non-gauss component, N is a sample number, and r is a variable number, and the specific implementation step is as follows:
(1) makes Z (1)=Z ', i=1 adopts the particle swarm optimization algorithm to ask for the strongest pairing separating vector b of non-Gauss's independent component of following formula 1, obtain first independent component and be s 1 = b 1 T Z ( 1 ) ;
b ~ 1 = arg max a J ( a T Z ( 1 ) / | | a | | )
b 1 = b ~ 1 / | | b ~ 1 | |
In the formula, J () is non-Gauss's metric function, its functional form be J (y) ≈ [E{G (y) }-E{G (v) }] 2, in the formula, v is zero-mean, unit variance gaussian variable, G () is a non-quadratic function, can select following form for use:
G 1 ( u ) = 1 a 1 log cosh ( a 1 u ) ,
G 2(u)=exp(-a 2u 2/2),
G 3(u)=u 4.
In the formula, 1≤a 1≤ 2, a 2≈ 1.
(2) check s iGauss:
1. calculate non-Gauss and measure J (s i) significance degree is the confidence limit J of α α(s i), can ask for by following theorem:
Suppose that it is y ∈ N (0,1) that y obeys the standard Gaussian distribution, y 1, y 2..., y NFor the capacity of independent draws from overall y is the simple sample of N, then when N → ∞, according to sample y 1, y 2..., y NThe non-Gauss of the y that calculates measures J (y 1, y 2..., y N) meet the following conditions:
N &CenterDot; J ( y 1 , y 2 , . . . , y N ) &cong; D ( G ( y ) ) &chi; 2
Promptly 1 D ( G ( v ) ) N &CenterDot; J ( y 1 , y 2 , . . . , y N ) Progressively obey degree of freedom and be 1 x 2Distribute, wherein J (), G () function definition are the same, and D () is a variance function.Given level of significance α, then
J &alpha; ( s i ) = 1 N D ( G ( s i ) ) &chi; 1 2 ( &alpha; )
α generally gets 0.05 or 0.1;
If 2. J (s i)≤J α, s then iBe gaussian signal, non-Gaussian signal is counted m=i-1, forwards (5) to, otherwise continues;
(3)i=i+1, Z ( i ) = ( I r , r - b i - 1 b i - 1 T ) Z ( i - 1 ) = ( I r , r - &Sigma; j = 1 i - 1 b j - 1 b j - 1 T ) Z ( 1 ) ;
(4) adopt the PSO algorithm to ask for the separating vector of i non-gauss component:
b ~ i = arg max a J ( a T M T Z ( i ) / | | Ma | | )
b i = M b ~ i / | | M b ~ i | |
In the formula, M = ( I r , r - &Sigma; j = 1 i - 1 b j - 1 b j - 1 T ) . By the projection of M battle array, guaranteed the orthogonality between the separating vector.I independent component is s i = b i T Z ( i ) , Return (2);
(5) output separation matrix B=(b 1, b 2..., b m), finish;
Described particle swarm optimization algorithm is used to find the solution unconstrained optimization problem, obtains globally optimal solution, adopts following steps to realize:
(1) initialization a group particulate comprises granule amount, particulate random site and speed; Atomic dimension is equal to dimension to be found the solution, and particulate scale (number) is 10~15 times of particle dimension, and position initial value, speed initial value are random number;
(2) estimate the fitness of each particulate, promptly calculate corresponding target function value;
(3) to each particulate, if adaptive value is greater than its desired positions, then with it as current desired positions; If adaptive value is then reset call number greater than full group's desired positions;
(4) as not reaching termination condition, then revise i particle's velocity and position, return (2) by following formula; Otherwise, finish
v i d &OverBar; k + 1 = wv i d &OverBar; k + c 1 r 1 ( p i d &OverBar; k - a ~ i d &OverBar; k ) + c 2 r 2 ( p g d &OverBar; k - a ~ i d &OverBar; k ) a ~ i d &OverBar; k + 1 = a ~ i d &OverBar; k + v i d &OverBar; k + 1 d &OverBar; = 1,2 , &CenterDot; &CenterDot; &CenterDot; , r &OverBar;
In the formula, a ~ i = [ a ~ i 1 , a ~ i 2 , . . . , a ~ ir ] Represent i particulate, V i=[V I1, V I2..., V Ir] be the speed of particulate, p i=[p I1, p I2..., p Ir] be the optimum position of this particulate experience, p g=[p G1, p G2..., p Gr] be the desired positions of all particulate experience in the colony, r is equal to dimension to be found the solution; W represents inertia weight, c 1And c 2Be positive acceleration constant, r 1, r 2Be the random number that is evenly distributed on interval [0,1].
