CN106907927A - The flexible manifold insertion electric melting magnesium furnace fault monitoring method of one seed nucleus - Google Patents

Abstract

The present invention relates to the flexible manifold insertion electric melting magnesium furnace fault monitoring method of a seed nucleus, step is：Gather all kinds of fault datas and normal data；Off-line modeling is carried out, according to the data acquisition KICA monitoring models for collecting, KFME fault diagnosis models is trained；On-line monitoring, real time on-line monitoring, gatherer process data are carried out using KICA monitoring models；If monitoring failure, Fault Identification is carried out by KFME monitoring models；If identification is out of order, primary fault monitoring process terminates；It is out of order if do not recognized, analyzes the fault data that is not diagnosed to be and be marked, goes to training KFME fault diagnosis model steps.Foundation of the inventive method using a small amount of flag data and a large amount of Unlabeled datas to realize for process monitoring model, model is more accurate, Data Dimensionality Reduction can well be realized and retain primary data information (pdi), the accuracy rate and antijamming capability of fault diagnosis model are improved, the monitoring to unknown failure is realized.

Description

The flexible manifold insertion electric melting magnesium furnace fault monitoring method of one seed nucleus

Technical field

The present invention relates to a kind of electric melting magnesium furnace Fault monitoring and diagnosis technology, the flexible manifold insertion of a specifically seed nucleus Electric melting magnesium furnace fault monitoring method.

Background technology

In China, the Automation of Manufacturing Process degree of magnesia is poor, and production process is complicated, has non-thread in production process Property, non-gaussian, the characteristic such as close coupling, be susceptible to failure, so as to cause huge economic loss, be badly in need of a kind of effective process Monitoring method is predicted to production status, reduces rate of breakdown, reduces economic loss.In recent years, with computer and The development of automation, the data in production process can be preserved, and the security of production is also increasingly taken seriously.Utilize The course monitoring method that one class of a large amount of historical datas is based on data-driven has obtained extensive concern, and becomes process prison A study hotspot in control field.

In process of production, veteran workman ensure that production safety is carried out and obtains high-quality product, so And, such production effect, general workman is but difficult to realize, and thereby how realizes industry using the Heuristics of veteran worker Production monitoring, becomes important research direction.In recent years, the data of a large amount of higher-dimensions can be by reliable data acquisition system System is obtained, but when fault detect is realized using data, data are more and dimension becomes greatly influence process monitoring effect Key factor, therefore when process monitoring is carried out using data, yojan data dimension becomes a critically important problem, and its is straight Connect the effect for affecting real process monitoring.In in the past few years, many process monitoring algorithms are suggested, and these algorithms all do not have Have and make full use of the Heuristics of veteran worker and realize the process monitoring of actual industrial.

The content of the invention

Production process monitoring algorithm for magnesia in the prior art does not make full use of Heuristics of veteran worker etc. Deficiency, the problem to be solved in the present invention is to provide a kind of Heuristics for combining veteran worker, using a small amount of flag data and A large amount of Unlabeled datas are realized for the flexible manifold insertion electric melting magnesium furnace fault monitoring method of core that process monitoring model is set up.

In order to solve the above technical problems, the technical solution adopted by the present invention is：

The flexible manifold insertion electric melting magnesium furnace fault monitoring method of a seed nucleus of the invention, comprises the following steps：

Gather all kinds of fault datas and normal data；

Off-line modeling is carried out, according to the data acquisition KICA monitoring models for collecting, KFME fault diagnosis models is trained；

On-line monitoring, real time on-line monitoring, gatherer process data are carried out using KICA monitoring models；

If monitoring failure, Fault Identification is carried out by KFME monitoring models；

If identification is out of order, primary fault monitoring process terminates.

Be out of order if do not recognized, analyze the fault data that is not diagnosed to be and be marked, go to training KFME therefore Barrier diagnostic model step.

According to the data acquisition KICA monitoring models for collecting, training KFME fault diagnosis models are comprised the following steps：

1) centralization and mark are carried out to the fault data under the malfunction that is collected into and the normal data under normal condition Quasi-ization treatment, obtains initial data；

2) above-mentioned initial data is mapped to feature space, by the normal data in feature space initial data as sample Data；

3) KICA models are set up by the general principle of core independent entry method using sample data；

4) be mapped to the sample data of feature space by the data after KICA model treatments as KFME methods modeling Data；

5) general principle of the flexible manifold embedded mobile GIS of core of knowledge based analysis is modeled, and obtains KFME models.

It is as follows that general principle according to core independent entry method sets up KICA model steps：

31) to being mapped to the sample data of feature space in normal data carry out centralization and standardization, marked Nuclear matrix after standardization

32) nuclear matrix after standardizationIt is middle calculate characteristic value and characteristic vector, extract d maximum characteristic value with And corresponding characteristic vector, its number of characteristic value for extracting determines according to following standards：

Wherein λ_iValue is characterized, i is characterized value numbering；

33) for the normal data of feature space, calculate whitening matrix and the data of mapping are carried out into albefaction, obtain white The data of change；

34) according to negentropy formula J (y)=[E { G (y) }-E { G (v) }]²To be processed by the data of albefaction, so that really Make transition matrix C_n, further determine that non-linear component.

