CN107065843A - Multi-direction KICA batch processes fault monitoring method based on Independent subspace - Google Patents
Multi-direction KICA batch processes fault monitoring method based on Independent subspace Download PDFInfo
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Abstract
The present invention relates to a kind of multi-direction KICA batch processes fault monitoring method based on Independent subspace, comprise the following steps：Batch process three-dimensional data X (I × J × K) is gathered, using multidirectional KICA, three-dimensional data is launched into 2-D data by batch and handled；Wherein I is number of batches, and J is variables number, and K is sampled point number；Off-line modeling is carried out to the 2-D data deployed by batch, geo-nuclear tracin4 is added on the basis of ICA, nonlinear data is mapped to high-dimensional feature space, then linear process is carried out in higher dimensional space；Using T2Process is monitored on-line with SPE statistics；The fault message that each subdata is obtained is collected, and whether Counting statistics amount transfinites.The present invention is improved the method for traditional KICA disposed of in its entirety, and many sub-spaces are divided into primary data and carry out detailed KICA analyses, the KICA for setting up multi-model is monitored, hiding information is amplified simultaneously, is effectively grasped local message, is improved the monitoring rate of failure.
Description
Technical field
It is specially a kind of based on the multi-direction of Independent subspace the present invention relates to a kind of fault detection and diagnosis technical field
KICA batch process fault monitoring methods.
Background technology
ICA (Independent Component Correlation Algorithm, independent component analysis) is raw to industry
The solution of the non-gaussian data of production process provides method, improves the accuracy and generality of malfunction monitoring.Batch process is not
Be same as common procedure, with it is multiple batches of the characteristics of, and substantially do not distinguished between batch, the time of each batch is not also fixed very much.
Throughput rate, production status of batch process etc. are again random changes.This production status allows workpeople to deal with very spine
Hand, it is desirable that this irregular change of reduction, make production process try one's best it is regular seek, feasible to the monitoring of batch process have
Effect.
For the heavy property of production process data, traditional KICA (kernel Independent Component
Correlation Algorithm, core independent component analysis) directly to data analysis, it can no doubt monitor the entirety of data
Information.But overall control limit can only embody overall performance, can not clearly be expressed for a certain local circumstance, some
Failure is only relevant with few number variable, or is seldom sampled, it is easy to is just diluted by overall data, causes monitoring effect not
Substantially or at all just monitoring does not come out, and causes the decline of monitoring rate.
The content of the invention
Directly there is monitoring effect to data analysis for KICA traditional in the prior art and substantially or do not cause monitoring rate
Decline the problems such as, the problem to be solved in the present invention be to provide it is a kind of can effectively grasp local message, improve failure monitoring
Multi-direction KICA batch process fault monitoring method of the rate based on Independent subspace.
In order to solve the above technical problems, the technical solution adopted by the present invention is：
A kind of multi-direction KICA batch processes fault monitoring method based on Independent subspace of the present invention, including following step
Suddenly：
1) collection batch process three-dimensional data X (I × J × K), using multidirectional KICA, three-dimensional data is launched into by batch
2-D data is handled；Wherein I is number of batches, and J is variables number, and K is sampled point number；
2) off-line modeling is carried out to the 2-D data deployed by batch, geo-nuclear tracin4 is added on the basis of ICA, will be non-linear
Data are mapped to high-dimensional feature space, then carry out linear process in higher dimensional space；
3) T is applied2Process is monitored on-line with SPE statistics；The fault message that each subdata is obtained is carried out
Collect, whether Counting statistics amount transfinites.
Off-line modeling is carried out to the 2-D data deployed by batch to comprise the following steps：
2.1) R.I. process three-dimensional data X carries out data normalization processing, the data X ' after being standardized；
2.2) the independent entry s of the non-gaussian distribution of the data X ' after normalized；
2.3) k sub- data spaces are divided according to independent metamessage；
2.4) KICA modelings are carried out to every sub-spaces respectively.
Step 2.3) in, dividing k sub- data spaces according to independent metamessage is：According to independent metamessage s1, s2,
s3,...skSeek out to the maximum data of its contribution degreeBuild similarity matrix R；Build i-th of subdata
Space, takes the process variable value corresponding to L maximum Similarity value of the row of similarity matrix i-th, is configured to a sub-spaces；Weight
Duplicate step, k sub- data spaces are constructed from 1 to k for i.
Step 2.4) in, KICA is carried out to every sub-spaces respectively and is modeled as：
2.4.1) to i-th of subdata space κiTo carry out KICA modeling analysis, for i-th of subdata space, its mistake
Cheng Bianliang isWillIt is standardized, the subdata steric course after being standardized
Data are
2.4.2) by Nonlinear Mapping by the subspace process data after standardizationIt is mapped to high dimensional feature
In the F of space,Obtaining new subdata space data sets is
Its covariance matrix is obtained first, and expression formula is：
It is expressed as：C=(1/L) Φ ΦT
Add kernel function K () to aid in calculating, take the kernel function to be：
Wherein, K ∈ RL×L, l=1,2 ... L, L is constant, and l is variable name, m=1,2 ... L；
Obtained result is standardized to nuclear matrix is：
In formula, ILFor constant matrices, its element is equal, is 1/N；
Nuclear matrix is standardized for：
It is rightCarry out Eigenvalues Decomposition：
In formula, λ ' isCharacteristic value, α be characteristic vector corresponding with λ ', obtainD characteristic vector, wherein d
For its maximum positive characteristic value number, characteristic value is arranged as：
λ′1≥λ′2≥…≥λ′d (2.38)
Corresponding characteristic vector is：
α1, α2..., αd (2.39)
The characteristic value number of highest dimension is defined, it is necessary to meet：
Obtain covariance matrix C d characteristic value respectively λ1′/L,λ2′/L,…,λd'/L, corresponding characteristic vector is
v1,v2,…,vd, physical relationship is as follows：
Write a Chinese character in simplified form into：
V=Φ H Λ-1/2 (2.42)
Wherein V=[v1,v2,…,vd] it is characterized vector matrix, Λ=diag (λ1,λ2,…,λd) and H=[α1, α2...,
αd] be respectivelyD eigenvalue of maximum diagonal matrix and its corresponding eigenvectors matrix；Covariance matrix C new table
It is shown as：
It is P to make whitening matrix, then：
PTCP=I (2.45)
Data matrix in feature space after albefaction is：
Obtained by formula (2.46)：
So obtaining independent entry y is：
Step 3) in apply T2Carrying out on-line monitoring to process with SPE statistics includes procedure below：
3.1) real-time batch process data X is gatherednew；
3.2) data prediction, seeks independent entry s, divides k sub-spaces；
3.3) every sub-spaces KICA is modeled and calculates the T of the data in every sub-spaces2With SPE statistics；
3.4) collect whether Counting statistics amount transfinites.
