CN107065843B - Multi-direction KICA batch process fault monitoring method based on Independent subspace - Google Patents
Multi-direction KICA batch process 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 process fault monitoring method based on Independent subspace, the following steps are included: acquisition batch process three-dimensional data X (I × J × K), using multidirectional KICA, three-dimensional data is launched into 2-D data by batch and is 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 by the 2-D data of batch expansion, geo-nuclear tracin4 is added on the basis of ICA, nonlinear data is mapped to high-dimensional feature space, then carries out linear process in higher dimensional space；Using T2Process is monitored on-line with SPE statistic；The fault message that each subdata obtains is summarized, whether Counting statistics amount transfinites.The present invention improves the method for traditional KICA disposed of in its entirety, is divided into multiple subspaces to primary data and carries out detailed KICA analysis, establishes the KICA of multi-model while monitoring, hiding information is amplified, local message is effectively grasped, improve 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 method.
Background technique
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
It is same as common procedure, has the characteristics that multiple batches of, and is not obviously distinguished between batch, the time of each batch is also not fixed very much.
Throughput rate, production status of batch process etc. are again random variations.This production status allows workpeople to deal with very spine
Hand makes production process is regular as far as possible to seek, feasible to the monitoring of batch process have it is desirable that reducing this irregular variation
Effect.
For the heavy property of production process data, traditional KICA (kernel Independent Component
Correlation Algorithm, core independent component analysis) directly data are analyzed, it can no doubt monitor the entirety of data
Information.But whole control limit can only embody whole performance, and a certain local circumstance can not clearly be expressed, some
Failure is only related with few number variable, or is seldom sampled, it is easy to just be diluted by overall data, lead to monitoring effect not
Obvious or basic just monitoring does not come out, and causes the decline of monitoring rate.
Summary of the invention
Directly data are analyzed unobvious there are monitoring effect for KICA traditional in the prior art or causes monitoring rate
Decline the problems such as, the problem to be solved in the present invention is to provide one kind 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 that:
A kind of multi-direction KICA batch process fault monitoring method based on Independent subspace of the present invention, including following step
It is rapid:
1) three-dimensional data is launched by acquisition batch process three-dimensional data X (I × J × K) using multidirectional KICA 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 by the 2-D data of batch expansion, geo-nuclear tracin4 is added on the basis of ICA, it 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 statistic；The fault message that each subdata is obtained carries out
Summarize, whether Counting statistics amount transfinites.
To by batch expansion 2-D data carry out off-line modeling the following steps are included:
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 modeling is carried out to every sub-spaces respectively.
In step 2.3), k sub- data spaces are divided according to independent metamessage are as follows: according to independent metamessage s1,s2,s3,…
skIt seeks out to the maximum data of its contribution degreeConstruct similarity matrix R；I-th of subdata space is constructed,
Process variable value corresponding to the maximum L similarity value of the i-th row of similarity matrix is taken, a sub-spaces are configured to；Repeat this
Step constructs i from 1 to k k sub- data spaces.
In step 2.4), KICA modeling is carried out to every sub-spaces respectively are as follows:
2.4.1) to i-th of subdata space κiKICA modeling analysis is carried out, for i-th of subdata space, mistake
Cheng Bianliang isIt willIt is standardized, the subdata space mistake after being standardized
Number of passes is according to being
2.4.2) pass through Nonlinear Mapping for 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, expression formula are found out first are as follows:
It indicates are as follows: C=(1/L) Φ ΦT
Kernel function K () is added to assist calculating, takes kernel function are as follows:
Wherein, K ∈ RL×L, l=1,2 ... L, L are constant, and l is variable name, m=1,2 ... L；
The result that nuclear matrix is standardized are as follows:
In formula, ILFor constant matrices, element is equal, and is 1/N；
Nuclear matrix is standardized are as follows:
It is rightCarry out Eigenvalues Decomposition:
In formula, λ ' isCharacteristic value, α be feature vector corresponding with λ ', obtainD feature vector, wherein d
For its maximum positive characteristic value number, characteristic value is arranged are as follows:
λ′1≥λ′2≥…≥λ′d (2.38)
Corresponding feature vector are as follows:
α1, α2..., αd (2.39)
The characteristic value number for defining highest dimension, needs to meet:
D characteristic value for obtaining covariance matrix C is respectively λ '1/L,λ′2/L,…,λ′d/ L, corresponding feature vector are
v1,v2,…,vd, physical relationship is as follows:
It writes 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 maximum eigenvalue diagonal matrix and its corresponding eigenvectors matrix；Covariance matrix C
New expression are as follows:
Enabling whitening matrix is P, then:
PTCP=I (2.45)
Data matrix in feature space after albefaction are as follows:
It is obtained by formula (2.46):
So obtain independent entry y are as follows:
T is applied in step 3)2Carrying out on-line monitoring to process with SPE statistic includes following procedure:
3.1) real-time batch process data X is acquirednew；
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 statistic；
3.4) summarize whether Counting statistics amount transfinites.