It is as follows that the general principle of the flexible manifold embedded mobile GIS of core analyzed according to knowledge based is modeled step：

51) according to characteristic vector y and training data X_w∈R^f×n, obtain eigenmatrix Y ∈ R^n×c；

52) according to eigenmatrix Y ∈ R^n×cConstruction neighbour scheme and calculate figure Laplce matrix L=D-S, wherein, D is spy Levy matrix Y ∈ R^n×cDiagonal matrix, S is characterized matrix Y ∈ R^n×cSymmetrical matrix, the diagonal element D of diagonal matrix D_iiIt is spy Levy every column element sum in matrix S；

53) training data is projected into high-dimensional feature space using nonlinear mapping function Φ ()；

54) according to the feature of data in high-dimensional feature space, kernel function is selected；

55) value of above-mentioned kernel function is calculated；

56) failure predication matrix F is calculated according to training data_w, obtain projection matrix W and bias term b；

57) according to online data, fault detect matrix F is calculated_t, obtain on-line monitoring matrix F_t。

Element S in symmetrical matrix S_ii'Calculate in the following way：If x_iIt is x_i'M Neighbor Points, then S_ii'=exp (- ||x_i-x_i'||²/ t), otherwise S_ii'=0, wherein, t is empirical value, x_i'It is historical data, i'=1,2 ..., n.

The feature space is the high-dimensional feature space of 4 dimensions and the 4 dimension above.

The invention has the advantages that and advantage：

1. the inventive method can be realized for mistake using a small amount of flag data and a large amount of Unlabeled datas well The foundation of journey monitoring model, this causes that this model is more accurate, and monitoring effect is improved.

2. data after the inventive method is processed using KICA are modeled to KFME, can not only reduce the computing of program into This and the fault diagnosis effect of KFME methods can be improved, can well realize Data Dimensionality Reduction and retain primary data information (pdi), The accuracy rate of fault diagnosis model is improved, effective fault diagnosis is realized, the antijamming capability of algorithm not only high, and realize Monitoring to unknown failure.

Brief description of the drawings

Fig. 1 is the inventive method flow chart；

Fig. 2 is the electric melting magnesium furnace structural representation being related in the present invention；

Fig. 3 A are the diagnostic result diagram of the modeling that 0.5% flag data is predicted model；

Fig. 3 B are the diagnostic result diagram of the modeling that 1% flag data is predicted model；

Fig. 3 C are the experimental result diagram of the modeling that 1.5% flag data is predicted model；

Fig. 4 A are the diagnostic result diagram of the modeling that 0.5% data are predicted model；

Fig. 4 B are the diagnostic result diagram of the modeling that 1% flag data is predicted model；

Fig. 4 C are the experimental result diagram of the modeling that 1.5% flag data is predicted model；

Fig. 5 is the diagnostic result figure to continuous break down 1 and failure 2 using the inventive method.

Specific embodiment

With reference to Figure of description, the present invention is further elaborated.

As shown in figure 1, the flexible manifold insertion electric melting magnesium furnace fault monitoring method of a seed nucleus of the invention, comprises the following steps：

Gather all kinds of fault datas and normal data；

Off-line modeling is carried out, according to the data acquisition KICA monitoring models for collecting, KFME fault diagnosis models is trained；

On-line monitoring, real time on-line monitoring, gatherer process data are carried out using KICA monitoring models；

If monitoring failure, Fault Identification is carried out by KICA monitoring models；

If identification is out of order, primary fault monitoring process terminates.

Be out of order if do not recognized, analyze the fault data that is not diagnosed to be and be marked, go to training KFME therefore Barrier diagnostic model step.

Wherein, according to the data acquisition KICA monitoring models for collecting, training KFME fault diagnosis models include following step Suddenly：

1) centralization and standardization are carried out to the data under the malfunction that is collected into and the data under normal condition, Obtain initial data；

2) above-mentioned initial data is mapped to feature space, by the data under the normal condition in feature space initial data As sample data；

3) KICA models are set up by the general principle of core independent entry method using sample data；

4) be mapped to the sample data of feature space by the data after KICA model treatments as KFME methods modeling Data；

5) general principle of the flexible manifold embedded mobile GIS of core of knowledge based analysis is modeled, and obtains KFME models.

Step 2) in, sample data is represented as x_k∈R^m, k=1 ..., n, by using nonlinear mapping function data Feature space is mapped to, nuclear matrix K ∈ R are calculated^n×n；

Step 3) KICA models are set up by the general principle of core independent entry method using sample data comprise the following steps：

31) data being mapped under the normal condition in the sample data of feature space are carried out at centralization and standardization Reason, the nuclear matrix after being standardized

32) nuclear matrix after standardizationIt is middle calculate characteristic value and characteristic vector, extract d maximum characteristic value with And corresponding characteristic vector, its number of characteristic value for extracting determines according to following standards：

Wherein λ_iValue is characterized, i is characterized value numbering；

33) for the data under the normal condition of feature space, calculate whitening matrix and the data of mapping carried out into albefaction, Obtain by the data of albefaction；

34) according to negentropy formula J (y)=[E { G (y) }-E { G (v) }]²To be processed by the data of albefaction, so that really Make transition matrix C_n, further determine that non-linear component.