Step 3.3) in every sub-spaces KICA modeled and calculate the T of the data in every sub-spaces2With SPE statistics
Amount, is to use T2Statistics and SPE count the calculating for being controlled limit, wherein using T2Statistics calculates control limit：
For 1~k sub- data spaces, its Hotelling-T2Statistical definition is：
Above formula expansion is obtained：
Wherein, y is independent entry, and D is the diagonal matrix of nuclear matrix characteristic value；
Using the method for Density Estimator, stochastic variable y independent same distribution sample is y1,y2,…,yn, its probability density
Function is f (y), and k () is kernel function, hnIt is a constant for smooth coefficients, it is relevant with sample number n, and hn＞ 0, then：
The probability density function calculated by Density Estimator method, be respectively to the parameter that it works sample size,
The selection of kernel function and smooth coefficients, wherein for known sample size, passing through smooth coefficients hnSize and kernel function k
The form of () obtains probability density；Selection for kernel function needs to meet three conditions:K (y)=K (- y)；K(y)≥0；∫
K (y) dy=1；
Optimal smooth coefficients are selected by mean square error, that is, the variance and the quadratic sum of deviation estimated：
N is total sample number, and u is correlated variables, and o is the symbol of dimensionless in mathematics；
Optimal smooth coefficients h is drawn accordinglynExpression formula：
Now, MSE is minimum, with n-4/5Speed tend to 0；hoptWith speed n-1/5→ 0 convergence；
Wherein, gaussian kernel function
hn=Cn-0.2δ
Wherein C=1.06, corresponding to a constant of gaussian kernel function, δ is the standard deviation of sampling, and n is total sample number；
By the T for calculating normal data2Statistic, estimates the probability density distribution of object, knows further according to probability statistics
Know the coboundary for obtaining the regions of occupation probability density function f (y) 99%, the value of border this point is T2The control of statistic
Limit.
Control limit is calculated with SPE statistics, is specially：
Wherein,ZiIt is characterized by the mapping data after albefaction in space, is calculated value,
K is k-th of constant of subspace one,CiFor i-th of vector in initial matrix C, CkTo be initial
K-th of vector in Matrix C, ekFor residual error, residual error is further calculated
For the sampling x at a new k momentnew∈Xnew, first it standardize obtains X "new, then pass through again
Subspace partition, the process data for obtaining i-th of subdata space isMonitoring and statisticses are calculated finally by Monitoring Data
Measure Ti 2And SPEi：
T2Statistic is：
SPE statistics are：
Wherein
For the monitoring result of each subdata, i.e., for i-th of subdata space, if T2Statistic transfinites, by it
1 is designated as, is otherwise 0, then obtains equation below：
s.t.1≤i≤m
For SPE statistics, formula is provided accordingly：
s.t.1≤i≤m
For the display result in each subdata space, statistical result is combined by a kind of method added up with weight,
For T2Statistic is as a result as follows：
For SPE statistics, as a result for：
In formula, σiFor the weight shared by i-th of spatial statistics, andδ is limit value, that is to say, that when
Accumulated weights and during more than this limit value, it is believed that failure occurs.
It is determined that weight σ shared by i-th of spatial statisticsiWhen, with exponential function form,
Wherein, ToS is T2Or SPE statistics, ToSlFor its corresponding control limit；Then again to σ 'iPlace is normalized
Reason, obtains σi。
The invention has the advantages that and advantage：
1. the present invention is directed to the multiple batches of problem of batch process, its data is set to turn into three-dimensional data battle array, using multidirectional
KICA, is effectively launched into 2-D data by three-dimensional data and is handled；Geo-nuclear tracin4 is added on the basis of traditional IC A, will be non-
Linear data is mapped to high-dimensional feature space, then carries out linear process in higher dimensional space, data are handled using KICA
Analysis, afterwards using T2Process is monitored on-line with SPE statistics；Method to traditional KICA disposed of in its entirety is improved, right
Primary data has carried out data cutting, is divided into many sub-spaces, and the subdata space for being directed to each data is carried out in detail
KICA analyses, the KICA for setting up multi-model monitor, hiding information amplified simultaneously, effectively grasps local message, and raising is former
The monitoring rate of barrier.
2. the present invention is in batch process there are multiple batches of, non-gaussian feature data to be supervised respectively by dividing subspace
Survey, data, which belong to the complex effects of different batches and control line in tradition KICA methods, before overcoming can only embody overall performance
And a small number of failures occur and the caused undesirable phenomenon of monitoring is diluted by overall data.
It is the independent metamessage according to data 3. the present invention is different from conventional random space RSM divisions, data is carried out
Selectively divide, make each subdata space that there is otherness and validity, then for the monitoring of failure, the present invention is every
The fault message that one subdata is obtained is collected, and makes monitoring effect more very clear.
4. the inventive method is monitored by subspace multi-model simultaneously, good effect can be played；Finally to penicillin
In fermentation process faulty operation change input quantity bottoms stream rate of acceleration and faulty operation change input quantity air mass flow this two
The validity of monitoring checking this method of class fault data.