5), make up the statistical variable and the control limit of non-Gaussian signal based on Support Vector data description; Ask for the hypersphere that non-Gaussian signal distributes, find the solution following quadratic programming problem:
max &alpha; &Sigma; i &alpha; i < x i &CenterDot; x i > - &Sigma; i &Sigma; j &alpha; i &alpha; j < x i &CenterDot; x j >
s . t . &Sigma; i &alpha; i = 1 , &alpha; i &Element; [ 0 , C ] , i = 1 , &CenterDot; &CenterDot; &CenterDot; , N .
Obtain hyperspherical center a = &Sigma; i &alpha; i x i And radius: R 2 = < x k &CenterDot; x k > - 2 &Sigma; i &alpha; i < x k &CenterDot; x i > + &Sigma; i &Sigma; j &alpha; i &alpha; j < x i &CenterDot; x j > , x i, x jBe the sample point of non-gauss component, x kBe the borderline support vector of hypersphere;
6) pivot is estimated: the T that makes up the pivot gaussian signal 2Statistic, the calculation control limit; When insolation level is α, the control limit is calculated as follows:
T &alpha; 2 = l ( N 2 - 1 ) N - l F l , N - l ; &alpha; , L is the pivot number.
7) residual analysis: make up residual error gaussian signal Q statistic, the calculation control limit;
For arbitrary input residual error e i, the Q statistic is:
Q = | | e i | | 2 = e i T e i ;
When insolation level is α, the control limit is calculated as follows:
&delta; &alpha; 2 = g&chi; h ; &alpha; 2 ,
Wherein g = &rho; 2 2 &mu; , h = 2 &mu; 2 &rho; 2 , ρ and μ are respectively the variance and the average of Q statistic.
(2) on-line monitoring
Above-mentioned steps is the process monitoring modeling process.After the modelling, obtain separation matrix and control limit, can realize on-line monitoring, may further comprise the steps:
8) read variable data up-to-date in the production run as diagnostic data VX;
9) fault detect;
To data to be tested VX with when training the TX and the σ that obtain x 2Carry out albefaction and handle, and with the input of the data after the albefaction as the pivot analysis model, the P that obtains with training with It is divided into principal component space and residual error residual error space, matrix is input to non-Gauss projection module respectively after the conversion, obtain non-gauss component, the gauss component of principal component space, non-gauss component and gauss component with the residual error space, non-gauss component calculates corresponding statistic by support vector description, and gauss component calculates corresponding T by the pivot analysis of routine 2Statistic and Q statistic are if all less than control limit separately, judge that then this sample point is normal; Otherwise, think that the sample point statistics is unusual, the process object may break down.
10) regularly the normal point of process status is added among the training set TX, repeats 2)~7) the training journey so that models such as the support vector description that upgrades in time, residual analysis and pivot statistics.
For actual industrial process, the present invention realizes that the specific implementation process of on-line monitoring is:
(1) sets time interval of each sampling with timer;
(2) each sampling period from the real-time data base of DCS, obtain up-to-date variable data, as diagnostic data VX;
(3) data to be tested VX is with training TX and the σ that obtains x 2Carry out albefaction and handle, and the data after will handling are as the input of pivot analysis model;
(4) with the P battle array that obtains of training conversion is carried out in input, obtain z and The input of calculating respectively as non-Gauss projection;
(5) during non-Gauss projection is calculated, the B that z obtains by training 1The battle array conversion obtains s 1And τ 1Signal; The B that obtains by training 2The battle array conversion obtains s 2And τ 2Signal is estimated as Support Vector data description, pivot respectively and the input of residual analysis.Here it should be noted that different according to process data X linear degree and non-Gauss's degree, may can only the acquisition unit sub-signal.
(6) in the Support Vector data description, to input data s 1, adopt following formula to calculate the D statistic of input data:
D 1 2 = | | s 1 - a 1 | | 2
If D 1 2 &le; R 1 2 , Illustrate that this sample point D statistics is normal, otherwise, illustrate that this sample point statistics is unusual.
In like manner, to input data s 2, if the non-gauss component in residual error space, adopt following formula to calculate the D statistic of input data:
D 2 2 = | | s 2 - a 2 | | 2
If D 2 2 &le; R 2 2 , Illustrate that this sample point D statistics is normal, otherwise, illustrate that this sample point statistics is unusual.
(7) during pivot is estimated, adopt following formula to calculate the T of input data 2Statistic:
T 2 = &tau; 1 T &tau; 1 ,
If T 2 < T &alpha; 2 , This sample point T is described 2Statistics is normal, otherwise, this sample point T 2Statistics is unusual.