Every sub-spaces KICA is modeled in step 3.3) and calculates the T of the data in every sub-spaces2It is counted with SPE
Amount is using T2Statistics and SPE statistics carry out the calculating of control limit, wherein using T2Statistics calculates control limit specifically:
For 1~k sub- data spaces, Hotelling-T2Statistical definition are as follows:
Above formula is unfolded to obtain:
Wherein, y is independent entry, and D is the diagonal matrix of nuclear matrix characteristic value；
Using the method for Density Estimator, the independent same distribution sample of stochastic variable y is y1,y2,…,yn, probability density
Function is f (y), and k () is kernel function, hnIt is a constant for smooth coefficients, it is related with sample number n, and hn> 0, then:
By the calculated probability density function of Density Estimator method, to the parameter that it works be respectively sample size,
The selection of kernel function and smooth coefficients, wherein passing through smooth coefficients h for known sample sizenSize and kernel function k
The form of () obtains probability density；Need to meet three conditions: K (y)=K (- y) for the selection of kernel function；K(y)≥0；∫
K (y) dy=1；
Optimal smooth coefficients are selected by mean square error, that is, the quadratic sum of the variance and 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 obtained accordinglynExpression formula:
At this point, MSE is minimum, tend to 0 with the rate of n-4/5；hoptWith rate 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
Knowledge obtains the coboundary in 99% region occupation probability density function f (y), and the value of boundary this point is T2The control of statistic
Limit.
It is counted with SPE and calculates control limit, specifically:
Wherein,ZiIt is characterized in space by the mapping data after albefaction, is calculated value,
K is k-th of constant of subspace one,CiFor i-th of vector in initial matrix C, CkIt is initial
K-th of vector in Matrix C, ekFor residual error, residual error is further calculated
The sampling x at the k moment new for onenew∈Xnew, it is standardized to obtain X " firstnew, then using
Subspace partition, the process data for obtaining i-th of subdata space areMonitoring and statistics are calculated finally by monitoring data
Measure Ti 2And SPEi:
T2Statistic are as follows:
SPE statistic are as follows:
Wherein
For the monitoring result of each subdata, i.e., for i-th of subdata space, if T2Statistic transfinites, by it
It is designated as 1, is otherwise 0, then obtains following formula:
For SPE statistic, formula is provided accordingly:
A kind of method as a result, cumulative with weight is shown for each subdata space, statistical result is combined,
For T2Statistic is as a result as follows:
For SPE statistic, as a result are as follows:
In formula, σiFor weight shared by i-th of spatial statistics, andδ is limit value, that is to say, that when
Accumulated weights and be more than this limit value when, it is believed that failure occur.
Determining weight σ shared by i-th of spatial statisticsiWhen, with exponential function form,
Wherein, ToS T2Or SPE statistic, ToSlIt is limited for its corresponding control；Then again to σ 'iPlace is normalized
Reason, obtains σi。
The invention has the following beneficial effects and advantage:
1. the present invention is directed to the multiple batches of problem of batch process, its data is made to become three-dimensional data battle array, application is multidirectional
Three-dimensional data is effectively launched into 2-D data and handled by KICA；Geo-nuclear tracin4 is added on the basis of traditional IC A, it will be non-
Linear data is mapped to high-dimensional feature space, then carries out linear process in higher dimensional space, handles using KICA data
T is applied in analysis later2Process is monitored on-line with SPE statistic；The method of traditional KICA disposed of in its entirety is improved, it is right
Primary data has carried out data cutting, is divided into multiple subspaces, and the subdata space for being directed to each data carries out in detail
KICA analysis, establish the KICA of multi-model while monitoring, hiding information is amplified, effectively grasp local message, improve former
The monitoring rate of barrier.
2. the present invention to have the characteristics that in batch process multiple batches of, non-gaussian data by division subspace supervise respectively
It surveys, data, which belong to control line in the complex effects and tradition KICA method of different batches, before overcoming can only embody overall performance
And there is a small number of failures undesirable phenomenon of monitoring caused by overall data dilution.
It is the independent metamessage according to data 3. the present invention is different from previous random space RSM division, data is carried out
It selectively divides, makes 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 obtains is summarized, and keeps monitoring effect more very clear.
4. the method for the present invention is monitored simultaneously by subspace multi-model, good effect can be played；Finally to penicillin
In fermentation process faulty operation change input quantity substrate flow rate and faulty operation change input quantity air mass flow this two
The validity of monitoring verifying this method of class fault data.
Detailed description of the invention
Fig. 1 is penicillin fermentation schematic diagram；
Fig. 2 is that the multi-direction of batch process presses batch expanded schematic diagram；
Fig. 3 A is independent component analysis schematic diagram；
Fig. 3 B does not have the division methods schematic diagram of common portion but exhaustive data between subspace；
Fig. 3 C is that subspace can have intersection or 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 is the T of the random space-division method under conventional process mode of failure one2Statistic curve graph；
Fig. 7 B is the SPE statistic curve graph of the random space-division method under conventional process mode of failure two；
Fig. 7 C is the T for the multi-direction KICA method that failure one is divided under processing mode of the present invention based on Independent subspace2
Statistic curve graph；
Fig. 7 D is the multi-direction KICA method that failure one is divided under processing mode of the present invention based on Independent subspace
SPE statistic curve graph；
Fig. 7 E is T in each Independent subspace in the present invention2Statistic curve graph；
Fig. 7 F is SPE statistic curve graph in each Independent subspace in the present invention；
Fig. 8 A is the T for the multi-direction KICA method that failure two is divided under processing mode of the present invention based on Independent subspace2
Statistic curve graph；
Fig. 8 B is the multi-direction KICA method that failure two is divided under processing mode of the present invention based on Independent subspace
SPE statistic curve graph.
