CN109491338A - A kind of relevant method for diagnosing faults of multimode procedure quality based on sparse GMM - Google Patents
A kind of relevant method for diagnosing faults of multimode procedure quality based on sparse GMM Download PDFInfo
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Abstract
The invention discloses a kind of relevant method for diagnosing faults of multimode procedure quality based on sparse GMM, the coefficient weights matrix of high quality is obtained using rarefaction representation, and merge manifold structure information, construct sparse gauss hybrid models, so that the probability distribution of gauss component is along data manifold structure smooth change, and it is similar between the local neighbor sample of gauss component, automatically obtain the number of gauss component, there is robustness to noise and outlier, obtain the relevant fault detection of quality, simultaneously according to the controlled neighbour for having detected failure, the root variable that positioning failure occurs.Compared with gauss hybrid models monitoring method, the method for the present invention characterizes the sparse relationship of process data local manifolds structure and data, obtains the local similarity relation between sample, reflects the situation of change of multi-modal process.Therefore, sparse GMM method according to the present invention can obtain better fault detection effect and the root variable that failure occurs is accurately positioned.
Description
Technical field
The present invention relates to industrial process monitoring technical field, especially a kind of multimode procedure quality phase based on sparse GMM
The method for diagnosing faults of pass.
Background technique
The process monitoring of modern industry has a decisive role guarantee production safety, raising yield etc..With point
The development of cloth control system, production scale and operation complexity sharply increase, and process acquires a large amount of high dimensional data.And
And since the product hierarchy of production, yield can constantly be adjusted with the market demand and seasonal effect, product composition, process settings,
The technological parameters such as charge proportion also will appear fluctuation, and modern industrial process can be cut between multiple and different operation mode
It changes.Random variation in these production processes is so that the features such as non-linear, multi-modal is presented in process data.Although being driven based on data
Dynamic multivariatestatistical process control (Multivariate Statistical Process Control, MSPC) method is in process
Successful application is achieved in monitoring, but great variation has occurred in the mean value and covariance of multimode nonlinear data, passes
The MSPC method of system ignores existing non-linear and multimode relationship between various process variable, may cause moving back for monitoring result
Change.Moreover, in the actual production process, yield and product quality are generally difficult to direct-on-line measurement, need after the completion of production
It measures.Therefore, the relational model multimode process monitoring relevant for quality between product variable and quality variable is constructed
It is even more important.Gauss hybrid models (Gaussian Mixture Model, GMM) are used for multi-modal process monitoring, utilize one
Complicated data distribution during serial gauss component estimation multimode, and construct the statistics based on mahalanobis distance and likelihood probability and refer to
Mark implementation process monitoring.
However, GMM assumes that each single mode of multimode process is in Gaussian Profile, actual process data, which is possible to concentrate, divides
Cloth is in the submanifold structure of low-dimensional.Therefore, the neighborhood sample of each manifold is likely distributed in identical gauss component, can be with
The manifold geological information of fusion process constructs manifold GMM monitoring model.Moreover, yield and product quality to production process this
For a little key variables, it is difficult to direct-on-line measurement, but measured after the completion of production.Therefore, building process variable and matter
Relational model between quantitative change amount is even more important to the relevant fault detection and diagnosis of quality.
Recently, horse etc. (Neurcomputing, 2015 (285)) proposes robust gauss hybrid models (robust
Gaussian mixture model, RGMM), it is automatic to obtain gauss component number, it is used for the relevant fault detection and diagnosis of quality.
However, being also required to the similitude of crawl neighbour's data distribution in modeling during multimode in each gauss component, sufficiently excavating
Multi-modal manifold distinguishing ability keeps local geometry feature inside Gauss.In addition, the weight square in local manifolds structure
Battle array plays an important role in the geometry of description data, and traditional manifold learning generallys use k neighbour or ε-spherical shape side
Method determines neighborhood value in the case where given parameters.These methods are sensitive to noise data and outlier.
Summary of the invention
It is provided the technical problem to be solved by the present invention is to overcome the deficiencies in the prior art a kind of based on the more of sparse GMM
The relevant method for diagnosing faults of mold process quality, sparse GMM method proposed by the present invention can sufficiently find the interior of multimode process
Changing, according to the controlled neighbour for having detected that failure, is choosing important failure variable relevant to quality；Compared to Traditional GM M
Monitoring method can obtain higher diagnostic accuracy and stronger faults analysis ability.