Step 5) general principle of the flexible manifold embedded mobile GIS of core of knowledge based analysis is modeled, and obtains KFME models Comprise the following steps：

51) the characteristic vector y and training data X according to normal data_w∈R^f×n, obtain eigenmatrix Y ∈ R^n×c；

Normal data, for setting up KICA models, it is necessary to (can be referred to as to new data after model is set up to be finished It is online data or real time data) it is monitored, it is determined whether meet model, it is incongruent to be failure.First use normal number According to KICA models are set up, real time data is monitored after obtaining model, judges whether faulty generation, so also determined that Which data is failure.It is input to again in KFME models, it is normal that such KFME models can just sort out data, or The first failure or second failure, are the refinements to failure.Equally, KFME is also required to training data and is modeled, and is related to The training data of KFME, comprising failure and normal data.

52) according to eigenmatrix Y ∈ R^n×cConstruction neighbour scheme and calculate figure Laplce matrix L=D-S, wherein, D is spy Levy matrix Y ∈ R^n×cDiagonal matrix, S is characterized matrix Y ∈ R^n×cSymmetrical matrix, the diagonal element D of diagonal matrix D_iiIt is spy Levy every column element sum in matrix S；

53) training data is projected into feature space using nonlinear mapping function Φ ()；

54) according to the feature of data in feature space, kernel function is selected；

55) value of above-mentioned kernel function is calculated；

56) failure predication matrix F is calculated according to training data_w, obtain projection matrix W and bias term b；

57) according to online data, fault detect matrix is calculated, obtains on-line monitoring matrix F_t。

Element S in symmetrical matrix S_ii'Calculate in the following way：If x_iIt is x_i'M Neighbor Points, then S_ii'=exp (- ||x_i-x_i'||²/ t), otherwise S_ii'=0, wherein, t is empirical value, x_i'It is historical data, i'=1,2 ..., n.

Feature space in the present invention refers to the high-dimensional feature space of 4 dimensions and the 4 dimension above.

The present invention is by KICA (Kernel Idependent Component Analysis, core independent entry) methods and KFME (Kernel Flexible Manifold Embedding, the flexible manifold insertion of core) method fusion, will be linear using geo-nuclear tracin4 Algorithm is promoted, and can process nonlinear data, and in the present invention, both approaches all use the core letter of same form Number.But they are the learning algorithms of different field, KFME is the semi-supervised algorithm based on figure, can diagnose known fault, right Interference is very sensitive, and KICA is unsupervised algorithm, can realize malfunction monitoring, removes interference information.Therefore in the present invention, make Gone to realize fault detect and removal interference information with KICA methods, fault diagnosis is realized using KFME, in order to realize this purpose, When failure is detected, the input data that the independent element of fault data is used as KFME methods goes to realize that failure is examined Disconnected, KFME carries out treatment to independent element and finds its corresponding fault category, so as to realize fault diagnosis.

The present invention in electric melting magnesium furnace running, gathers electric smelting respectively by taking the electric melting magnesium furnace of structure as shown in Figure 2 as an example Three magnitudes of voltage of electrode (UA, UB, UC) of magnesium stove, the current value (IA, IB, IC) of three electrodes, three electrode position values (PA, PB, PC) and furnace temperature Temp, and data are processed.

Make X=[x₁,x₂,...,x_n]∈R^m×nIt is data set, it is considered to each column data x in data matrix_k∈R^m(k= 1 ..., n), n represents the number of sample, and m represents variable number.Nonlinear function Φ:R^m→ F throws the observed data of luv space Shadow is to high-dimensional feature space Φ (x_k) ∈ F, data x_kMapping be represented as Φ (x_k), therefore in the covariance square of feature space Battle array is represented as：

Make Θ=[Φ (x₁),...,Φ(x_n)], the covariance matrix C of feature space_ΦC can be written as_Φ=(1/n) Θ Θ^T.Θ is to be mapped to the data set after high-dimensional feature space.

Define a n × n Gram matrix Ks be：

[K]_ij=K_ij=<Φ(x_i),Φ(x_j)>=k (x_i,x_j)

Gram matrixes are expressed as K=Θ^TΘ, this kernel function k (x_i,x_j)=<Φ(x_i),Φ(x_j)>Avoid non-linear The execution of mapping and inner product is calculated in higher dimensional space, it is final to cause that the inner product of feature space is calculated and realized.Using radially Base kernel function (k (x_i,x_j)=exp (- | | x_i-x_j||²/ σ)) and to feature space data Φ (x_k) implementation center and standard Change operation, the nuclear matrix after centralization is expressed as：

In formula1_nIt is being for all elementsSquare formation.