Specific embodiment
The present invention is further elaborated with reference to the accompanying drawings of the specification.
The multi-direction KICA batch process fault monitoring method that a kind of Independent subspace of the present invention divides, including following step
It is rapid:
1) three-dimensional data is launched by acquisition batch process three-dimensional data X (I × J × K) using multidirectional KICA by batch
2-D data is handled；
2) off-line modeling is carried out to by the 2-D data of batch expansion, geo-nuclear tracin4 is added on the basis of ICA, it 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 statistic；The fault message that each subdata is obtained carries out
Summarize, whether Counting statistics amount transfinites.
In step 1), 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 are variables number, and K is sampled point number.By each batch as a direction, by the data of time and process variable
It is blended together and forms new 2-D data, so that two-dimensional matrix X (I × KJ) is converted into, then such 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
To the different batches of process variable, different sampling instants and the standardization of different variables, data processing can be facilitated in this way,
Data characteristics is also remained simultaneously.
In step 2), to by batch expansion 2-D data carry out off-line modeling the following steps are included:
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 modeling is carried out to every sub-spaces respectively.
In step 2.1), data are standardized, i.e., each variable is become average value is 0, variance 1
Standardized variable.Specific step is as follows:
2.1.1) the training dataset X obtained after multi-direction expansion are as follows:
Wherein, xi(i=1,2 ..., n) it is one group of sampling column vector.
It is hereby achieved that the process variable matrix after standardization, are as follows:
Wherein, xi,jFor an element in former data matrix, x 'I, jFor one in the data matrix after standardization
Element, xjFor j column element,For the mean value of j column element, 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 column, X ' are the later process data of standardization；
2.1.2 the covariance matrix S of sample) is found out:
Wherein, X ' is the later process data of standardization.
2.1.3 after) obtaining covariance matrix, continue covariance matrix SsEigenvalues Decomposition is carried out, P can be indicated
Are as follows:
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 the load vector of X ', by eigenvalue λiCorresponding unitization feature vector is constituted, and PTP=I, I are units
Matrix.
2.1.4 score matrix T) is found out
Select a load matrix P ∈ Rm×lColumn, keep it corresponding with the associated load vector of preceding l characteristic value, 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 be it is highly important, usually selection l (l < m) a principal component replaces former m related change
Amount, this l principal component can represent the information that former m variable is included.Generalling use principal component accumulation contribution rate is more than
85% retains the number of pivot, such as following formula
Data X ' after standardization is decomposed into the form of the sum of apposition, 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.Matrix form is converted by above formula, are as follows:
X '=TPT (2.11)
Wherein, T=[t1 t2 … tm] it is known as score matrix, P=[p1 p2 … pm] it is known as load matrix.
2.1.5) show that ICA model seeks independent metamessage
By 2.1.4) it obtainsAs shown in fig.3 a 3 c, the independent entry of non-gaussian distribution
It is expressed asWherein k is independent entry number, then relationship between the two are as follows:
X '=As (2.12)
In formula,It is a unknown hybrid matrix, this matrix is found out, so as to find out only
Vertical member s, available by formula (2.12):
S=A-1x′ (2.13)
Take inverse matrix W, the W ∈ R of Ak×n, W is to solve mixed matrix, so formula 3.13 can be write as:
S=WX ' (2.14)
Present purpose is exactly to seek solving mixed matrix W.The present embodiment utilize differential entropy criterion, it is assumed that y be one at random to
Amount, probability density are p (y), then the differential entropy of y are as follows:
So the negentropy of y are as follows:
J (y)=H (yg)-H(y) (2.16)
It is difficult to accomplish due to calculating negentropy in practice, calculates for convenience, for formula (2.16), take the approximate table of J
Up to formula:
J(y)≈τ[E{G(y)}-E{G(yg)}]2 (2.17)
In formula: τ is a constant,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, it is available that J is made to reach the smallest w.Find out the mixed matrix W of solution are as follows:
So S can be found out.
S=[s1,s2,…,sk] (2.20)
About Subspace partition as shown in figure 4, in step 2.3), k sub- data spaces are divided according to independent metamessage are as follows:
According to independent metamessage s1,s2,s3,…skIt seeks out to the maximum data of its contribution degreeConstruct similarity moment
Battle array R；I-th of subdata space is constructed, takes the i-th row of similarity matrix to process variable corresponding to L big similarity value
Value, is configured to a sub-spaces；Step 2.3) is repeated, constructs k sub- data spaces from 1 to k for i.
Subdata space is divided around each independent entry, the problem of very good solution otherness, because of independent metamessage
Independent between batch, information difference is larger, just has otherness naturally around the subspace that independent metamessage is established, and draws at random
Divide not this property.