(8) in the residual analysis, adopt following formula to calculate the Q statistic of input data:
Q = &tau; 2 T &tau; 2 ,
If Q < &delta; &alpha; 2 , Illustrate that this sample point Q statistics is normal, otherwise this sample point Q statistics is unusual, the process object breaks down;
(9) the process monitoring result is passed to DCS, by DCS system and fieldbus procedural information is delivered to operator station simultaneously and shows, make the execute-in-place worker can in time handle anomalous event.
In the on-line monitoring process, regularly the normal point of process status to be added among the training set TX, the repetition training process is so that the model in the support vector description that upgrades in time, residual analysis and the pivot statistics keeps model to have better dynamic.
The course monitoring method based on non-gauss component extraction and Support Vector data description in order to illustrate that better the present invention proposes utilizes industrial glass to melt process data, adds up method for supervising with traditional pivot analysis and compares.Fig. 4 has provided both monitored results.The result shows that the method that the present invention proposes can detect fault earlier, and is sensitiveer than pca method, and the alert rate of mistake is low.

Claims (5)

1, a kind of course monitoring method based on non-gauss component extraction and support vector description is characterized in that may further comprise the steps:
The data of key variables are as training sample TX when 1) reading production run and normally move;
2) training sample TX is carried out pre-service, make that the average of each variable is 0, variance is 1, obtains input matrix X ∈ R N * n, step is:
(1) computation of mean values: TX &OverBar; = 1 N &Sigma; i = 1 N T X i
(2) calculate variance: &sigma; x 2 = 1 N - 1 &Sigma; i = 1 N ( TX i - TX &OverBar; ) 2
(3) albefaction is handled: X = TX - TX &OverBar; &sigma; x 2
Wherein, TX is a training sample, and N is a number of training, and n is a variable number;
3) set up the pivot analysis model;
4) calculate based on the non-Gauss projection of particle swarm optimization algorithm, extract the non-gauss component in the data;
5), make up the statistical variable and the control limit of non-Gaussian signal based on Support Vector data description; Ask for the hypersphere that non-Gaussian signal distributes, find the solution following quadratic programming problem:
max &alpha; &Sigma; i &alpha; i < x i &CenterDot; x i > - &Sigma; i &Sigma; j &alpha; i &alpha; j < x i &CenterDot; x j >
s . t . &Sigma; i &alpha; i = 1 , &alpha; i &Element; [ 0 , C ] , i = 1 , &CenterDot; &CenterDot; &CenterDot; , N .
Obtain hyperspherical center a = &Sigma; i &alpha; i x i And radius: R 2 = < x k &CenterDot; x k > - 2 &Sigma; i &alpha; i < x k &CenterDot; x i > + &Sigma; i &Sigma; j &alpha; i &alpha; j < x i &CenterDot; x j > , x i, x jBe the sample point of non-gauss component, x kBe the borderline support vector of hypersphere;
6) pivot is estimated: the T that makes up the pivot gaussian signal 2Statistic, the calculation control limit; When insolation level is α, the control limit is calculated as follows:
T &alpha; 2 = l ( N 2 - 1 ) N - l F l , N - l ; &alpha; , L is the pivot number.
7) residual analysis: make up residual error gaussian signal Q statistic, the calculation control limit;
For arbitrary input residual error e i, the Q statistic is:
Q = | | e i | | 2 = e i T e i ;
When insolation level is α, the control limit is calculated as follows:
&delta; &alpha; 2 = g&chi; h ; &alpha; 2 ,
Wherein g = &rho; 2 2 &mu; , h = 2 &mu; 2 &rho; 2 , ρ and μ are respectively the variance and the average of Q statistic.
8) read variable data up-to-date in the production run as diagnostic data VX;
9) fault detect;
10) regularly the normal point of process status is added among the training set TX, repeats 2)~7) training process so that models such as the support vector description that upgrades in time, residual analysis and pivot statistics.