The present invention uses following technical scheme to solve above-mentioned technical problem:
A kind of relevant method for diagnosing faults of multimode procedure quality based on sparse GMM proposed according to the present invention, including
Following steps:
Step A, the sparse representation model between establishment process variable and quality variable obtains the sparse reconstruction weights of sample
Matrix S；
Step B, sparse gauss hybrid models are constructed: in the sparse reconstruction weights matrix S obtained according to sparse representation model
Sparse coefficient, formed gauss component around neighbour's sample similarity constraint condition, the neighborhood of adaptively selected training sample
Range obtains the similar conditional probability distribution of gauss component, maintains the locality and sparsity of data manifold structure, automatically
Ground identifies gauss component number；
Step C, it constructs sparse GMM monitoring index, utilizes the output result and each mode of sparse gauss hybrid models
Local mahalanobis distance design error failure detection and diagnosis index, the output of the fusion process overall situation and local message, assess multi-modal process
Operating status.
It is further as a kind of relevant method for diagnosing faults of multimode procedure quality based on sparse GMM of the present invention
Prioritization scheme, the step A are specific as follows:
Given N number of sample from multimode process, each sample include process variable x ∈ RmWith quality variable y ∈ R, then
History data set D is indicated are as follows:
Wherein, RmIndicate that m ties up variable, R indicates 1 dimension variable, [y (1) x (1)]TIndicate that quality variable and the 1st process become
Amount, writes a Chinese character in simplified form into d1, and so on, [y (1) x (N)]TIt indicates quality variable and n-th process variable, writes a Chinese character in simplified form into dN, subscript T is to turn
It sets；
Rarefaction representation calculates the rarefaction representation amount of training sample by following equation combined optimization objective function:
In formula, the sum of the absolute value of L1- normal form representing matrix element, λ is regularization parameter positive value, and E is sparse error, e
The column vector for being 1 for element；Sparse reconstruction weights matrix S=[s is solved using convex optimization method1,s2,…,sN]∈RN×N, RN ×NIndicate that row and column is the memory space of N, wherein sn=[sn1,sn2,…,snn-1,0,snn+1,…,snN]T, n=1,2..., N,
snFor n-th of sample data dnSparse coefficient variable, its each element snjIndicate dnTo j-th of sample d of reconstructjContribution
Degree.
It is further as a kind of relevant method for diagnosing faults of multimode procedure quality based on sparse GMM of the present invention
Prioritization scheme, constructing sparse gauss hybrid models, specific step is as follows:
Step a, the probability density function p (d | Θ) of building gauss hybrid models relevant to quality, each sample is indicated
Are as follows:
Wherein, d is sample data, and C is gauss component number, ωkIt is the posterior probability of k-th of gauss component, meetsGaussian parameter θk={ μk,Σk, μkIt is kth class mean value, ΣkIt is kth class covariance matrix, Θ={ θ1,
θ2,...,θCBe global Gauss model parameter set, θ1,θ2,...,θCRespectively represent the 1st, the 2nd ..., the C part
Gauss component；For k-th of gauss component, its probability density function g (d θk) be expressed as
If Z={ z1,z2,…,zNIndicate the missing data of classification, and zi∈ { 1,2 ..., C }, ziIndicate the i-th sample category
In classification；If zi=k, then it represents that the i-th sample belongs to k-th of gauss component, then latent variable zki=1, otherwise zki=0；M is sample
The parameter Θ of this dimension, the relevant gauss hybrid models of quality is solved by maximizing following likelihood function:
In formula, L (ω, Θ；D, Z) it is likelihood function, ω is posterior probability；
Step b, the principle being still close to based on the similar sample in rarefaction representation and manifold structure in embedded space,
The geometry knowledge of fusion conditions probability distribution, constructs sparse GMM in GMM objective function；To gaussian probability distribution at
Similar constraint is realized and minimizes sparse regular terms, bound term indicates are as follows:
Wherein, γn=p (zn|dn), indicate n-th of sample dnBelong to znThe probability of classification, γj=p (zj|dj), indicate jth
A sample djBelong to zjThe probability of classification, H (| |) two kinds of similarity degrees being distributed have been measured, it is minimum using KL distance metric
After changing bound term, data will be along manifold geometry ranging smooth distribution；The sparse regular terms is merged with the likelihood function of GMM,
Obtain the objective function J of sparse GMM:
Wherein, δ > 0 is regularization parameter；The parameter of sparse GMM is solved using desired value maximization approach；
Step c, according to original GMM and bayes rule, latent variable z is calculatedki:
Wherein, ωlIt is the posterior probability of gauss component l, g (di|θk) it is sample diIn gauss component θkDensity probability, g
(di|θl) it is sample diIn gauss component θlDensity probability；
Step d, model parameter is updated:
In formula,It is the classification summation of the sample of k-th of gauss component, Ωnk=(dn-μk)(dn-μk)T,
It is the sample covariance of k-th of gauss component.