Brief description of the drawings
Fig. 1 is penicillin fermentation schematic diagram；
Fig. 2 presses batch expanded schematic diagram for the multi-direction of batch process；
Fig. 3 A are independent component analysis schematic diagram；
Fig. 3 B be subspace between there is no the division methods schematic diagram of common portion but exhaustive data；
Fig. 3 C are that subspace can have common factor to abandon the division methods schematic diagram of data；
Fig. 4 is Subspace partition schematic diagram；
Fig. 5 is the off-line data modeling procedure figure in the specific embodiment of the invention；
Fig. 6 is the online data malfunction monitoring flow chart in the specific embodiment of the invention；
Fig. 7 A are the T of the random space-division method under conventional process mode of failure one2Statistic curve map；
Fig. 7 B are the SPE statistic curve maps of the random space-division method under conventional process mode of failure two；
Fig. 7 C are the T for the multi-direction KICA methods that failure one is divided under processing mode of the present invention based on Independent subspace2
Statistic curve map；
Fig. 7 D are the SPE for the multi-direction KICA methods that failure one is divided under processing mode of the present invention based on Independent subspace
Statistic curve map；
Fig. 7 E are T in each Independent subspace in the present invention2Statistic curve map；
Fig. 7 F are SPE statistic curve maps in each Independent subspace in the present invention；
Fig. 8 A are the T for the multi-direction KICA methods that failure two is divided under processing mode of the present invention based on Independent subspace2
Statistic curve map；
Fig. 8 B are the SPE for the multi-direction KICA methods that failure two is divided under processing mode of the present invention based on Independent subspace
Statistic curve map.
Embodiment
With reference to Figure of description, the present invention is further elaborated.
The multi-direction KICA batch processes fault monitoring method that a kind of Independent subspace of the present invention is divided, including following step
Suddenly：
1) collection batch process three-dimensional data X (I × J × K), using multidirectional KICA, three-dimensional data is launched into by batch
2-D data is handled；
2) off-line modeling is carried out to the 2-D data deployed by batch, geo-nuclear tracin4 is added on the basis of ICA, will be non-linear
Data are mapped to high-dimensional feature space, then carry out linear process in higher dimensional space；
3) T is applied2Process is monitored on-line with SPE statistics；The fault message that each subdata is obtained is carried out
Collect, whether Counting statistics amount transfinites.
Step 1) in, as shown in Fig. 2 obtaining the three dimensional process data X (I × J × K) of batch process, wherein I is batch number
Mesh, J is variables number, and K is sampled point number.By each batch as a direction, by time and the data of process variable
Be blended together the new 2-D data of composition, so as to be converted into two-dimensional matrix X (I × KJ), then so the two-dimensional matrix is every
Row all includes all data of a batch.Data normalization processing is still carried out after same variable expansion, this needs
Different batches, different sampling instants and the standardization of different variables to process variable, can so facilitate data processing,
Also remain data characteristics simultaneously.
Step 2) in, off-line modeling is carried out to the 2-D data deployed by batch and comprised the following steps：
2.1) training dataset X carries out data normalization processing, the data X ' after being standardized；
2.2) the independent entry s of the non-gaussian distribution of the data X ' after normalized；
2.3) k sub- data spaces are divided according to independent metamessage；
2.4) KICA modelings are carried out to every sub-spaces respectively.
Step 2.1) in, data are standardized, each will be changed into average value for 0 by variable, variance is 1
Standardized variable.Comprise the following steps that：
2.1.1) the training dataset X obtained after multi-direction expansion is：
Wherein, xi(i=1,2 ..., it is n) one group of sampling column vector.
It is hereby achieved that the process variable matrix after standardization, is：
Wherein, xi,jFor an element, x ' in former data matrixI, jFor one in the data matrix after standardization
Element, xjFor j column elements,For the average of j column elements, i is line number, and j is columns, and n is total line number, and m is total columns, sjFor j
The standard deviation of row, X ' is the later process data of standardization；
2.1.2 the covariance matrix S of sample) is obtained：
Wherein, X ' is the later process data of standardization.
2.1.3) draw after covariance matrix, continue covariance matrix SsEigenvalues Decomposition is carried out, P can be represented
For：
Ss=P Λ PT (2.7)
Wherein, diagonal matrix Λ includes non-negative eigenvalue λ1≥λ2≥...≥λi>=0, λiIt is i-th of characteristic value, m is spy
Value indicative number, P is X ' load vector, by eigenvalue λiCorresponding unitization characteristic vector is constituted, and PTP=I, I are units
Matrix.
2.1.4 score matrix T) is obtained
Select a load matrix P ∈ Rm×lRow, the load vector for making it be associated with preceding l characteristic value is corresponding, then
The projection of X ' to lower dimensional space is included in score matrix T：
T=X ' P (2.8)
The selection of pivot number is highly important, generally chooses l (l ＜ m) individual principal components to replace former m related change
Amount, this l principal component can just represent the information that former m variable is included.Generally exceeded using principal component accumulation contribution rate
85% retains the number of pivot, such as following formula
Data X ' after standardization is decomposed into the form of apposition sum, is shown below
Wherein, ti∈RnReferred to as score vector (score vector), also referred to as principal component；pi∈RmReferred to as load vector
(loading vector), represents the projecting direction of principal component.Above formula is converted into matrix form, is：
X '=TPT (2.11)
Wherein, T=[t1 t2…tm] it is referred to as score matrix, P=[p1 p2…pm] it is referred to as load matrix.
2.1.5) show that ICA models ask for independent metamessage
By 2.1.4) drawAs shown in fig.3 a 3 c, the independent entry of its non-gaussian distribution
It is expressed asWherein k is independent entry number, then relation therebetween is：
X '=As (2.12)
In formula,It is a unknown hybrid matrix, obtains this matrix, so as to obtains solely
Vertical member s, can be obtained by formula (2.12)：
S=A-1x′ (2.13)
Take A inverse matrix W, W ∈ Rk×n, W is the mixed matrix of solution, so formula 3.13 can be write as：
S=WX ' (2.14)
Present purpose is exactly to ask for solving mixed matrix W.The present embodiment utilizes differential entropy criterion, it is assumed that y is a random vector,
Its probability density is p (y), then y differential entropy is：
So y negentropy is：
J (y)=H (yg)-H(y) (2.16)
Due to being difficult to accomplish in the actual central negentropy that calculates, calculate for convenience, for formula (2.16), take J approximate table
Up to formula：
J(y)≈τ[E{G(y)}-E{G(yg)}]2 (2.17)
In formula：τ is a constant, and τ ＞ 0, G () is any non-quadratic function.