To nuclear matrixStandardization can be obtained：

Carry out Eigenvalues Decomposition for above-mentioned matrix, below calculating formula can obtain：

By Eigenvalues Decomposition, make the nuclear matrix after standardizationD maximum eigenvalue λ₁≥λ₂≥...≥λ_dWith And corresponding orthogonal vectors α₁,α₂,…,a_d, according to the relation between Gram nuclear matrix and feature space covariance matrix, association side The characteristic value of difference matrix is λ₁/n,λ₂/n,…,λ_d/ n, its corresponding characteristic vector is expressed as follows：

Content according to the above discussion, C_ΦEigenvectors matrix V=[v₁,v₂,...,v_d] be expressed as：

V=Θ H Λ^-1/2H is characterized vector matrix, and Λ is characterized the diagonal matrix of value composition

In formula, H=[α₁,α₂,...,α_d] and Λ=diag (λ₁,λ₂,...,λ_d), then this whitening matrix P is expressed as：

P^TC_ΦP=I

Thus, carrying out albefaction to the data in high-dimensional feature space by following expression formula goes interference to process：

Z=P^TΦ (x) z are the data after albefaction

Albefaction details is as follows：

In formulaIt is K_xCarry out what average centralization was obtained, K_x=Θ^TΦ(x)。

According to z ∈ R^d, it is necessary to look for meetingIndependent entry Then independent entry can be written as：

Transformation matrix C ∈ R in formula^d×pAnd C^TC=D.

In order to be met the independent element of requirement, standardized independent element y is made_nFor：

From above formula it is recognised thatAndAccording to albefaction step, obtain Unrelated whitened data z such that it is able to matrixInitialization.

I in formula_pBe p dimension unit matrix and 0 be p × (d-p) dimension null matrix.

The committed step of KICA methods is exactly calculating matrix C_n, in order to calculate C_n, each column vector is initialised, and Constantly the value is updated, i-th independent element y is finally caused_n,i=(c_n,i)^TZ can obtain Gaussian, the c of maximum_n,i Represent C_nI-th row, in order to realize independent entry y_n,i(i=1 ..., statistical iteration p) then make its non-Gaussian system maximize.It is negative Entropy as non-Gaussian system evaluation criterion, negentropy is bigger, and non-Gaussian system is stronger.Following formula is the calculating formula of negentropy value.

J (y)=[E { G (y) }-E { G (v) }]²

The average that y is assumed in formula is 0, and variance is 1.V is gaussian variable, and its average is 0, and variance is 1, and G is any Non- quadratic function；E is to seek the functional symbol used by entropy.

Matrix C_nCalculation procedure：

(1) number of selection independent element p, in order to remove calculating matrix C_n, counter i ← 1 is set.

(2) initialization vector c_n,iIt is the i-th row of matrix in equation (4.13).

(3) maximize negentropy to estimate, orderG is the first derivative of G in formula, G ' is the second dervative of G.

(4) in order to exclude the information having been found that, orthogonalization is performed：

(5) standardize

(6) if c_n,iDo not restrain, then return to step 3.

(7) if c_n,iRestrain, then output vector c_n,i.I ← i+1 is made if i≤p and step 2 is returned to.

The core independent element of initial data can be obtained.

In order to by the monitoring to production process, realize safety in production, control limit needs are defined, therefore in KICA failures In monitoring method, Hotelling ' s T²Statistic and SPE statistics are defined, and Hotelling ' s T²Statistic The control limit of control limit and SPE statistics is also defined respectively.Then said when statistic exceedes its corresponding control limit Bright failure occurs.In KICA methods, Hotelling ' s T²It is defined：

The present invention calculates T using single argument Density Estimator²The control limit of statistic, Density Estimator function is as follows：

L is the control limit that calculate in formula, and normal sampled data is represented as l_i, i=1 ..., n, sample Number is n, and for the calculating of control limit, h is critically important, and it is referred to as smoothing factor, and K () represents kernel function, accounts for probability Density function99% coboundary as T²The control limit of statistic.

In order to monitor the change of residual error space non-statistical part in KICA models, then SPE statistics are defined：

In formulaAndIt is the estimation of z, it can be calculated by following formula：

SPE control limits are according to χ²Distribution is calculated.

μ=b/2a, h=2a²/b

A and b are respectively the average and variance for estimating to obtain from normal data in formula.

In actual monitoring process, real-time industrial data are collected, now with the KICA models for establishing to real-time Data carry out malfunction monitoring, and detailed step is summarized as follows：

(1) real time data is obtained, centralization and normalizing operation is carried out to it, the real time data is designated as x_i∈R^m

(2) core vector k is calculated_t∈R^1×n, its calculating formula is [k_t]_j=[k_t(x_j,x_t)], x in formula_jIt is normal operational data x_j∈R^m, j=1 ..., n, x_tIt is the data after step one treatment.

(3) to core vector k_tDo average centralization treatment：

(4) standardization：

(5) by following formulas, whitening processing is carried out to real time data, its non-linear component can be extracted.

(6) independent element of the data is obtained, its calculating formula is

(7) T of real time data is calculated²With SPE monitoring statisticss amounts.

(8) T is monitored², SPE whether exceed its corresponding statistic.