It is further as a kind of relevant method for diagnosing faults of multimode procedure quality based on sparse GMM of the present invention
Prioritization scheme, the step of constructing sparse GMM monitoring index, are specific as follows:
Step 1., for each monitoring sample dt, the output of global structure information is characterized according to sparse GMM as a result, utilizing
Model exports JoutMeasurement monitoring sample deviates the degree of controlled trained baseline, and measurement monitoring sample deviates controlled trained baseline
Degree JoutIt indicates are as follows:
Jout=-ln p (dt|Θ) (12)
In formula, p (dt| Θ) indicate monitoring sample dtProbability density based on training pattern；
The output valve of the monitoring sample probability smaller than training sample output valve is counted, L is designedotQuantification of targets process shape
State:
Lot(dt)=Pr (Jout(dt)≤Jout(dtrain)) (13)
In formula, Jout(dtrain) indicate training set output, Jout(dt) indicate test sample output, Lot(dt) it is the overall situation
Information index；Pr(Jout(dt)≤Jout(dtrain)) indicate probability of the test sample output lower than training set output；
Mahalanobis distance is used to measure the relevant fault detection of quality in single mode, calculates monitoring sample dtTo each mould
State CkMahalanobis distance MD are as follows:
Mahalanobis distance follows the χ approached2Distribution, i.e.,And
Pass through amalgamation of global information index Lot(dt) and local information index MD(k)(dt|dt∈ k), one synthesis failure of design
Testing index GL, reduces monitoring cost and operating burden, and GL is indicated are as follows:
Given control limit ηα, when monitoring sample GL beyond the control limit, then detect failure relevant to quality, it is no
Then, illustrate fault-free；
Step 2., after the relevant failure of detection mass, further determine that the root variable that failure occurs；Process is become
The contribution degree of amount is defined as fault sample the distance between to controlled neighbour, passes through the virtual controlled neighbour for solving failure, obtains
Failure deviates the direction of normal operating, determines the root variable that failure generates；
The majorized function of the controlled neighbour of failure definition are as follows:
Wherein, dfaultIt is the fault sample detected, dnicnIt is virtual controlled neighbour's sample of failure, from training sample
Initialization input of the sample as Nonlinear Programming Technique is randomly choosed, solves controlled neighbour's sample, then fault sample is into one
Step indicates are as follows:
dfault=dnicn+f (17)
In formula, f indicates the fault vectors estimated, the minimum value for being adjusted to normal condition for evaluating fault sample；
The contribution degree of each variable is defined as dfaultAnd dnicnBetween Euclidean distance CONq:
In formula,And fqRespectively indicate dnicn, dfaultWith q-th of element of f；
The contribution degree CONMD of variable is redefined using mahalanobis distanceq:
In formula, ξqIt is the unit vector that q-th of element is 1, there will be maximum CONMDqThe variables set of value is isolated, and threshold is arranged
Value τ are as follows:
If the variable of failure has exceeded this threshold tau, it is determined that the variation of the variable causes process exception, triggering event
Barrier.
It is further as a kind of relevant method for diagnosing faults of multimode procedure quality based on sparse GMM of the present invention
Prioritization scheme, α=0.05.
The invention adopts the above technical scheme compared with prior art, and it is sparse to have following technical effect that the present invention utilizes
It indicates the weight matrix of characterization manifold structure, keeps the local geometry feature of data manifold in gauss component, automatically obtain
Take gauss component quantity, in the process noise and outlier have robustness；This method merges manifold on the basis of GMM
The sparsity and locality of geometry construct sparse GMM, grab process variable characteristic relevant to quality variable, reflect more
The state change situation of mold process, and according to the controlled neighbour for having detected that failure, identify out of order root variable；The present invention
Method is suitble to the relevant fault detection and diagnosis of quality during multimode.