So can be obtained by following expression：
J(s)≈k[E{G(wTt)}]2-2k*E{G(wTt)}*E{G(sg)}+k[E{G(sg)}]2 (2.18)
S in formulag=wTT, can obtain the w for making J reach minimum.Obtaining the mixed matrix W of solution is：
So can be to obtain S.
S=[s1,s2,…,sk] (2.20)
On Subspace partition as shown in figure 4, step 2.3) in, dividing k sub- data spaces according to independent metamessage is：
According to independent metamessage s1,s2,s3,…skSeek out to the maximum data of its contribution degreeBuild similarity moment
Battle array R；I-th of subdata space is built, the row of similarity matrix i-th is taken to the process variable value corresponding to L big Similarity value,
It is configured to a sub-spaces；Repeat step 2.3), k sub- data spaces are constructed from 1 to k for i.
Subdata space, the problem of solving otherness well, because independent metamessage are divided around each independent entry
Independent between batch, information difference is larger, and just there is otherness the subspace set up around independent metamessage naturally, and draws at random
Divide not this property.
Build the similarity matrix of independent entry
It can be obtained by formula (2.14)：
So, for i-th of independent entry si, can be expressed as：
si=wi1×x1′+wi2×x2′+…+win×xn′, (2.22)
Wherein：I=1,2 ... k.
In order to around siSubdata space is set up, s can most be given expression to by selectingiThe data volume of information, due to s and x dimension not
Together, it has not been convenient to directly ask for similitude, so first to select to siThe maximum data of contribution degree, closest to si'sAgain by
Similitude is calculated with each data volume, subdata space is obtained.Think herein withSimilarity it is higher, data x is just to independence
Metamessage s contribution degree highest.Herein, each x ' is first defined to siContribution degree：
That data for taking contribution degree maximum represent si, so accordinglyFor：
Wherein j is to make μijThe j corresponding to maximum is obtained, if xsiRepeat to choose, then postpone to making μijObtain Second Largest Value
J, by that analogy, obtain representing the data set x of each independent metamessages',
Set up subdata space κ nowi, for whole process variable x1', x2′,x3′,…,xn', ask for respectively its withLinear correlation degree, as only corresponding to the subspace that the high volume of data of linear correlation degree is built intensively embodies it
Vertical member siCharacteristic information, thenWith xj' the degree of correlation be：
So to wholeIt is correlating with x ', it is represented by：
Accordingly, for all independent metamessage s1,s2,s3,...skWith all process variable x '1, x '2,x′3,…,x′n, give
Going out correlation matrix is：
From formula (2.28), obtained rijIt is bigger, mean that corresponding x 'jWith independent entry siSimilarity it is bigger,
So this variable information just can more clearly embody independent entry siCharacteristic information.Again with such a subspace data
Collection carrys out modeling analysis, and just the detailed fault message detected in this direction of energy, thus can targetedly be monitored very much
Go out the fault message of various aspects, the concrete condition of careful understanding internal system makes monitoring effect be greatly improved.
Only need to according to obtained similarity matrix, it is possible to mark off desired subdata space.So obtain
Subdata space κ1, κ2, κ3... κkS can be just represented well1,s2,s3,...skInformation, while also meet it is above right
The requirement of each Subspace difference and validity.Otherness is it is well understood that because independent entry s1,s2,s3,...skInherently that
This is separate, so have very big otherness between them, so around the subdata space of their foundation, it is natural with regard to body
Show the different respective characteristics of independent entry, be also just provided with obvious otherness；On validity, the subdata space of foundation has
Enough data volumes, and also according to effective standard when foundation, it is ensured that validity.
The present embodiment is to build subdata space κiExemplified by, specific method is：
Take the i-th row r of similarity matrixi1,ri2,ri3,…rin, i=1,2 ... k, corresponding each coefficient correlation represents
For independent metamessage siRespectively with each process data x '1, x '2,x′3,…,x′nSimilarity situation, choose and siSimilarity
L high data set up subdata space κi, that is to say, that for every a line, a ranking will be done to similarity, can be obtained
To as follows：
Then L corresponding x ' variableJust constitute subdata space κiWhole modeling numbers
According to thus just constructing subspace κi。
I repeats this process by 1 to k, it is possible to construct 1~k sub- data space κ1, κ2, κ3... κk。
It is not arbitrarily to choose on the selection of the size in each subdata space, that is, constant L.L chose
Greatly, then the data volume in each subdata space is excessive, and the amount of calculation in so each subdata space also can be very big, and otherness is not
It is obvious that local details can not be embodied well；If L chooses too small, the data in each subdata space
Amount is very few, and space is too small and to have met with into data unicity too strong, without rational validity.So, on L selection, this hair
The method of bright use is：
First, obtain for each independent metamessage siSimilarity absolute value average it is as follows：
Then, the number u that similarity is more than average is calculatedi, such computing is done for each independent metamessage,
Obtain u1,u2,u3,…uk, then obtain
Wherein,It is more than the number u of average for similarityiAverage.
According to one by adding up the optimization inequality that similarity is constituted：
Thus the minimum L for meeting inequality is obtained, enough information is so can guarantee that, meets validity, while
Meet the otherness in each subdata space.