Construct the similarity matrix of independent entry
It is available by formula (2.14):
So for i-th of independent entry si, can indicate are as follows:
si=wi1×x′1+wi2×x2′+…+win×xn′, (2.22)
Wherein: i=1,2 ... k.
In order to surround siSubdata space is established, s can most be given expression to by selectingiThe data volume of information, due to the dimension of s and x
It is different, it has not been convenient to similitude directly to be sought, so first to select to siThe maximum data of contribution degree, closest to si'sAgain bySimilitude is calculated with each data volume, obtains subdata space.Think herein withSimilarity it is higher, data x is just to only
The contribution degree highest of vertical metamessage s.Herein, each x ' is first defined to siContribution degree:
That maximum data of contribution degree are taken to represent si, so accordinglyAre as follows:
Wherein j is to make μijJ corresponding to maximum value is obtained, ifIt repeats to choose, then postpones to making μijObtain Second Largest Value
J, and so on, obtain the data set x that can represent each independent metamessages',
Establish subdata space κ nowi, for whole process variable x1', x2′,x3′,…,xn', seek respectively its withLinearly related degree, intensively embodied corresponding to it as the subspace that the high volume of data of linearly related degree constructs
Independent entry siCharacteristic information, thenWith xj' the degree of correlation are as follows:
In this way to entireIt is correlating with x ', it may be expressed as:
Accordingly, for all independent metamessage s1,s2,s3,…skWith all process variable x '1, x '2,x′3,…,x′n, give
Correlation matrix out are as follows:
By formula (2.28) it is found that obtained rijIt is bigger, mean that corresponding x 'jWith independent entry siSimilarity it is bigger,
This variable information can more clearly embody independent entry s in this wayiCharacteristic information.Again with such a subspace data
Collection carrys out modeling analysis, and the detailed fault message detected in this direction of energy thus can be monitored targetedly very much
The fault message of various aspects out, the concrete condition of careful understanding internal system, makes monitoring effect be greatly improved.
It only needs according to obtained similarity matrix, so that it may mark off desired subdata space.It obtains in this way
Subdata space κ1, κ2, κ3... κkS can be represented well1,s2,s3,...skInformation, while also meet front
Requirement to each Subspace difference and validity.Otherness is it is well understood that because independent entry s1,s2,s3,…skInherently
It is mutually independent, so having very big otherness between them, so around the subdata space that they are established, naturally
The different respective characteristics of independent entry are embodied, apparent otherness is also just provided with；About validity, the subdata space of foundation
Also it ensure that validity according to effective standard when having enough data volumes, and establish.
The present embodiment is to construct subdata space κiFor, specific method are as follows:
Take the i-th row r of similarity matrixi1,ri2,ri3,…rin, i=1,2 ... k, corresponding each related coefficient indicates
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, so that it may construct 1~k sub- data space κ1, κ2, κ3... κk。
It is not arbitrarily to choose about the size in each subdata space, that is, the selection of constant L.L chose
Greatly, then the data volume in each subdata space is excessive, and the calculation amount in subdata space each so 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
Measure it is very few, space it is too small and meet at data unicity it is too strong, without reasonable validity.So the selection about L, this hair
The method of bright use is:
Firstly, finding out for each independent metamessage siSimilarity absolute value mean value it is as follows:
Then, the number u that similarity is greater than mean value is calculatedi, such operation is done for each independent metamessage,
Obtain u1,u2,u3,…uk, then obtain
Wherein,It is greater than the number u of mean value for similarityiAverage.
The optimization inequality formed according to one by adding up similarity:
Thus the smallest L for meeting inequality is found out, can guarantee enough information in this way, meets validity, while
Meet the otherness in each subdata space.
In step 2.4), off-line data modeling procedure figure as shown in Figure 5 carries out KICA modeling to every sub-spaces respectively
Are as follows:
2.4.1) to i-th of subdata space κiTo carry out KICA modeling analysis.For i-th of subdata space, mistake
Cheng Bianliang isFirst willIt is standardized, the subdata space after being standardized
Process data is
2.4.2) pass through Nonlinear Mapping for the subspace process data after standardizationIt is mapped to high dimensional feature
In the F of space,Just having obtained new subdata space data sets isIts covariance matrix, expression formula are found out first are as follows:
The covariance matrix of this feature space is a unit matrix, can indicate that C is C=(1/L) Φ ΦT, in feature
In space, need to find out the feature vector of C, it is non-linear due to data, very big trouble is caused to calculating, can not be directly obtained
φ () function, for the mapping function that initial data is mapped to higher dimensional space, so kernel function K () is added herein to assist
It calculates.Kernel function takes kernel function in the present invention there are many kinds of mode are as follows:
Wherein, K ∈ RL×L, l=1,2 ... L, m=1,2 ... L.Then knot nuclear matrix being standardized
Fruit are as follows:
In formula, ILFor constant matrices, element is equal as L, is standardized to nuclear matrix are as follows:
Next rightCarry out Eigenvalues Decomposition:
In formula, λ ' isCharacteristic value, α be feature vector corresponding with λ '.Herein, availableD it is special
Vector is levied, wherein d is its maximum positive characteristic value number, and is arranged characteristic value are as follows:
λ′1≥λ′2≥…≥λ′d (2.38)
Corresponding feature vector are as follows:
α1, α2..., αd (2.39)
Theoretically, the number of nonzero eigenvalue is equal to highest dimension, defines the feature of highest dimension herein
It is worth number, needs to meet:
D characteristic value for obtaining C is respectively λ '1/L,λ′2/L,…,λ′d/ L, corresponding feature vector are 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 maximum eigenvalue diagonal matrix and its corresponding eigenvectors matrix.Thus, it is possible to
To the new expression of covariance matrix C are as follows:
Enabling whitening matrix is P, then:
PTCP=I (2.45)
After obtaining whitening matrix, so that it may obtain the data matrix in feature space after albefaction are as follows:
It is detailed, available by formula (2.46):
So independent entry y are as follows:
In step 3), as shown in fig. 6, using T2Carrying out on-line monitoring to process with SPE statistic includes following procedure:
3.1) real-time batch process data X is acquirednew；
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 statistic；
3.4) summarize whether Counting statistics amount transfinites.
