CN106950945A - A kind of fault detection method based on dimension changeable type independent component analysis model - Google Patents

Abstract

The present invention discloses a kind of fault detection method based on dimension changeable type independent component analysis model, this method is first according to the difference of each column vector element numerical value of separation matrix in traditional independent component analysis (ICA) model in the off-line modeling stage, corresponds to each variable and assigns different weights to embody the difference of dimension.Then, due in separation matrix each column vector embody difference of the measurand on the projecting direction, therefore can have a variety of dimension changeable-shapeds, correspondence can set up multiple ICA Fault Models.During on-line monitoring, then this multiple ICA model is called to calculate corresponding monitoring and statisticses amount, and obtain final probabilistic type monitoring index to facilitate failure decision-making using Bayesian inference.Compared with conventional method, the inventive method not only takes into account the not equal importance of measurand in modeling, but also implements fault detect using multi-model.Description of this method to normal data feature is just more comprehensive, utilizes and obtains more superior fault detect effect.

Description

A kind of fault detection method based on dimension changeable type independent component analysis model

Technical field

Divide the present invention relates to a kind of industrial process fault detection method, more particularly to a kind of dimension changeable type independent entry that is based on Analyse the fault detection method of model.

Background technology

With extensive use of the computer technology in industrial system, modernization industry production process is marched toward " big to count According to the epoch ", the production process data resource of magnanimity provides solid number for monitoring, hard measurement, control, optimization of data-driven etc. According to basis.Wherein, the fault detection method of data-driven in having obtained unprecedented development in recent years, various Fault Models layers Go out not poor.With principal component analysis (Principal Component Analysis, PCA) and independent component analysis (Independent Component Analysis, ICA) algorithm obtains for the multivariate statistical process monitoring method of representative Academia and the extensive concern of industrial quarters, generate the fault detect embodiment of suitable different operating mode types.With based on PCA's Fault detection method is compared, and ICA algorithm is intended to be extracted in separate in higher order statistical meaning during modeling Composition information, the process data object of non-gaussian can be tackled.Just because of this, the fault detection method based on ICA is in monitoring When modernizing complex industrial process object, its acquired fault detect effect is generally superior to traditional PCA methods.

It is worthy of note that, either based on PCA, ICA Fault Model is also based on, they are in off-line modeling rank Section is required for pre-processing with the difference eliminating measurand dimension the sampled data execution standardization under nominal situation.Due to The corresponding sampled data of any one measurand goes wrong, it may be said that process enters improper running status, therefore The importance of each measurand is consistent.Before modeling in order to eliminate each measurand excursion (dimension) to modeling As a result influence, it is an imperative process that standardization, which unitizes the dimension of all measurands,.But, from event The angle of barrier detection is set out, if can embody the dimension difference of measurand, is equivalent to impart not for different variables Same weight coefficient, corresponding Fault Model will be more sensitive to some failure modes, so as to effectively be lifted Fault detect effect.Sampled data set under only make use of nominal situation at the off-line modeling stage due to Fault Model, A kind of modeling approach of unsupervised type can be regarded as.Therefore, only normal data and under conditions of lacking fault data, it is impossible to Targetedly dimension difference is embodied, at this moment standardization is seemingly just into the pretreatment side of " doing something against one's will " Case.In order to improve the monitoring effect of traditional Fault Model based on ICA, variable dimension is a kind of feasible embodiment party Case.Unique difficult point is the excavation dimension difference for having directiveness how on the premise of only normal data can be used to model, So as to set up the variable Fault Model of dimension on this basis.

The content of the invention

Technical problem underlying to be solved by this invention is：From normal data statistical property angle, excavate measurement and become Dimension difference between amount, and set up based on the ICA Fault Models of dimension changeable type to implement online fault detect.It is specific next Say, the thinking that the inventive method is first according to traditional IC A modelings in the off-line modeling stage obtains the separation matrix of model, Ran Houyi According to the difference of element numerical value in each column vector of separation matrix, different weights accordingly are assigned with the amount of embodiment for process measurement variable The difference of guiding principle, and ICA Fault Models are set up again.Because separation matrix has multiple column vectors, each column vector embodies Difference of the measurand on the projecting direction, to that should have a variety of different dimension changeable-shapeds, can set up multiple ICA failures Detection model.Therefore, during on-line implement fault detect, then this multiple ICA model is called to calculate corresponding monitoring and statisticses amount, and profit Final probabilistic type monitoring index is obtained with Bayesian inference, so as to simplify the last decision-making for whether triggering fault alarm.