Step 2.4) in, off-line data modeling procedure figure as shown in Figure 5 carries out KICA modelings to every sub-spaces respectively
For：
2.4.1) to i-th of subdata space κiTo carry out KICA modeling analysis.For i-th of subdata space, its mistake
Cheng Bianliang isFirst willIt is standardized, the subdata space after being standardized
Process data is
2.4.2) by Nonlinear Mapping by the subspace process data after standardizationIt is mapped to high dimensional feature empty
Between in F,Just having obtained new subdata space data sets is
Its covariance matrix is obtained first, and expression formula is：
The covariance matrix of this feature space is a unit matrix, and it is C=(1/L) Φ Φ that can represent CT, in feature
It is non-linear due to data, it is necessary to obtain C characteristic vector in space, cause very big trouble to calculating, it is impossible to directly obtain
φ () function, for initial data to be mapped to the mapping function of higher dimensional space, so adding kernel function K () herein to aid in
Calculate.Kernel function has a variety of modes, in the present invention, takes the kernel function to be：
Wherein, K ∈ RL×L, l=1,2 ... L, m=1,2 ... L.Then obtained knot is standardized to nuclear matrix
It is really：
In formula, ILFor constant matrices, it is L that its element is equal, nuclear matrix is standardized for：
Next it is rightCarry out Eigenvalues Decomposition：
In formula, λ ' isCharacteristic value, α be characteristic vector corresponding with λ '.Herein, it can obtainD it is special
Vector is levied, wherein d is its maximum positive characteristic value number, and characteristic value is arranged as：
λ′1≥λ′2≥…≥λ′d (2.38)
Corresponding characteristic vector is：
α1, α2..., αd (2.39)
In theory, the number of nonzero eigenvalue is equal to highest dimension, and the feature of highest dimension is defined herein
Value number is, it is necessary to meet：
D characteristic value for obtaining C is respectively λ '1/L,λ′2/L,…,λ′d/ L, corresponding characteristic vector is v1,v2,…,vd,
Physical relationship is as follows：
Formula (2.41) can write a Chinese character in simplified form into：
V=Φ H Λ-1/2 (2.42)
Wherein V=[v1,v2,…,vd] it is characterized vector matrix, Λ=diag (λ1,λ2,…,λd) and H=[α1, α2...,
αd] be respectivelyD eigenvalue of maximum diagonal matrix and its corresponding eigenvectors matrix.Thus, it is possible to obtain association side
The new of poor Matrix C is expressed as：
It is P to make whitening matrix, then：
PTCP=I (2.45)
After obtaining whitening matrix, it is possible to which obtaining the data matrix in feature space after albefaction is：
Detailed, it can be obtained by formula (2.46)：
So independent entry y is：
Step 3) in, as shown in fig. 6, using T2Carrying out on-line monitoring to process with SPE statistics includes procedure below：
3.1) real-time batch process data X is gatherednew；
3.2) data prediction, seeks independent entry s, divides k sub-spaces；
3.3) every sub-spaces KICA is modeled and calculates each T2With SPE statistics；
3.4) collect whether Counting statistics amount transfinites.
Step 3.3) in, every sub-spaces KICA is modeled and each T is calculated2It is to use T with SPE statistics2Statistics
The calculating for being controlled limit is counted with SPE, is specially：
For 1~k sub- data spaces, its Hotelling-T2Statistical definition is：
Above formula is deployed, obtained：
For KICA modeling analysis, independent metamessage s is typically to disobey Gaussian Profile, so calculating T2System
When counting upper control limit, it is impossible to directly calculated with F distributions.Here the method for using Density Estimator.
Stochastic variable y independent same distribution sample is y1,y2,…,yn, its probability density function is f (y).K () is real
A given probability density function, h on number fieldnIt is a constant, it is relevant with sample number n, and hn＞ 0.Note：
So a unknown density function f Density Estimator is exactly fn, k () expression kernel functions, hnReferred to as smooth system
Number, from formula (2.51), the probability density function calculated by Density Estimator method is respectively to the parameter that it works
The selection of sample size, kernel function and smooth coefficients.
For known sample size, as long as there is smooth coefficients hnSize and kernel function k () form, it is possible to
Obtain probability density.Selection for kernel function needs to meet three conditions:K (y)=K (- y)；K(y)≥0；∫ K (y) dy=1.
Conventional kernel function has polynomial kernel (polynomial), homogeneous nucleus (Uniform), Gaussian kernel (Gaussian), nucleus vestibularis triangularis
(Triangle) etc..
Next it is exactly to ask for smooth coefficients h after selected kernel functionn.For hnSelection it is very crucial.Theoretically
Say, hn0 can be tended to number of samples n → ∞.Work as hnValue it is too small when, the influence of randomness can be strengthened so that fn(y)
The shape of very irregular is presented, so as to shield its key property；Conversely, hnWhen choosing excessive, fn(y) will be excessively smooth,
So that the careful property of the comparison that f (y) can not be appeared.Mean square error (MSE) is one and selects the conventional of optimal smooth coefficients
Principle, that is, the variance and the quadratic sum of deviation estimated：
It can be obtained by formula above, hnValue it is bigger, the variance of data is bigger, be fitted it is more rough；hnValue get over
Small, variance is bigger, is at this time fitted just too smooth.Optimal smooth coefficients h is drawn accordinglynExpression formula：
Now, MSE is minimum, with n-4/5Speed tend to 0；hoptWith speed n-1/5→ 0 convergence.
Here kernel function selects gaussian kernel functionAgain due to the purpose of KICA modelings
Complex industrial process monitoring, the precision of fitting is not required for it is too high, so choosing hnWhen need not reach it is highly optimal
Change in theory, then can just pass through hn=Cn-0.2δ is obtained, and wherein C=1.06 corresponds to one of gaussian kernel function often
Number, δ is the standard deviation of sampling, and n is total sample number.
By the T for calculating normal data2Statistic, the probability density distribution with regard to object can be estimated, further according to probability
Statistical knowledge obtains the coboundary in the regions of population density function f (y) 99%, and the value of border this point is required T2Statistic
Control limit.
Calculating T2After statistic, the calculating of the SPE statistics in 1~k subdatas space is obtained, detailed process is such as
Under：
Wherein,
In order to realize the monitoring to process, for the sampling x at a new k momentnew∈Xnew, specification is carried out to it first
Change obtains X "new, Subspace partition is then passed through again, the process data for obtaining i-th of subdata space isFinally by
Monitoring Data calculates monitoring and statisticses amount Ti 2And SPEi：
T2Statistic is：
SPE statistics are：
Wherein
For the monitoring result of each subdata, calculate for convenience, normal condition is represented with 0, represent occur event with 1
Barrier, that is to say, that for i-th of subdata space, if T2Statistic transfinites, and is just designated as 1, is otherwise 0, then can be with
Obtain equation below：
s.t.1≤i≤m
For SPE statistics, formula is provided accordingly：
s.t.1≤i≤m
For the display result in each subdata space, hell to pay is observed one by one, it is necessary to think that a method collects result, is united
One observation.A kind of method that the present invention is added up using weight, statistical result is combined, for T2Statistic is as a result as follows：
For SPE statistics, as a result for：
In formula, σiFor the weight shared by i-th of spatial statistics, andδ is limit value, that is to say, that when
Accumulated weights and during more than this limit value, be considered as failure and there occurs.So fault message just it is concise more, but this side
In method, σiSelect permeability with δ is very crucial, directly affects the result of monitoring, so it is determined that during their value, it should be noted that several
Point demand：
A. it is determined that when weight, in respective subdata space, its T2The son not transfinited with SPE statistics
Space, should have less weight among total collect, hardly to its effect of total output result, in respective subnumber
According in space, its T2Exceed the subspace of limit value with SPE statistics, larger weight should be occupied in total summarized results,
Output result is played a major role.This ensures that trouble-free space will not produce interference, what faulty space was highlighted
Effect is obvious.