KICA methods by using going to realize fault detect, the faulty generation in KICA methods detect real-time industrial production When, the fault data is input in the KFME models having built up as input, is realized failure by KFME methods and is examined It is disconnected.Its step is as follows：

(1) new product practice is collected as input, is input in the KICA models having built up；

(2) when statistic is prescribed a time limit beyond its corresponding control, then faulty generation is shown；

(3) KICA treatment fault data as KFME models input；

(4) by KFME methods, failure is implemented accurately classification；

But it is over time, old due to equipment in actual production because known failure is limited Change, and equipment change, unknown failures before some can also occur, and work as conduct after these failures are found by KICA monitorings The input of KFME, it can not carry out fault diagnosis by KFME models because KFME methods are semi-supervised methods, the method according to Rely in flag data, that is to say, that its known fault that can only classify, now need to carry out new fault data fault signature and Failure cause is analyzed, and finally adds it to again in the training data of KFME models, updates KFME models, and it is right finally to realize The fault diagnosis of the failure.

History data set X=[x in electric melting magnesium furnace running₁,x₂,...,x_i,x_i+1,...,x_n]∈R^f×n, wherein, x_i It is historical data, n is the number of data sampling, and f is variable number, i=1,2 ..., n；Partial history data are marked, Flag data is[1, n), the class label of flag data is y to k ∈_i∈ { 1,2 ..., j ..., C }, y_iValue be mark Data x_iAffiliated class, j=1,2 ..., C, C represents the number of the affiliated class of flag data, and assigns y using priori_iIt is actual Meaning；

In the present invention, normal data, the data of failure 1, the class label of the data of failure 2 take 1,2,3, i.e. y respectively_i∈{1,2, 3}。

Structural feature matrix Y ∈ R^n×c, in formula

Construction symmetrical matrix S ∈ R^n×n, element S in matrix S_ii'Calculate in the following way：If x_iIt is x_i'M neighbour Point, then S_ii'=exp (- | | x_i-x_i'||²/ t), otherwise S_ij=0, wherein, t is empirical value, i'=1,2 ..., n；

Calculate figure Laplce matrix L=D-S, L ∈ R^n×n, D is diagonal matrix, and its diagonal element is

History data set X is mapped to high-dimensional feature space, i.e. X → Φ (X) by kernel function Φ from original data space； In kernel method, existing characteristics mappingF therein_fIt is a feature space, input Data are mapped to this feature space by Feature Mapping function, in the present invention, will by nonlinear mapping function Φ () All data include that mark and Unlabeled data are mapped to higher dimensional space from lower dimensional space, and this treatment can cause nonlinear problem It is converted into linear problem or approximately linear problem.

According to the principle of manifold embedded mobile GIS, foundation can obtain the Optimized model of failure predication matrix：

Failure predication matrix may be defined as F=Φ (X_w)^TW+eb^T, from this formula, it is known that failure predication matrix is subject to The hard constraints of data, such constraint often causes that acquisition final mask generalization ability is not strong, therefore, in order that obtain it using More flexibly, failure predication matrix is rewritten as F=h (Φ (X_w))+F₀=Φ (X_w)^TW+eb^T+F₀, projection matrix is W ∈ in formula R^f×c, bias term is b ∈ R^c×¹And e=[1,1 ..., 1]^T, in this approach, target is while finding optimal failure Prediction matrix F, regression residuals matrix F₀And linear regression function h (Φ (X)).

Initial optimization function is Tr (F-Y)^TU(F-Y)+Tr(F^TMF), in order to prevent over-fitting, and fitting is caused Error is minimum, and regular terms α (| | W | | are added in above-mentioned optimization object function²+ξ||F₀||²), obtain more accurately pre- Mark remembers matrix.By analyzing, following object function is can obtain：

Wherein, two factor alphas are for balancing two different regular terms, α >=0, ξ >=0 and M=L=D-S, M with ξ ∈R^n×nIt is Laplacian Matrix, the concrete form of diagonal matrix U is as follows：

Make F- Φ (X_w)^TW-eb^TGo to replace residual error F₀, new optimization object function can be obtained as follows：

Failure predication matrix F is calculated according to history off-line data X, eigenmatrix Y and Laplacian Matrix L_w：

Solve projection matrix W and bias term b：

According to final majorized function, in order to obtain optimal solution, so as to seek local derviation to b and W respectively to the formula, and It is 0 to make its local derviation：

Obtain projection matrix W and bias term b：

W=ξ (ξ Φ (X) H_cΦ(X)^T+I)^-1Φ(X)H_cF_w=PF_w

In formula, P=ξ (ξ Φ (X_w)H_cΦ(X_w)^T+I)^-1Φ(X_w)H_c。

The new object function on failure predication matrix is as follows：

Processed by above formula, obtained：

G (F)=Tr (F-Y)^TU(F-Y)+Tr(F^TMF)+α(Tr(F^TP^TPF)+ξTr(QF-F)^T(QF-F))

Variable F derivations to function g (F) and to make it be that 0 can obtain：

Above formula is solved, the analytic expression of failure predication matrix can be expressed：