The present invention solve the technical scheme that is used of above-mentioned technical problem for：One kind is based on dimension changeable type independent component analysis The fault detection method of model, comprises the following steps：

(1) data sample under collection production process normal operating condition, composition training dataset X ∈ R^n×m, and to each Variable is standardized, and it is 0 to obtain average, and standard deviation is 1 new data matrixWherein, n is number of training, and m is Process measurement variable number, R is set of real numbers, R^n×mRepresent the real number matrix of n × m dimensions.

(2) using PCA methods to data matrixCarry out whitening processing and obtain data matrix Z ∈ R^n×M.Wherein, M≤m is Variable number in matrix Z.

(3) it is training data using ICA algorithmSolution obtains separation matrix W ∈ R^m×p, wherein p is in separation matrix The number of column vector.

(4) according to separation matrix W=[w₁, w₂..., w_p] in each column vector w_j∈R^m×1The difference of element, corresponds to square Battle arrayIn each row assign different weights, data matrix X is obtained accordingly_j, wherein, lower label j=1,2 ..., p.

(5) it is respectively the training data matrix X after dimension changes to reuse ICA algorithm₁, X₂..., X_pSolve separation square Battle array (W₁, W₂..., W_p) and hybrid matrix (A₁, A₂..., A_p), set up corresponding p ICA models.

(6) the control limit corresponding to each ICA models malfunction monitoring statistic, reserving model parameter set Θ are determined₁, Θ₂..., Θ_pIn case on-line monitoring is called.

(7) the data x of the new sampling instant of gatherer process object_new∈R^m×1, to granting training dataset X identical marks in fact Quasi-ization processing is obtained

(8) according to each column vector w in separation matrix W_j, it is rightIn each measurand implement identical weighting processing, it is right The data vector y after dimension changes should be obtained₁, y₂..., y_p。

(9) calling model parameter set Θ₁, Θ₂..., Θ_pImplement online fault detect, and will be multiple using Bayesian inference A permeate probabilistic type index of monitoring and statisticses amount facilitates decision-making failure whether to occur.

Compared with conventional method, the advantage of the inventive method is essentially consisted in：

First, the inventive method makes the dimension of each measurand inconsistent by the way that different variables are assigned with different weights, It is achieved thereby that the not equal importance of measurand is taken into account in modeling.In addition, the inventive method implements dimension changeable type During modeling, employ multigroup different dimension variable manner to set up multiple ICA Fault Models.It is single compared to tradition For the fault detection method of ICA models, the inventive method is to implement fault detect with multi-model, to normal data feature Description is just more comprehensive.Therefore, the inventive method can lift the process monitoring of traditional fault detection method based on ICA Energy.It is worthy of note that, present invention side sets up the non-gaussian that Fault Model mainly considers process data using ICA algorithm Characteristic, the inventive method can certainly use for reference other nonlinear modeling algorithms, to realize the event to non-linear process object Barrier detection.

Brief description of the drawings

Fig. 1 is the implementing procedure figure of the inventive method.

Fig. 2 is ICA algorithm solution procedure schematic diagram.

Embodiment

The inventive method is described in detail below in conjunction with the accompanying drawings.

As shown in figure 1, the present invention discloses a kind of fault detection method based on dimension changeable type independent component analysis model.Tool The implementation steps of body are as follows：

Step 1：Gather the data sample under production process normal operating condition, composition training dataset X ∈ R^n×m, and it is right Each variable is standardized, and it is 0 to obtain average, and standard deviation is 1 new data matrixWherein, n is training sample Number, m is process measurement variable number, and R is set of real numbers, R^n×mRepresent the real number matrix of n × m dimensions.

Step 2：Using PCA methods to data matrixCarry out whitening processing and obtain data matrix Z ∈ R^n×M.Wherein, M≤m For variable number in matrix, specific implementation process is as follows：

1. calculateCovariance matrixWherein S ∈ R^m×m；

2. calculating matrix S all characteristic values and characteristic vector, and reject characteristic value less than 0.0001 and its corresponding Characteristic vector, obtains matrix B=[b of characteristic vector composition₁, b₂..., b_M]∈R^m×MAnd eigenvalue cluster into diagonal matrix D ∈R^M×M；

3. according to formulaIt is rightWhitening processing is carried out to obtain matrix Z；