B. weighted value is relevant with each subdata space, does not write out without foundation, so can guarantee that the close of contact
Type.And for excessively transfinite value in the case of, shared weight can not be infinitely great, it is to avoid a space determines final result, has
Effect avoids contingency, so can not direct adoption rate functional form, it should select exponential function form.
C. for the selection of limit value, if excessive, the not clear sense of result can be caused, malfunction monitoring is inefficient, if too small,
It is then excessively sensitive, the situation of wrong report can be produced.Because in a practical situation, some failures can be embodied in many sub-spaces
Come, it is this obvious, it is easy to monitor.And some failures only have embodiment in several sub-spaces of very few, even if it is this than
More hidden, it is desirable to have the limit value δ of very little, which can just be detected, to be come.So, in order to embody the advantage of this algorithm, fill
Local details are revealed in split, and the present invention chooses a less δ value.If the δ values are excessive, result can be caused to fail to understand
Sense, malfunction monitoring is inefficient, if too small, excessively sensitive, can produce the situation of wrong report.Some failures are only seldom simultaneously
There is embodiment in several sub-spaces of number, it is therefore desirable to which the limit value δ for having very little, which can just be detected, to be come.
So the requirement in order to meet 3 points of the above, as follows The present invention gives a kind of computational methods of weight：
Wherein, ToS is T2Or SPE statistics, ToSlFor its corresponding control limit.Then again to σ 'iPlace is normalized
Reason, obtains σi。
The present embodiment is using penicillin fermentation process as industrial background, and penicillin fermentation schematic diagram is as shown in Figure 1.To non-linear
Batch process fault detect is studied.Using penicillin B enchmark models, using Pensim analogue systems generation emulation number
According to.It is about 300 hours in each batch time of penicillin fermentation process, the sampling interval of the present embodiment selection is 0.1 hour,
3000 data sample points are gathered altogether in each fermentation process.Each sample point has 16 process variables, that is, needs to hair
16 amounts that ferment process is controlled, failure will be produced by having one to change.
The present embodiment gathers the data of 50 normal batches as training data, obtains a three-dimensional data X (50*16*
3000), it is possible thereby to carry out off-line modeling.After multi-model KICA analyses in subspace are set up according to the inventive method, selection
Two groups of faulty data carry out simulation analysis：
Failure one：In a selected batch, introduce because faulty operation changes the bottoms stream rate of acceleration of input quantity, from
And failure is formed, this is a both phase step fault.And the variable of the change influence of bottoms stream rate of acceleration is seldom, and is in fermentation
The variable that the second stage of process just works, its change is not easy to embody in the result, belongs to a kind of local
Failure.In experiment this failure is introduced in the 200th sampled point, and in the case of failure continues to the 500th sampled point, Fig. 7 A,
7B is respectively the T of traditional random space-division method2With SPE schematic diagrames.Fig. 7 C and 7D is respectively proposed by the present invention based on only
T of the multi-direction KICA methods of vertical Subspace partition for the monitoring situation of failure one2Statistic and SPE statistic schematic diagrames.
Fig. 7 E and 7F is that the present invention marks off T in each Independent subspace come respectively2Statistic and SPE statistics；
Failure two：Another batch is selected, is introduced because a faulty operation changes the air mass flow of input quantity, this is one
Individual both phase step fault.The change of air mass flow all has an impact to the temperature of whole fermentation process, dissolved oxygen concentration, pH value etc., belongs to
One more extensive variable of influence.Therefore it is easier what is embodied during this failure, belongs to global fault.This failure
The introducing time be the 300th sampled point, be also that Fig. 8 A and 8B is respectively the present invention in the case of continueing to the 500th sampled point
T of the multi-direction KICA methods based on Independent subspace division proposed for the monitoring situation of failure one2Statistic and SPE systems
Metering；
For the monitoring of failure 1, according to the random space-division method of contrast tradition and set forth herein it is empty based on independent son
Between the multi-direction KICA methods that divide, found out by Fig. 7 A and 7B in T2In SPE statistics, the hair of failure can be monitored
It is raw.But the two have one what is common is that some delays of the generation of failure, it can be seen that about in the 210th sample point
Statistic just exceedes control limit.And either the fluctuation of score statistics or residual error statistics is all very big, 200 sampled points it
Before, the fluctuation more than control limit is all about occurred in that in 50,80 and 175 sample points, this is due to system in fermentation process
Caused by fluctuation, although can have bigger fluctuation unavoidably by setting warning system to avoid this interference and cause wrong report
Phenomenon.And after the failure occurs, some fluctuations cause statistic and are down under control limit again, although being imitated to whole monitoring
Fruit can also interfere without substantial influence to output result.On the whole, monitoring of the conventional method for failure 1
Effectively, but there is delay, have fluctuation, effect is general.By Fig. 7 C and 7D find out new space-division method proposed by the present invention for
The monitoring effect of failure 1, due to adding weight distribution when each space is collected, when the space proportion that does not transfinite
Small, the space proportion that transfinites is big, makes smaller, greatly bigger that overall output result is small.Middle display is found out by Fig. 7 C and 7D
It is clear that step effect is clearly, failure is very big with statistic gap afterwards before occurring, and in the 200th sampling
The more point of point, also just occurs step saltus step with regard to 201 or 202 sample points, does not almost postpone.And statistic is whole
Bulk wave moves very little, occasionally have it is several than larger fluctuation also far away from control limit, output result is not interfered with.Wherein adopted 200
Fluctuation before sampling point is due to have larger statistics value in the space transfinited individually, and shared large percentage produces result
Raw fluctuation.And some fluctuations are also generated after 200 sampled points, it is due to that control limit is not reaching in some spaces, leads
Cause proportion very little, it is small and small resulted in fluctuation.But on the whole, the inventive method can effectively be monitored and is out of order
1, and fluctuate small, do not interfere with, it may be said that effect is very good.