F=(U+M+ α ξ (Q-I)^T(Q-I)+αP^TP)^-1UY

OrderΦ(X_c)=Φ (X) H_c, can obtain：

αξP^TΦ(X)H_cΦ(X)^TP+αP^TP=α ξ P^TΦ(X)H_c=α ξ H_cΦ(X)^TP

Q=H_cΦ(X)^TP+(1/n)ee^T

P=ξ (ξ Φ (X) H_cΦ(X)Φ(X)^T+I)^-1Φ(X)H_c

After abbreviation, can obtain：

Q=H_cΦ(X)^Tξ(ξΦ(X)H_cΦ(X)^T+I)^-1Φ(X)H_c+(1/n)ee^T

=H_cΦ(X)^Tξ(ξΦ(X_w)H_cΦ(X_w)^T+I)^-1Φ(X_c)+(1/n)ee^T

=ξ H_cΦ(X)^TΦ(X_c)(ξΦ(X)H_cΦ(X)^T+I)^-1+(1/n)ee^T

Obtain failure predication matrix F_wExpression formula it is as follows：

In formula, K (X, X)=Φ (X)^TΦ (X), H_c=I- (1/n) ee^T。

In electric melting magnesium furnace production process, the online process variable Monitoring Data X of electric melting magnesium furnace is obtained_tIt is standardized, and counts Calculate malfunction monitoring matrix F_t。

F_t=Φ (X_t)^TW+eb^T=[ξ H_cK(X_t,X_w)H_c(ξK(X_w,X_w)H_c+I)^-1+I-H_c]F_w

According to F_tThe feature of test data can directly be understood, that is, can know that the data are fault data or normal number According to because F_tEvery a line correspond to each data point, only one of which is 1 data, and actual conditions in theory in often going It is that every a line has a numerical value for maximum,, close to 1, the row corresponding to the number are the class belonging to the data, i.e. row correspondence for it The class in C classes, you can fault detection and diagnosis are carried out according to following formula：

First group of 670 sampled data is emulated, the data containing normal data and failure 1 in these data, its Preceding 300 data are normal data, start to introduce failure 1 after 300 points, in order to determine that flag data number is examined for failure The influence of disconnected effect, has carried out three experiments, in first time experiment (experiment one), have selected each mark in three class data Data are predicted the modeling of model；In second experiment (experiment two), each two flag datas in three class data are have selected It is predicted the modeling of model；In third time experiment (experiment three), each three flag datas are carried out in have selected three class data The modeling of forecast model.The experimental result of these three experiments is distinguished as shown in fig.3 a 3 c, the normal condition broken line table in figure Show, failure 1 represents that failure 2 is represented with "+" with point.

From Fig. 3 A as can be seen that before 300 points, normal status value is near 0.6, and the state value of failure 1 is in Near 0.4, the state value of failure 2 is near 0, and normal status value is maximum in the figure, i.e., tables of data reveals its feature, institute Can consider that preceding 300 data points are the data point of normal condition, but due to normal condition and the state value of the state of failure 2 Very close to so in the case where parameter regulation is bad, it is easy to same data occur and had not only showed 2 states that are out of order but also had showed Go out the situation of normal condition, that is, ambiguity occur, cannot thus understand the real feature of data, so as to cannot realize that failure is examined Survey, and it could be theoretically argued that each data point uniquely only shows a kind of state, and the corresponding state of state for showing Value should be close to 1.Although the state value of normal condition is maximum herein, but its value is only 0.6, not close to 1, so Its fault detect effect of expression of experiment one is simultaneously bad.

From Fig. 3 B as can be seen that in preceding 300 data points, the state value of normal condition is near 0.8, failure 1 State value be near 0, the state value of failure 2 is near 0, because the state value of the normal condition of preceding 300 points is in Near 0.8, very close to 1, and in preceding 300 data points, close to 0, this just can be sufficiently for the state value of failure 1 and failure 2 Illustrate that preceding 300 data points show normal condition, i.e., now electric melting magnesium furnace production safety is carried out.In rear 370 points, can send out The state value of existing failure 1 is near 0.9, and close to 1, while the state value of normal condition and failure 2 is near 0, this just says It is bright to break down 1 in rear 370 points, and in this experiment, state value tends to 1 state and the state value of two other state Wide apart, it is to avoid ambiguous appearance, this just illustrates well realize failure when using this small amount of flag data Monitoring.

From Fig. 3 C it is recognised that in preceding 300 data points, its tables of data reveals normal condition, i.e. electric-melting magnesium production Normal condition is operated in, in rear 370 data points, failure 1 occurs, and in figure, moreover it is possible to knew before 300 points, The change that the state value of failure 1 starts slowly is big, and this just imply that failure 1 will may occur.Observation Fig. 3 B and 3C, Neng Goufa Now, the experiment effect of experiment two and experiment two is basically identical, but experiment three has used more flag datas, and in reality In production, flag data is very unobtainable, therefore experiment three wastes flag data, and is illustrated using the mark in experiment two Numeration evidence can just reach effective fault diagnosis effect.