In step 3.3), every sub-spaces KICA is modeled and calculates each T2It is using T with SPE statistic2Statistics
The calculating of control limit is carried out with SPE statistics, specifically:
For 1~k sub- data spaces, Hotelling-T2Statistical definition are as follows:
Above formula is unfolded, is obtained:
For KICA modeling analysis, independent metamessage s is usually to disobey Gaussian Profile, so calculating T2System
When counting upper control limit, it cannot be distributed with F and directly be calculated.Here the method for Density Estimator is used.
The independent same distribution sample of stochastic variable y is y1,y2,…,yn, probability density function is f (y).K () is real
A given probability density function, h on number fieldnIt is a constant, it is related with sample number n, and hn> 0.Note:
So a Density Estimator of unknown density function f is exactly fn, k () expression kernel function, hnReferred to as smooth system
It counts, by formula (2.51) it is found that by the calculated probability density function of 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, so that it may
Obtain probability density.Need to meet three conditions: K (y)=K (- y) for the selection of kernel function；K(y)≥0；∫ K (y) dy=1.
Common kernel function has polynomial kernel (polynomial), homogeneous nucleus (Uniform), Gaussian kernel (Gaussian), nucleus vestibularis triangularis
(Triangle) etc..
It is next exactly to seek smooth coefficients h after selected kernel functionn.For hnSelection it is very crucial.Theoretically
It says, hnIt can tend to 0 with number of samples n → ∞.Work as hnValue it is too small when, the influence of randomness can be reinforced, so that fn(y)
The shape that very irregular is presented, to shield its key property；Conversely, hnWhen choosing excessive, fn(y) will be excessively smooth,
To which the more careful property of f (y) can not be appeared.Mean square error (MSE) is the common of the optimal smooth coefficients of selection
Principle, that is, the quadratic sum of the variance and deviation estimated:
Available, the h by formula abovenValue 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 obtained accordinglynExpression formula:
At this point, MSE is minimum, tend to 0 with the rate of n-4/5；hoptWith the convergence of rate n-1/5 → 0.
Here kernel function selects gaussian kernel functionAgain due to the purpose of KICA modeling
Be complex industrial process monitoring, the precision of fitting is not required for it is too high, so choose hnWhen not need to reach height optimal
Change theoretically, then h can be passed throughn=Cn-0.2δ is obtained, and wherein C=1.06 corresponds to one of gaussian kernel function often
Number, δ are the standard deviations of sampling, and n is total sample number.
By the T for calculating normal data2Statistic can estimate the probability density distribution of object, further according to probability
Statistical knowledge obtains the coboundary in 99% region population density function f (y), and the value of boundary this point is required T2Statistic
Control limit.
T is having been calculated2After statistic, the calculating of the SPE statistic in 1~k subdata space is found out, detailed process is such as
Under:
Wherein,
In order to realize the monitoring to process, the sampling x at the k moment new for onenew∈Xnew, it is standardized first
Change obtains X "new, then using Subspace partition, the process data for obtaining i-th of subdata space isFinally by
Monitoring data calculate monitoring and statistics amount Ti 2And SPEi: T2Statistic are as follows:
SPE statistic are as follows:
Wherein
It for the monitoring result of each subdata, calculates for convenience, use 0 indicates that normal condition, use 1 indicate that event occurs
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 following formula:
For SPE statistic, formula is provided accordingly:
Display for each subdata space needs to think that a method summarizes result, unites as a result, observe hell to pay one by one
One observation.A kind of method that the present invention uses weight to add up, statistical result is combined, for T2Statistic is as a result as follows:
For SPE statistic, as a result are as follows:
In formula, σiFor weight shared by i-th of spatial statistics, andδ is limit value, that is to say, that when
Accumulated weights and be more than this limit value when, be considered as failure and have occurred.In this way fault message just it is concise mostly, but this side
In method, σiIt is very crucial with the select permeability of δ, directly affect monitoring as a result, so in the value for determining them, it should be noted that it is several
Point demand:
A. when determining weight, in respective subdata space, T2The son not transfinited with SPE statistic
Space should have lesser weight, hardly to its effect of total output result, in respective subnumber in total summarize
According in space, T2It is more than the subspace of limit value with SPE statistic, biggish weight should be occupied in total summarized results,
It plays a major role to output result.This ensures that trouble-free space will not generate interference, what faulty space highlighted
Effect is obvious.