On subspace, from Fig. 7 E and 7F it can be seen that, in subspace 1 and 4 (i.e. in Fig. 7 E and Fig. 7 F
Subspace1 and subspace4) in, almost monitor the generation less than failure；In subspace 5 (i.e. in Fig. 7 E and Fig. 7 F
Subspace5 in), although can be reached after 200 sampled points on control limit, not overall to exceed, its result is very not
It is stable；And in subspace 2,3 and 6 (i.e. subspace2, subspace3 and subspace6 in Fig. 7 E and Fig. 7 F), can
Out of order generation is monitored well.When picture amplification is seen, it can be seen that monitor the sky that the point of generation that is out of order has
Between be just to occur Spline smoothing in 200 sampled points, and in 203 and 205 sampled points Spline smoothing, this explanation occur for some spaces
In different spaces, the time of origin of failure is slightly different.On the whole, the different original of monitoring result in different spaces is caused
Because the space-division method for being exactly this paper is divided according to independent information, the otherness in each space is very big.Change substrate
Flow velocity rate has had influence on some variables, does not have an impact to other variables, so the space resulted in does not have failure hair
It is raw, and some space failures occur substantially.Because the weight ratio shared by the subspace broken down is larger, so just existing well
Embody out in total statistic.This illustrates set forth herein method for these for a small amount of variable produce influence
The superiority of malfunction monitoring effect, improves monitoring efficiency, reduces fluctuation interference, is a kind of highly effective method.
For the monitoring of failure two, (as shown in Fig. 8 A, 8B, 8A is the random space-division method of tradition to two methods, and 8B is
This paper independent information space-division method) it is all fine to the monitoring effect of failure 2, the inventive method still more preferably, its failure
The corresponding time does not postpone, and overall fluctuation is also very small.Although even have interference, there is no any influence on result.
Claims (8)
1. a kind of multi-direction KICA batch processes fault monitoring method based on Independent subspace, it is characterised in that including following step
Suddenly：
1) collection batch process three-dimensional data X (I × J × K), using multidirectional KICA, two dimension is launched into by three-dimensional data by batch
Data are handled；Wherein I is number of batches, and J is variables number, and K is sampled point number；
2) off-line modeling is carried out to the 2-D data deployed by batch, geo-nuclear tracin4 is added on the basis of ICA, by nonlinear data
High-dimensional feature space is mapped to, then linear process is carried out in higher dimensional space；
3) T is applied2Process is monitored on-line with SPE statistics；The fault message that each subdata is obtained is collected,
Whether Counting statistics amount transfinites.
2. the multi-direction KICA batch processes fault monitoring method that Independent subspace according to claim 1 is divided, it is special
Levy and be that carrying out off-line modeling to the 2-D data deployed by batch comprises the following steps：
2.1) R.I. process three-dimensional data X carries out data normalization processing, the data X ' after being standardized；
2.2) the independent entry s of the non-gaussian distribution of the data X ' after normalized；
2.3) k sub- data spaces are divided according to independent metamessage；
2.4) KICA modelings are carried out to every sub-spaces respectively.
3. the multi-direction KICA batch processes fault monitoring method according to claim 2 based on Independent subspace, it is special
Levy and be：Step 2.3) in, dividing k sub- data spaces according to independent metamessage is：According to independent metamessage s1,s2,s3,…
skSeek out to the maximum data of its contribution degreeBuild similarity matrix R；I-th of subdata space is built,
The process variable value corresponding to L maximum Similarity value of the row of similarity matrix i-th is taken, a sub-spaces are configured to；Repeat this
Step, k sub- data spaces are constructed from 1 to k for i.
4. the multi-direction KICA batch processes fault monitoring method according to claim 2 based on Independent subspace, it is special
Levy and be：Step 2.4) in, KICA is carried out to every sub-spaces respectively and is modeled as：
2.4.1) to i-th of subdata space κiTo carry out KICA modeling analysis, for i-th of subdata space, its process variable
ForWillIt is standardized, the subdata steric course data after being standardized are
2.4.2) by Nonlinear Mapping by the subspace process data after standardizationIt is mapped to high-dimensional feature space F
In,Obtaining new subdata space data sets is
Its covariance matrix is obtained first, and expression formula is：
It is expressed as：C=(1/L) Φ ΦT
Add kernel function K () to aid in calculating, take the kernel function to be：
Wherein, K ∈ RL×L, l=1,2 ... L, L is constant, and l is variable name, m=1,2 ... L；
Obtained result is standardized to nuclear matrix is：
In formula, ILFor constant matrices, its element is equal, is 1/N；
Nuclear matrix is standardized for：
It is rightCarry out Eigenvalues Decomposition：
In formula, λ ' isCharacteristic value, α be characteristic vector corresponding with λ ', obtainD characteristic vector, wherein d be its
Maximum positive characteristic value number, is arranged as to characteristic value：
λ′1≥λ′2≥…≥λ′d (2.38)
Corresponding characteristic vector is：
α1, α2..., αd (2.39)
The characteristic value number of highest dimension is defined, it is necessary to meet：
D characteristic value for obtaining covariance matrix C is respectively λ '1/L,λ′2/L,…,λ′d/ L, corresponding characteristic vector is v1,
v2,…,vd, physical relationship is as follows：
Write a Chinese character in simplified form into：
V=Φ H Λ-1/2 (2.42)
Wherein V=[v1,v2,…,vd] it is characterized vector matrix, Λ=diag (λ1,λ2,…,λd) and H=[α1, α2..., αd]
RespectivelyD eigenvalue of maximum diagonal matrix and its corresponding eigenvectors matrix；Covariance matrix C new expression
For：
It is P to make whitening matrix, then：
PTCP=I (2.45)
Data matrix in feature space after albefaction is：
Obtained by formula (2.46)：
So obtaining independent entry y is：
。
5. the multi-direction KICA batch processes fault monitoring method according to claim 1 based on Independent subspace, it is special
Levy and be：Step 3) in apply T2Carrying out on-line monitoring to process with SPE statistics includes procedure below：
3.1) real-time batch process data X is gatherednew；
3.2) data prediction, seeks independent entry s, divides k sub-spaces；
3.3) every sub-spaces KICA is modeled and calculates the T of the data in every sub-spaces2With SPE statistics；
3.4) collect whether Counting statistics amount transfinites.