Test data is mainly the data including normal data and failure 1, its data volume pair for testing flag data In the influence of the monitoring effect of failure 1, not shadow of the data volume of test badge data for the fault diagnosis effect of failure 2 Ring.Therefore used 670 test datas in Fig. 4 A~4C to study the shadow of the data volume for fault diagnosis of flag data Ring, in this 670 flag datas, preceding 330 data points are normal data, and 340 data points are the data of failure 2 afterwards.For this Test data, have also been made three experiments, in first time experiment (experiment one), have selected each flag data in three class data It is predicted the modeling of model；In second experiment (experiment two), each two flag datas are carried out in have selected three class data The modeling of forecast model；In third time experiment (experiment three), each three flag datas are predicted in have selected three class data The modeling of model, its experimental result is respectively Fig. 4 A~4C.

From Fig. 4 A as can be seen that before 330 points, normal status value is near 0.6, at the state value of failure 2 Near 0.4, the state value of failure 1 is near 0, and normal state value is maximum in figure, i.e., tables of data reveals its feature, Before 330 data points be the data point of normal condition, but because the state value of normal condition and the state of failure 2 connects very much Closely, so in the case where parameter regulation is bad, it is easy to same data point occurs and ambiguity occurs, cannot thus understand The real feature of data, this cannot just realize fault detect, and it could be theoretically argued that each data point uniquely only shows one The state of kind, and the corresponding state value of state for showing should be close to 1.Although the state value of normal condition is maximum herein , but its value is only 0.6, not close to 1, so experiment one fault detect effect and bad.

From Fig. 4 B as can be seen that in preceding 330 data points, the state value of normal condition is near 0.8, failure 1 State value be near 0, the state value of failure 2 is near 0, because the state value of the normal condition of preceding 330 points is in Near 0.8, very close to 1, and in preceding 300 data points, close to 0, this just can be sufficiently for the state value of failure 1 and failure 2 Illustrate that preceding 330 data points show normal condition, i.e., now electric melting magnesium furnace is operated under security situation.In rear 340 points, Can find that the state value of failure 2 is near 0.8, close to 1, while the state value of normal condition and failure 1 is near 0, this Just explanation breaks down 2 in rear 340 points, and in this experiment, state value tends to 1 state and the shape of two other state State value wide apart so that same data point can not possibly occur in monitoring and both show normal condition, the shape that is out of order is showed again State, this just illustrates well realize malfunction monitoring when using this flag data.

It is recognised that in preceding 330 data points, its tables of data reveals normal condition from Fig. 4 C, in rear 340 data In point, failure 2 occurs, and before 330 points, the change that the state value of failure 1 starts slowly is big, and this just imply that failure 2 may Will occur.Observation Fig. 4 B and 4C, it can be found that, the experiment effect of experiment two and experiment three is basically identical, but experiment three makes With more flag datas, and in actual production, flag data is very unobtainable, therefore experiment three wastes mark Data, and illustrate to can be achieved with effective fault diagnosis using the flag data in experiment 2.

Comparison diagram 3A~3C and Fig. 4 A~4C, the effect that the effect of this Model Diagnosis failure 2 does not have tracing trouble 1 is good, For Fig. 4 A~4C, after 330 points, it fluctuates very seriously up and down, and is occurred in that near the 360th data point both faulty 2 occur, while there is the feature of normal condition again, this illustrates this model in tracing trouble 2, and effect is not fine, and this is Because the modeling data of, failure 2 is not enough, and the feature and normal data of failure 2 are distinguished not substantially so that the algorithm without The good tracing trouble 2 of method.

In order to whether verification algorithm can continuously diagnose two failures, so having done a new experiment simulation, the emulation Parameter still as Simulation Parameters above, i.e. α=10^-8, ξ=10⁵, and 1370 data points have been selected as survey Examination data, the analogous diagram of this experiment can find that failure 1 occurs after 300 points, in 1000 points as shown in figure 5, observe the figure Failure 2 occurs afterwards.

The method that the present invention proposes the flexible manifold insertion of core based on core independent entry knowledge analysis, because it is combined always The Heuristics of workman, has certain superiority compared to other algorithms.This method carrys out logarithm by using veteran worker's knowledge According to being marked, Heuristics is set to be represented by machine language, so that machine can learn to this knowledge.By In in real process, the mark to data needs to expend substantial amounts of manpower and materials, therefore the quantity with acquainted data is very Few, and the inventive method can be realized being supervised for process using a small amount of flag data and a large amount of Unlabeled datas well The foundation of model is surveyed, this causes that this model is more accurate, and monitoring effect is improved.Because KFME is more sensitive and raw to noise Producing data has non-Gaussian feature, therefore proposes the KFME fault monitoring methods based on KICA knowledge analysis, and the method is used Data after KICA treatment to model KFME, can not only reduce the computing cost of program and can improve KFME methods Fault diagnosis effect, this be due to being processed by KICA after data can realize well Data Dimensionality Reduction and retain original number it is believed that Breath, improves the accuracy rate of fault diagnosis model, realizes effective fault diagnosis.Therefore method proposed by the present invention, not only improves The antijamming capability of algorithm, and realize the monitoring to unknown failure.