Step 3：It is training data using ICA algorithmSolution obtains separation matrix W ∈ R^m×p, wherein p is in separation matrix Column vector number, corresponding implementation process is as shown in Fig. 2 specifically include below scheme：

1. setting needs the independent element number p extracted, and initializes k=1；

2. unit matrix I ∈ R are chosen^M×MIn kth arrange as vectorial c_kInitial value；

3. according to formula c_k←E{Zg(c_k ^TZ)}-E{h(c_k ^TZ)}c_kRenewal vector c_k, wherein, g (c_k ^TZ) with h (c_k ^TZ) Calculation is as follows：

g(c_k ^TZ)=4 (c_k ^TZ)³ (1)

h(c_k ^TZ)=12 (c_k ^TZ)² (2)

E { } represents to ask for the average value of vector；

4. to the vectorial c after renewal_kCarry out orthonomalization processing according to the following formula successively：

c_k←c_k/||c_k|| (4)

5. repeat 3.~4. until vector c_kMiddle each element no longer changes, and then preserves vector c_k

6. k ＜ p are judgedReturned 2. after k=k+1 if so, being put；If it is not, by d vector c of preservation₁, c₂..., c_pComposition one Individual Matrix C=[c₁, c₂..., c_d]∈R^M×d。

7. the hybrid matrix A and separation matrix W of ICA models are calculated respectively according to formula as follows：

A=C^TD^1/2B^T (5)

W=BD^-1/2C (6)

Step 4：According to separation matrix W=[w₁, w₂..., w_p] in each column vector w_j∈R^m×1The difference of element, is corresponded to MatrixIn each row assign different weights, obtain data matrix X according to formula as follows_j：

Wherein, the element w on lower label j=1,2 ..., p, diagonal_{J, 1}, w_{J, 2}..., w_{J, m}It is vectorial w respectively_jIn the 1st, 2 ..., m elements.

Step 5：It is respectively the training data matrix X after dimension changes to reuse ICA algorithm₁, X₂..., X_pSolve separation Matrix (W₁, W₂..., W_p) and hybrid matrix (A₁, A₂..., A_p), specific implementation process is similar with step 3, no longer goes to live in the household of one's in-laws on getting married here State.

Step 6：It is determined that the control limit corresponding to each ICA model malfunction monitoring statistics, reserving model parameter set Θ₁, Θ₂..., Θ_pIn case on-line monitoring is called, specific implementation process is as follows：

1. according to formula Y_j=X_jW_jCalculating obtains independent element matrix Y_j∈R^n×p；

2. according to formula E_j=X_j-Y_jA_j ^TCalculating obtains residual matrix E_j∈R^n×m；

3. according to formula t=diag (Y_jY_j ^T) calculate vector t ∈ R^n×1, wherein diag (Y_jY_j ^T) represent matrix Y_jY_j ^T's Diagonal entry constitutes column vector；

4. the numerical value for coming the n-th/10 is defined as statistic I by the element in vectorial t from being arranged to small descending greatly_j ² Control limit

5. according to formula q=diag (E_jE_j ^T) calculate vector q ∈ R^n×1；

6. the numerical value for coming the n-th/10 is defined as statistic Q by the element in vectorial q from being arranged to small descending greatly_j Control limit Q_{J, hm}；

7. reserving model parameter set

Step 7：The data x of the new sampling instant of gatherer process object_new∈R^m×1, it is identical to granting training dataset X in fact Standardization obtain

Step 8：According to each column vector w in separation matrix W_j, according to formula pair as followsIn each measurand it is real Apply identical weighting processing：

Correspondence obtains the data vector y after dimension changes_j∈R^1×m, wherein, the transposition of upper label T representing matrixs or vector.

Step 9：Calling model parameter set Θ₁, Θ₂..., Θ_pImplement online fault detect, and utilization Bayesian inference will Multiple monitoring and statisticses amounts are fused to probability level to facilitate decision-making failure whether to occur, and specific implementation process is as follows：

1. parameter set Θ is utilized_jIn separation matrix W_jAnd A_j, monitoring and statisticses amount I is calculated according to formula as follows_j ²With Q_{J, hm}：

I_j ²=y_jW_jW_j ^Ty_j ^T (9)

Q_j=| | y_j-y_jW_jA_j ^T||² (10)

In above formula, symbol | | | | represent to ask for the length of vector；

2. according to formula design conditions probability as follows

In above formula, N and F represent normal and fault condition respectively；

3. probability is calculated according to formula as follows

In above formula, β is confidence limit, generally takes β=99%；

4. new data is calculated according to formula as followsBelong to the probability of failure

5. calculated according to formula as follows and obtain corresponding to I_j ²The probability fusion index BI of statistic：

6. calculate and correspond to Q_jThe probability fusion index BQ of statistic implementation process and above step 2.~it is 5. similar, this In just repeat no more；

7. judge whether BI or BQ index values are more than 1- βIf so, then triggering fault warning；If it is not, it is next to continue monitoring The data sample of individual sampling instant.