6. the multi-direction KICA batch processes fault monitoring method according to claim 5 based on Independent subspace, it is special
Levy and be：Step 3.3) in every sub-spaces KICA modeled and calculate the T of the data in every sub-spaces2With SPE statistics,
It is to use T2Statistics and SPE count the calculating for being controlled limit, wherein using T2Statistics calculates control limit：
For 1~k sub- data spaces, its Hotelling-T2Statistical definition is：
Above formula expansion is obtained：
Wherein, y is independent entry, and D is the diagonal matrix of nuclear matrix characteristic value；
Using the method for Density Estimator, stochastic variable y independent same distribution sample is y1,y2,…,yn, its probability density function
For f (y), k () is kernel function, hnIt is a constant for smooth coefficients, it is relevant with sample number n, and hn＞ 0, then：
The probability density function calculated by Density Estimator method, is respectively sample size, core letter to the parameter that it works
The selection of number and smooth coefficients, wherein for known sample size, passing through smooth coefficients hnSize and kernel function k ()
Form obtains probability density；Selection for kernel function needs to meet three conditions:K (y)=K (- y)；K(y)≥0；∫K(y)dy
=1；
Optimal smooth coefficients are selected by mean square error, that is, the variance and the quadratic sum of deviation estimated：
N is total sample number, and u is correlated variables, and o is the symbol of dimensionless in mathematics；
Optimal smooth coefficients h is drawn accordinglynExpression formula：
Now, MSE is minimum, with n-4/5Speed tend to 0；hoptWith speed n-1/5→ 0 convergence；
Wherein, gaussian kernel function
hn=Cn-0.2δ
Wherein C=1.06, corresponding to a constant of gaussian kernel function, δ is the standard deviation of sampling, and n is total sample number；
By the T for calculating normal data2Statistic, estimates the probability density distribution of object, is obtained further according to probability statistics knowledge
The coboundary in the regions of occupation probability density function f (y) 99%, the value of border this point is T2The control limit of statistic.
7. the multi-direction KICA batch processes fault monitoring method according to claim 6 based on Independent subspace, it is special
Levy and be：Control limit is calculated with SPE statistics, is specially：
Wherein,ZiIt is characterized in space by the mapping data after albefaction, is calculated value, k is
One constant of k sub-spaces,CiFor i-th of vector in initial matrix C, CkFor initial matrix C
In k-th vector, ekFor residual error, residual error is further calculated
For the sampling x at a new k momentnew∈Xnew, first it standardize obtains X "new, it is then empty by son again
Between divide, the process data for obtaining i-th of subdata space isMonitoring and statisticses amount T is calculated finally by Monitoring Datai 2
And SPEi：
T2Statistic is：
SPE statistics are：
Wherein
For the monitoring result of each subdata, i.e., for i-th of subdata space, if T2Statistic transfinites, and is designated as 1,
Otherwise it is 0, then obtains equation below：
s.t.1≤i≤m
For SPE statistics, formula is provided accordingly：
s.t.1≤i≤m
For the display result in each subdata space, statistical result is combined by a kind of method added up with weight, for
T2Statistic is as a result as follows：
For SPE statistics, as a result for：
In formula, σiFor the weight shared by i-th of spatial statistics, and 0≤σi≤1；δ is limit value, that is to say, that when accumulative
Weighting and during more than this limit value, it is believed that failure occurs.
8. the multi-direction KICA batch processes fault monitoring method according to claim 7 based on Independent subspace, it is special
Levy and be：
It is determined that weight σ shared by i-th of spatial statisticsiWhen, with exponential function form,
Wherein, ToS is T2Or SPE statistics, ToSlFor its corresponding control limit；Then again to σi' be normalized, obtain
To σi。
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| CN112817291B (en) * | 2019-11-15 | 2022-03-08 | 中国科学院沈阳自动化研究所 | Hierarchical fault monitoring method based on mixed characteristic evaluation and subspace decomposition |
| CN111814849A (en) * | 2020-06-22 | 2020-10-23 | 浙江大学 | DA-RNN-based wind turbine generator key component fault early warning method |
| CN111814848A (en) * | 2020-06-22 | 2020-10-23 | 浙江大学 | Self-adaptive early warning strategy design method for temperature fault of wind turbine generator |
| CN111814849B (en) * | 2020-06-22 | 2024-02-06 | 浙江大学 | DA-RNN-based wind turbine generator set key component fault early warning method |
| CN111814848B (en) * | 2020-06-22 | 2024-04-09 | 浙江大学 | Self-adaptive early warning strategy design method for temperature faults of wind turbine generator |
| CN112016624A (en) * | 2020-08-28 | 2020-12-01 | 西北农林科技大学 | Spectrum data dimension reduction method for optimizing kernel independent components based on sparrow search algorithm |
| CN113189968A (en) * | 2021-05-08 | 2021-07-30 | 哈尔滨工业大学 | Distributed fault diagnosis method for interconnected industrial process |
| CN113156908A (en) * | 2021-05-25 | 2021-07-23 | 中南大学 | Multi-working-condition industrial process monitoring method and system with mechanism and data combined fusion |
| CN114089717A (en) * | 2021-10-18 | 2022-02-25 | 兰州理工大学 | Intermittent process quality related fault detection method based on multidirectional weighting elastic network |
| CN114089717B (en) * | 2021-10-18 | 2023-08-15 | 兰州理工大学 | Intermittent process quality related fault detection method based on multidirectional weighted elastic network |
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