Kernel method be latest developments get up one kind in the widely used non-linear regression method in machine learning field, it lead to Cross nonlinear conversion Φ (x) and the sample vector x in the n dimension input spaces is mapped to high-dimensional feature space F, by former space Nonlinear problem be converted into the problem of linear or approximately linear in higher dimensional space, line is then used in high-dimensional feature space The method of property is processed.Kernel method has an application, such as constituent analysis of core pivot in many algorithms, core deflected secondary air, Composite copolymer method etc..

Core Independent Component Analysis are the popularizations of independent entry method, and independent entry method can be good at extracting non-gaussian data In independent element and remove the influence of interference signal, but it is also restricted, because it assumes that data are all linear, institutes So that independent entry extraction can not be carried out to nonlinear data, therefore core Independent Component Analysis are generated, it is by by non-linear number Linearization approximate treatment is carried out according to higher dimensional space is projected to, and the complicated calculations of higher dimensional space are avoided using geo-nuclear tracin4, finally Realize and the independent entry of nonlinear data is extracted.

Claims (6)

1. the flexible manifold of a seed nucleus is embedded in electric melting magnesium furnace fault monitoring method, it is characterised in that comprise the following steps：

Gather all kinds of fault datas and normal data；

Off-line modeling is carried out, according to the data acquisition KICA monitoring models for collecting, KFME fault diagnosis models is trained；

On-line monitoring, real time on-line monitoring, gatherer process data are carried out using KICA monitoring models；

If monitoring failure, Fault Identification is carried out by KFME monitoring models；

If identification is out of order, primary fault monitoring process terminates；

It is out of order if do not recognized, analyzes the fault data that is not diagnosed to be and be marked, is gone to training KFME failures and examine Disconnected model step.

2. the flexible manifold insertion electric melting magnesium furnace fault monitoring method of core as described in claim 1, it is characterised in that according to collection The data acquisition KICA monitoring models for arriving, training KFME fault diagnosis models are comprised the following steps：

1) centralization and standardization are carried out to the fault data under the malfunction that is collected into and the normal data under normal condition Treatment, obtains initial data；

2) above-mentioned initial data is mapped to feature space, by the normal data in feature space initial data as sample number According to；

3) KICA models are set up by the general principle of core independent entry method using sample data；

4) be mapped to the sample data of feature space by the data after KICA model treatments as KFME methods modeling data；

5) general principle of the flexible manifold embedded mobile GIS of core of knowledge based analysis is modeled, and obtains KFME models.

3. the flexible manifold insertion electric melting magnesium furnace fault monitoring method of core as described in claim 1, it is characterised in that：It is only according to core It is as follows that the general principle of vertical unit's method sets up KICA model steps：

31) to being mapped to the sample data of feature space in normal data carry out centralization and standardization, standardized Nuclear matrix afterwards

32) nuclear matrix after standardizationIt is middle to calculate characteristic value and characteristic vector, extract the d characteristic value and right of maximum The characteristic vector answered, the number of its characteristic value extracted determines according to following standards：

$\frac{{\mathrm{\&lambda;}}_i}{\mathrm{sum}\left({\mathrm{\&lambda;}}_i\right)}\&GreaterEqual;0.0001$

Wherein λ_iValue is characterized, i is characterized value numbering；

33) for the normal data of feature space, calculate whitening matrix and the data of mapping are carried out into albefaction, obtain by albefaction Data；

34) according to negentropy formula J (y)=[E { G (y) }-E { G (v) }]²To be processed by the data of albefaction, so that it is determined that going out Cross Matrix C_n, further determine that non-linear component.

4. the flexible manifold insertion electric melting magnesium furnace fault monitoring method of core as described in claim 1, it is characterised in that：According to being based on It is as follows that the general principle of the flexible manifold embedded mobile GIS of core of knowledge analysis is modeled step：

51) according to characteristic vector y and training data X_w∈R^f×n, obtain eigenmatrix Y ∈ R^n×c；

52) according to eigenmatrix Y ∈ R^n×cConstruction neighbour scheme and calculate figure Laplce matrix L=D-S, wherein, D is characterized square Battle array Y ∈ R^n×cDiagonal matrix, S is characterized matrix Y ∈ R^n×cSymmetrical matrix, the diagonal element D of diagonal matrix D_iiIt is characterized square Per column element sum in battle array S；

53) training data is projected into high-dimensional feature space using nonlinear mapping function Φ ()；

54) according to the feature of data in high-dimensional feature space, kernel function is selected；

55) value of above-mentioned kernel function is calculated；

56) failure predication matrix F is calculated according to training data_w, obtain projection matrix W and bias term b；

57) according to online data, fault detect matrix F is calculated_t, obtain on-line monitoring matrix F_t。

5. the flexible manifold insertion electric melting magnesium furnace fault monitoring method of core as described in claim 4, it is characterised in that：Symmetrical matrix Element S in S_ii'Calculate in the following way：If x_iIt is x_i'M Neighbor Points, then S_ii'=exp (- | | x_i-x_i'||²/ t), it is no Then S_ii'=0, wherein, t is empirical value, x_i'It is historical data, i'=1,2 ..., n.

6. the flexible manifold insertion electric melting magnesium furnace fault monitoring method of core as described in claim 1, it is characterised in that：The feature Space is the high-dimensional feature space of 4 dimensions and the 4 dimension above.