2. a kind of course monitoring method based on non-gauss component extraction and support vector description as claimed in claim 1 is characterized in that the described pivot analysis model step of setting up:
(1) covariance matrix of calculating X is designated as ∑ x;
(2) ∑ x is carried out svd, obtain characteristic root λ 1, λ 2..., λ n, λ wherein 1〉=λ 2〉=... 〉=λ n, the characteristic of correspondence vector matrix is U;
(3) calculate population variance and each eigenwert corresponding variance contribution rate, adding up from big to small by the variance contribution ratio of each eigenwert reaches set-point up to total variance contribution ratio, and it is r that note is chosen number;
(4) the preceding r row of selected characteristic vector matrix U constitute principal component space P ∈ R N * r, remaining columns constitutes the residual error space P ~ &Element; R n &times; ( n - r ) ;
(5) calculate respectively that PCA keeps variation per minute Z=XP and remain variation per minute Z ~ = X P ~ ;
3. a kind of course monitoring method based on non-gauss component extraction and support vector description as claimed in claim 1 is characterized in that the described step of calculating based on the non-Gauss projection of particle swarm optimization algorithm:
(1) makes Z (1)=Z ', i=1 asks for the strongest pairing separating vector b of non-Gauss's independent component of following formula by adopting the particle swarm optimization algorithm 1:
b ~ 1 = arg max a J ( a T Z ( 1 ) / | | a | | )
b 1 = b ~ 1 / | | b ~ 1 | |
Wherein J () is non-Gauss's metric function, its functional form be J (y) ≈ [E{G (y) }-E{G (v) }] 2, in the formula, v is zero-mean, unit variance gaussian variable, and G () is a non-quadratic function, and first independent component is s 1 = b 1 T Z ( 1 ) ;
(2) check s iGauss; Calculate non-Gauss and measure J (s i) significance degree is the confidence limit J of α αIf J is (s i)≤J α, s then iBe gaussian signal, non-Gaussian signal is counted m=i-1, forwards (5) to, otherwise continues;
(3)i=i+1, Z ( i ) = ( I r , r - b i - 1 b i - 1 T ) Z ( i - 1 ) = ( I r , r - &Sigma; j = 1 i - 1 b j - 1 b j - 1 T ) Z ( 1 ) , R in the formula is the dimension of input sample point;
(4) adopt the PSO algorithm to ask for the separating vector of i non-gauss component:
b ~ i = arg max a J ( a T M T Z ( i ) / | | Ma | | )
b i = M b ~ i / | | M b ~ i | |
In the formula, M = ( I r , r - &Sigma; j = 1 i - 1 b j - 1 b j - 1 T ) . By the projection of M battle array, guaranteed the orthogonality between the separating vector.I independent component is s i = b i T Z ( i ) , Return (2);
(5) output separation matrix B=(b 1, b 2..., b m), finish;
4, a kind of course monitoring method based on non-gauss component extraction and support vector description as claimed in claim 3 is characterized in that described particle swarm optimization algorithm steps:
(1) initialization a group particulate comprises granule amount, particulate random site and speed;
(2) estimate the fitness of each particulate;
(3) to each particulate, if adaptive value is greater than its desired positions, then with it as current desired positions; If adaptive value is then reset call number greater than full group's desired positions;
(4) as not reaching termination condition, then revise i particle's velocity and position, return (2) by following formula; Otherwise, finish
v i d &OverBar; k + 1 = wv i d &OverBar; k + c 1 r 1 ( p i d &OverBar; k - a ~ i d &OverBar; k ) + c 2 r 2 ( p g d &OverBar; k - a ~ i d &OverBar; k ) a ~ i d &OverBar; k + 1 = a ~ i d &OverBar; k + v i d &OverBar; k + 1 d &OverBar; = 1,2 , &CenterDot; &CenterDot; &CenterDot; , r &OverBar;
In the formula, a ~ i = [ a ~ i 1 , a ~ i 2 , . . . , a ~ ir ] Represent i particulate, V i=[V I1, V I2..., V Ir] be the speed of particulate, p i=[p I1, p I2..., p Ir] be the optimum position of this particulate experience, p g=[p G1, p G2..., p Gr] be the desired positions of all particulate experience in the colony, r is equal to dimension to be found the solution; W represents inertia weight, c 1And c 2Be positive acceleration constant, r 1, r 2Be the random number that is evenly distributed on interval [0,1].
5, a kind of course monitoring method based on non-gauss component extraction and support vector description as claimed in claim 1 is characterized in that described fault detect:
To data to be tested VX with when training the TX and the σ that obtain x 2Carry out albefaction and handle, and with the input of the data after the albefaction as the pivot analysis model, the P that obtains with training with It is divided into principal component space and residual error residual error space, matrix is input to non-Gauss projection module respectively after the conversion, obtain non-gauss component, the gauss component of principal component space, non-gauss component and gauss component with the residual error space, non-gauss component calculates corresponding statistic by support vector description, and gauss component calculates corresponding T by the pivot analysis of routine 2Statistic and Q statistic are if all less than control limit separately, judge that then this sample point is normal; Otherwise, think that the sample point statistics is unusual, the process object may break down.
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