Above-mentioned case study on implementation is only used for illustrating the specific implementation process of the present invention, rather than the present invention is limited System.In the protection domain of spirit and claims of the present invention, any modification made to the present invention both falls within the present invention's Protection domain.

Claims (4)

1. a kind of fault detection method based on dimension changeable type independent component analysis model, it is characterised in that comprise the following steps：

(1)：Gather the data sample under production process normal operating condition, composition training dataset X ∈ R^n×m, and become to each Amount is standardized, and it is 0 to obtain average, and standard deviation is 1 new data matrixWherein, n is number of training, and m was Journey measurand number, R is set of real numbers, R^n×mRepresent the real number matrix of n × m dimensions；

(2)：Using principal component analysis (Principal Component Analysis, PCA) method to data matrixCarry out Whitening processing obtains data matrix Z ∈ R^n×M.Wherein, M≤m is variable number in matrix；

(3)：It is training data using independent component analysis (Independent Component Analysis, ICA) algorithmAsk Solution obtains separation matrix W ∈ R^m×p, wherein p be separation matrix in column vector number；

(4)：According to separation matrix W=[w₁, w₂..., w_p] in each column vector w_j∈R^m×1The difference of element, corresponds to matrix In each row assign different weights, obtain data matrix X according to formula as follows_j：

Wherein, the element w on lower label j=1,2 ..., p, diagonal_{J, 1}, w_{J, 2}..., w_{J, m}It is vectorial w respectively_jIn the 1st, 2 ..., m elements；

(5)：It is respectively the training data matrix X after dimension changes to reuse ICA algorithm₁, X₂..., X_pSolve separation matrix (W₁, W₂..., W_p) and hybrid matrix (A₁, A₂..., A_p), specific implementation process is similar with step 3, repeats no more here；

(6)：It is determined that the control limit corresponding to each ICA model malfunction monitoring statistics, reserving model parameter set Θ₁, Θ₂..., Θ_pIn case on-line monitoring is called；

(7)：The data x of the new sampling instant of gatherer process object_new∈R^m×1, to granting training dataset X identical standards in fact Change processing is obtained

(8)：According to each column vector w in separation matrix W_j, according to formula pair as followsIn each measurand implement identical Weighting processing：

Correspondence obtains the data vector y after dimension changes_j∈R^1×m, wherein, the transposition of upper label T representing matrixs or vector；

(9)：Calling model parameter set Θ₁, Θ₂..., Θ_pImplement online fault detect, and utilize Bayesian inference by multiple prisons Survey statistic to be fused to probability level to facilitate decision-making failure whether to occur, specific implementation process is as follows：

1. parameter set Θ is utilized_jIn separation matrix W_jAnd A_j, monitoring and statisticses amount I is calculated according to formula as follows_j ²With Q_{J, hm}：

I_j ²=y_jW_jW_j ^Ty_j ^T (3)

Q_j=| | y_j-y_jW_jA_j ^T||² (4)

In above formula, symbol | | | | represent to ask for the length of vector；

2. according to formula design conditions probability as followsWith

$P_{I_j^2}\left({\stackrel{\‾}{x}}_{new}\right|N)=\exp (-\frac{I_j^2}{I_{j,\lim }^2}),P_{I_j^2}\left({\stackrel{\‾}{x}}_{new}\right|F)=\exp (-\frac{I_{j,\lim }^2}{I_j^2})---\left(5\right)$

In above formula, N and F represent normal and fault condition respectively；

3. probability is calculated according to formula as follows

$P_{I_j^2}\left({\stackrel{\‾}{x}}_{new}\right)=P_{I_j^2}\left({\stackrel{\‾}{x}}_{new}\right|N)\mathrm{\β}+P_{I_j^2}\left({\stackrel{\‾}{x}}_{new}\right|F)(1-\mathrm{\β})---\left(6\right)$

In above formula, β is confidence limit, generally takes β=99%；

4. new data is calculated according to formula as followsBelong to the probability of failure