B. weighted value is related with each subdata space, does not write out without foundation, can guarantee the close of connection in this way
Type.And for the case where being worth of excessively transfiniting, shared weight cannot be infinitely great, avoids a space from determining final result, has
Effect avoids contingency, so proportion function form cannot be directlyed adopt, it should select exponential function form.
C. for the selection of limit value, if excessive, will cause the unknown sense of result, malfunction monitoring is inefficient, if too small,
It is then too sensitive, the case where wrong report can be generated.Since in a practical situation, some failures can embody 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 covert, the limit value δ for needing very little, which can just be detected, to be come.So being filled in order to embody the advantage of this algorithm
Fission reveals local details, and the present invention chooses a lesser δ value.If the δ value is excessive, it is unknown to will cause result
The case where sense, malfunction monitoring is inefficient, too sensitive if too small, can generate wrong report.Some failures are only seldom simultaneously
There is embodiment in several sub-spaces of number, it is therefore desirable to have the limit value δ of very little that can just detect and come.
So in order to meet above 3 points of the requirement, it is as follows The present invention gives a kind of calculation method of weight:
Wherein, ToS T2Or SPE statistic, ToSlIt is limited for its corresponding control.Then again to σ 'iPlace is normalized
Reason, obtains σi。
For the present embodiment using penicillin fermentation process as industrial background, penicillin fermentation schematic diagram is as shown in Figure 1.To non-linear
Batch process fault detection is studied.Using penicillin B enchmark model, emulation number is generated using Pensim analogue system
According to.It is about 300 hours in each batch time of penicillin fermentation process, the sampling interval that the present embodiment selects is 0.1 hour,
3000 data sample points are acquired 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 generated by having one to change.
The present embodiment acquires 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 establishing multi-model KICA analysis in subspace according to the method for the present invention, selection
Two groups of faulty data carry out simulation analysis:
Failure one: in a selected batch, introducing the substrate flow rate due to faulty operation change input quantity, from
And failure is formed, this is a both phase step fault.And the variable that the change of substrate flow rate influences is seldom, and is to ferment
The variable that the second stage of process just works, its change are not easy to embody in the result, belong to a kind of part
Failure.This failure is introduced in the 200th sampled point in experiment, and in the case of failure continues to the 500th sampled point, Fig. 7 A,
7B is respectively the T of the random space-division method of tradition2With SPE schematic diagram.Fig. 7 C and 7D is respectively proposed by the present invention based on only
T of the multi-direction KICA method of vertical Subspace partition for the monitoring situation of failure one2Statistic and SPE statistic schematic diagram.
Fig. 7 E and 7F is that the present invention marks off T in each Independent subspace come respectively2Statistic and SPE statistic；
Failure two: selecting another batch, introduces since a faulty operation changes the air mass flow of input quantity, this is one
A both phase step fault.The change of air mass flow all has an impact to the temperature of entire fermentation process, dissolved oxygen concentration, pH value etc., belongs to
One influences more extensive variable.Therefore it is easier reflected when this failure, belongs to global fault.This failure
The introducing time be the 300th sampled point, and in the case of continueing to the 500th sampled point, Fig. 8 A and 8B are respectively the present invention
T of the multi-direction KICA method divided based on Independent subspace proposed for the monitoring situation of failure one2Statistic and SPE system
Metering；
Monitoring for failure 1, according to the random space-division method of comparison tradition and proposed in this paper empty based on independent son
Between the multi-direction KICA method that divides, found out by Fig. 7 A and 7B in T2In SPE statistic, the hair of failure can be monitored
It is raw.But the two have one what is common is that failure generation some delay, it can be seen that about at the 210th sampled point
Statistic is just more than control limit.And the fluctuation of either score statistics or residual error statistics is all very big, 200 sampled points it
Before, about all occur the fluctuation more than control limit at 50,80 and 175 sampled points, this is because system in fermentation process
Caused by fluctuation, although this interference can be avoided by the way that alarm system is arranged, inevitably has bigger fluctuation and cause to report by mistake
The phenomenon that.And after the failure occurs, some fluctuations cause statistic and are down under control limit again, although imitating to whole monitoring
Fruit not substantive influence, but output result can also be interfered.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 joined weight distribution when each space is summarized, when the space proportion that does not transfinite
Small, the space proportion that transfinites is big, makes small smaller of overall output result, and big is bigger.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 later before occurring, and in the 200th sampling
The more point of point, also with regard to step jump just occurs at 201 or 202 sampled points, almost without delay.And statistic is whole
Bulk wave moves very little, occasionally has several bigger fluctuations also to limit far away from control, does not interfere with to output result.Wherein adopted 200
Fluctuation before sampling point is due to there is biggish statistics magnitude in the space transfinited individually, and shared large percentage produces result
Raw fluctuation.And some fluctuations are also produced after 200 sampled points, it is to be led due to not reaching control limit in some spaces
Cause proportion very little, it is small and it is small resulted in fluctuation.But on the whole, the method for the present invention can be monitored effectively and is out of order
1, and fluctuate small, it does not interfere with, it may be said that effect is very good.