$P_{I_j^2}\left(F\right|{\stackrel{\‾}{x}}_{new})=(1-\mathrm{\β})\frac{P_{I_j^2}\left({\stackrel{\‾}{x}}_{new}\right|F)}{P_{I_j^2}\left({\stackrel{\‾}{x}}_{new}\right)}---\left(7\right)$

5. calculated according to formula as follows and obtain corresponding to I_j ²The probability fusion index BI of statistic：

$BI=\underset{j=1}{\overset{p}{\Σ}}\left\{\frac{P_{I_j^2}\left({\stackrel{\‾}{x}}_{new}\right|F)P_{I_j^2}\left(F\right|{\stackrel{\‾}{x}}_{new})}{{\mathrm{\Σ}}_{j=1}^p{P}_{I_j^2}\left({\stackrel{\‾}{x}}_{new}\right|F)}\right\}---\left(8\right)$

6. calculate and correspond to Q_jThe probability fusion index BQ of statistic implementation process and above step 2.~it is 5. similar, here Repeat no more；

7. judge whether BI or BQ index values are more than 1- βIf so, then triggering fault warning；If it is not, continuing to monitor next adopt The data sample at sample moment.

2. a kind of fault detection method based on dimension changeable type independent component analysis model according to claim 1, it is special Levy and be, the specific implementation process that whitening processing is carried out in the step (2) is as follows：

1. calculateCovariance matrixWherein S ∈ R^m×m；

2. calculating matrix S all characteristic values and characteristic vector, and reject the characteristic value and its corresponding feature less than 0.0001 Vector, obtains matrix B=[b of characteristic vector composition₁, b₂..., b_M]∈R^m×MAnd eigenvalue cluster into diagonal matrix D ∈ R^{M ×M}；

3. according to formulaIt is rightWhitening processing is carried out to obtain matrix Z；

3. a kind of fault detection method based on dimension changeable type independent component analysis model according to claim 1, it is special Levy and be, the specific implementation process that separation matrix is solved in the step (3) is as follows：

1. setting needs the independent element number p extracted, and initializes k=1；

2. unit matrix I ∈ R are chosen^M×MIn kth arrange as vectorial c_kInitial value；

3. according to formula c_k←E{Zg(c_k ^TZ)}-E{h(c_k ^TZ)}c_kRenewal vector c_k, wherein, g (c_k ^TZ) with h (c_k ^TZ calculating) Mode is as follows：

g(c_k ^TZ)=4 (c_k ^TZ)³ (9)

h(c_k ^TZ)=12 (c_k ^TZ)² (10)

E { } represents to ask for the average value of vector；

4. to the vectorial c after renewal_kCarry out orthonomalization processing according to the following formula successively：

$c_k\←c_k-{\mathrm{\Σ}}_{l=1}^{k-1}\left({c_k}^T{c}_k\right)c_l---\left(11\right)$

c_k←c_k/||c_k|| (12)

5. repeat 3.~4. until vector c_kMiddle each element no longer changes, and then preserves vector c_k

6. k ＜ p are judgedReturned 2. after k=k+1 if so, being put；If it is not, by d vector c of preservation₁, c₂..., c_pConstitute a square Battle array C=[c₁, c₂..., c_d]∈R^M×d。

7. the hybrid matrix A and separation matrix W of ICA models are calculated respectively according to formula as follows：

A=C^TD^1/2B^T (13)

W=BD^-1/2C (14)

4. a kind of fault detection method based on dimension changeable type independent component analysis model according to claim 1, it is special Levy and be, the specific implementation process of the step (6) is as follows：

1. according to formula Y_j=X_jW_jCalculating obtains independent element matrix Y_j∈R^n×p；

2. according to formula E_j=X_j-Y_jA_j ^TCalculating obtains residual matrix E_j∈R^n×m；

3. according to formula t=diag (Y_jY_j ^T) calculate vector t ∈ R^n×1, wherein diag (Y_jY_j ^T) represent matrix Y_jY_j ^TIt is diagonal Line element constitutes column vector；

4. the numerical value for coming the n-th/10 is defined as statistic I by the element in vectorial t from being arranged to small descending greatly_j ²Control System limit

5. according to formula q=diag (E_jE_j ^T) calculate vector q ∈ R^n×1；

6. the numerical value for coming the n-th/10 is defined as statistic Q by the element in vectorial q from being arranged to small descending greatly_jControl Limit Q_{J, hm}；

7. reserving model parameter set