About 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
It subspace5 is more than that result is very not there is no entirety although can reach on control limit after 200 sampled points in)
Stablize；It, can and in subspace 2,3 and 6 (i.e. subspace2, subspace3 and subspace6 in Fig. 7 E and Fig. 7 F)
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 occurs for some spaces, this says
It is bright in different spaces, the time of origin of failure is slightly different.On the whole, cause monitoring result in different spaces different
Reason is exactly that the space-division method of this paper is divided according to independent information, and the otherness in each space is very big.Change bottom
Logistics rate has influenced some variables, does not have an impact to other variables, so the space resulted in does not have failure
Occur, and some space failures occur obviously.The weight as shared by the subspace broken down is bigger, so just well
It embodies out in total statistic.This illustrates methods proposed in this paper to have an impact a small amount of variable these
Malfunction monitoring effect superiority, improve monitoring efficiency, reduce fluctuation interference, be a kind of highly effective method.
Monitoring for failure two, (as shown in Fig. 8 A, 8B, 8A is the random space-division method of tradition to two methods, and 8B is
The independent information space-division method of this paper) it is all fine to the monitoring effect of failure 2, the method for the present invention still more preferably, failure
The corresponding time does not postpone, and whole fluctuation is also very small.Although even have interference, there is no any influence to result.
Claims (6)
1. a kind of multi-direction KICA batch process fault monitoring method based on Independent subspace, it is characterised in that including following step
It is rapid:
1) three-dimensional data is launched into two dimension by batch using multidirectional KICA by acquisition batch process three-dimensional data X (I × J × K)
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 by the 2-D data of batch expansion, geo-nuclear tracin4 is added on the basis of ICA, by nonlinear data
It is mapped to high-dimensional feature space, then carries out linear process in higher dimensional space；
3) T is applied2Process is monitored on-line with SPE statistic；The fault message that each subdata obtains is summarized,
Whether Counting statistics amount transfinites；
To by batch expansion 2-D data carry out off-line modeling the following steps are included:
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 modeling is carried out to every sub-spaces respectively；
T is applied in step 3)2Carrying out on-line monitoring to process with SPE statistic includes following procedure:
3.1) real-time batch process data X is acquirednew；
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 statistic；
3.4) summarize whether Counting statistics amount transfinites.
2. the multi-direction KICA batch process fault monitoring method according to claim 1 based on Independent subspace, special
Sign is: in step 2.3), dividing k sub- data spaces according to independent metamessage are as follows: according to independent metamessage s1,s2,s3,…
skIt seeks out to the maximum data of its contribution degreeConstruct similarity matrix R；I-th of subdata space is constructed,
Process variable value corresponding to the maximum L similarity value of the i-th row of similarity matrix is taken, a sub-spaces are configured to；Repeat this
Step constructs i from 1 to k k sub- data spaces.
3. the multi-direction KICA batch process fault monitoring method according to claim 1 based on Independent subspace, special
Sign is: in step 2.4), carrying out KICA modeling to every sub-spaces respectively are as follows:
2.4.1 KICA modeling analysis) is carried out to i-th of subdata space κ i, for i-th of subdata space, process becomes
Amount isIt willIt is standardized, the subdata steric course data after being standardized
For
2.4.2) pass through Nonlinear Mapping for 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, expression formula are found out first are as follows:
It indicates are as follows: C=(1/L) Φ ΦT
Kernel function K () is added to assist calculating, takes kernel function are as follows:
Wherein, K ∈ RL×L, l=1,2 ... L, L are constant, and l is variable name, m=1,2 ... L；
The result that nuclear matrix is standardized are as follows:
In formula, ILFor constant matrices, element is equal, and is 1/N；
Nuclear matrix is standardized are as follows:
It is rightCarry out Eigenvalues Decomposition:
In formula, λ ' isCharacteristic value, α be feature vector corresponding with λ ', obtainD feature vector, wherein d be its
Maximum positive characteristic value number arranges characteristic value are as follows:
λ′1≥λ′2≥…≥λ′d (2.38)
Corresponding feature vector are as follows:
α1, α2..., αd(2.39)
The characteristic value number for defining highest dimension, needs to meet:
D characteristic value for obtaining covariance matrix C is respectively λ '1/L,λ′2/L,…,λ′d/ L, corresponding feature vector are v1,
v2,…,vd, physical relationship is as follows:
It writes 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 maximum eigenvalue diagonal matrix and its corresponding eigenvectors matrix；The new expression of covariance matrix C
Are as follows:
Enabling whitening matrix is P, then:
PTCP=I (2.45)
Data matrix in feature space after albefaction are as follows:
It is obtained by formula (2.46):
So obtain independent entry y are as follows:
。
4. the multi-direction KICA batch process fault monitoring method according to claim 1 based on Independent subspace, special
Sign is: modeling in step 3.3) to every sub-spaces KICA and calculates the T of the data in every sub-spaces2With SPE statistic,
It is using T2Statistics and SPE statistics carry out the calculating of control limit, wherein using T2Statistics calculates control limit specifically:
For 1~k sub- data spaces, Hotelling-T2Statistical definition are as follows:
Above formula is unfolded to obtain:
Wherein, y is independent entry, and D is the diagonal matrix of nuclear matrix characteristic value；
Using the method for Density Estimator, the independent same distribution sample of stochastic variable y is y1,y2,…,yn, probability density function
It is kernel function, h for f (y), k ()nIt is a constant for smooth coefficients, it is related with sample number n, and hn> 0, then:
It is respectively sample size, core letter to the parameter that it works by the calculated probability density function of Density Estimator method
Several and smooth coefficients selections, wherein passing through smooth coefficients h for known sample sizenSize and kernel function k ()
Form obtains probability density；Need to meet three conditions: K (y)=K (- y) for the selection of kernel function；K(y)≥0；∫K(y)dy
=1；
Optimal smooth coefficients are selected by mean square error, that is, the quadratic sum of the variance and 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 obtained accordinglynExpression formula:
At this point, MSE is minimum, with n-4/5Rate tend to 0；hoptWith rate 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, obtains further according to probability statistics knowledge
The coboundary in 99% region occupation probability density function f (y), the value of boundary this point are T2The control of statistic limits.
5. the multi-direction KICA batch process fault monitoring method according to claim 4 based on Independent subspace, special
Sign is: it is counted with SPE and calculates control limit, specifically:
Wherein,ZiIt is characterized in space by the mapping data after albefaction, is calculated value, k the
One constant of k sub-spaces,CiFor i-th of vector in initial matrix C, CkFor initial matrix C
In k-th of vector, ekFor residual error, residual error is further calculated
The sampling x at the k moment new for onenew∈Xnew, it is standardized to obtain X " firstnew, then using sub empty
Between divide, the process data for obtaining i-th of subdata space isMonitoring and statistics amount T is calculated finally by monitoring datai 2
And SPEi: T2Statistic are as follows:
SPE statistic are as follows:
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 following formula:
For SPE statistic, formula is provided accordingly:
A kind of method as a result, cumulative with weight is shown for each subdata space, statistical result is combined, for
T2Statistic is as a result as follows:
For SPE statistic, as a result are as follows:
In formula, σiFor weight shared by i-th of spatial statistics, andδ is limit value, that is to say, that when accumulative
Weighting and be more than this limit value when, it is believed that failure occur.
6. the multi-direction KICA batch process fault monitoring method according to claim 5 based on Independent subspace, special
Sign is:
Determining weight σ shared by i-th of spatial statisticsiWhen, with exponential function form,
Wherein, ToS T2Or SPE statistic, ToSlIt is limited for its corresponding control；Then again to σi' be normalized, it obtains
To σi。
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Citations (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN101158693A (en) * | 2007-09-26 | 2008-04-09 | 东北大学 | Bulk production process malfunction detection method based on multiple nucleus independent elements analyse |
| CN103853152A (en) * | 2014-03-21 | 2014-06-11 | 北京工业大学 | Batch process failure monitoring method based on AR-PCA (Autoregressive Principal Component Analysis) |
| CN104965949A (en) * | 2015-06-30 | 2015-10-07 | 东北大学 | Method for monitoring faults in smelting process of multimode magnesia electrical smelting furnace |
| CN105739489A (en) * | 2016-05-12 | 2016-07-06 | 电子科技大学 | Batch process fault detecting method based on ICA-KNN |
-
2017
- 2017-06-09 CN CN201710434406.4A patent/CN107065843B/en active Active
Patent Citations (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN101158693A (en) * | 2007-09-26 | 2008-04-09 | 东北大学 | Bulk production process malfunction detection method based on multiple nucleus independent elements analyse |
| CN103853152A (en) * | 2014-03-21 | 2014-06-11 | 北京工业大学 | Batch process failure monitoring method based on AR-PCA (Autoregressive Principal Component Analysis) |
| CN104965949A (en) * | 2015-06-30 | 2015-10-07 | 东北大学 | Method for monitoring faults in smelting process of multimode magnesia electrical smelting furnace |
| CN105739489A (en) * | 2016-05-12 | 2016-07-06 | 电子科技大学 | Batch process fault detecting method based on ICA-KNN |
Non-Patent Citations (4)
| Title |
|---|
| Decentralized Fault Diagnosis of;ZHANG Ying-Wei，ZHOU Hong，QIN S. Joe;《ACTA AUTOMATICA SINICA》;20100430;第36卷(第4期);第593-597页 |
| Process Monitoring of Multimode Processes Using Kernel Independent Component;Yingwei Zhang，Jiayu An，Chi Ma;《8th IFAC Symposium on Advanced Control of Chemical Processes》;20120731;第697-701页 |
| 一种基于动态独立子空间分析的过程监控方法;高翔，刘飞;《系统仿真学报》;20080731;第20卷(第13期);第3589-3592页 |
| 基于多元统计的复杂工业过程监测方法研究;冯淑敏;《中国优秀硕士学位论文全文数据库 信息科技辑》;20140715(第07期);正文第9-66页 |
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