Detailed description of the invention
Fig. 1 is the implementation flow chart of the method for the present invention.
Specific embodiment
To make the objectives, technical solutions, and advantages of the present invention clearer, below in conjunction with the accompanying drawings and the specific embodiments
The present invention will be described in detail.
The present invention uses a kind of sparse representation method of printenv robustness, constructs the eigenmatrix of manifold structure, automatically
Ground decision sample contiguous range.
In view of rarefaction representation and the relevant GMM model of quality in the advantage of process monitoring, the multimode based on sparse GMM is proposed
The relevant method for diagnosing faults of procedure quality keeps local similarity geometrically between sample of the manifold of gauss component and sparse
Property, strengthen GMM model learning performance, the diagnosis capability of lift scheme.
The present invention is special for the potential labyrinth of the relevant multimode process of quality on the basis of gauss hybrid models
Property, the weight matrix of manifold structure is robustly characterized using rarefaction representation printenv, and be based on gauss component upstream graphic data sample
Similitude between this constructs sparse gauss hybrid models, keeps the local feature and sparse features of multimode process data.It proposes
Sparse GMM method can sufficiently find the inherent variation of multimode process, according to the controlled neighbour for having detected that failure, choose with
The relevant important failure variable of quality.Compared to Traditional GM M monitoring method, higher diagnostic accuracy and stronger event can be obtained
Hinder distinguishing ability.
The relevant method for diagnosing faults of multimode procedure quality based on sparse GMM characterizes gauss component using rarefaction representation
Geological information distribution situation, construct sparse GMM, analyze the data distribution characteristics of multimode process, extract mistake relevant to quality
Journey characteristics of variables, the inherent variation of crawl multimode process, the root variable that analysis failure occurs enhance the event of sparse GMM method
Hinder diagnosis capability.
As shown in Figure 1, the present invention relates to a kind of relevant fault diagnosis side of multimode procedure quality based on sparse GMM
The specific implementation step of method, this method is as follows:
(1) sparse representation model between establishment process variable and quality variable obtains the sparse reconstruction weights square of sample
Battle array S.
Given N number of sample from multimode process, each sample include process variable x ∈ RmWith quality variable y ∈ R, then
History data set D is indicated are as follows:
Wherein, RmIndicate that m ties up variable, R indicates 1 dimension variable, [y (1) x (1)]TIndicate that quality variable and the 1st process become
Amount, writes a Chinese character in simplified form into d1, and so on, [y (1) x (N)]TIt indicates quality variable and n-th process variable, writes a Chinese character in simplified form into dN, subscript T is to turn
It sets；
Rarefaction representation calculates the rarefaction representation amount of training sample by following equation combined optimization objective function:
In formula, the sum of the absolute value of L1- normal form representing matrix element, λ is regularization parameter positive value, and E is sparse error, e
The column vector for being 1 for element；Sparse reconstruction weights matrix S=[s is solved using convex optimization method1,s2,…,sN]∈RN×N, RN ×NIndicate that row and column is the memory space of N, wherein sn=[sn1,sn2,…,snn-1,0,snn+1,…,snN]T, n=1,2..., N,
snFor n-th of sample data dnSparse coefficient variable, its each element snjIndicate dnTo j-th of sample d of reconstructjContribution
Degree.
(2) sparse gauss hybrid models are constructed.By increasing the constraint condition of neighbour's sample similarity around gauss component,
The contiguous range of adaptively selected training sample obtains the similar conditional probability distribution of gauss component, maintains data manifold
The locality and sparsity of structure automatically identify gauss component number, have robustness to noise data and outlier.It solves
The sub-step of sparse gauss hybrid models is as follows:
Step a, the probability density function p (d | Θ) of building gauss hybrid models relevant to quality, each sample is indicated
Are as follows:
Wherein, d is sample data, and C is gauss component number, ωkIt is the posterior probability of k-th of gauss component, meetsGaussian parameter θk={ μk,Σk, μkIt is kth class mean value, ΣkIt is kth class covariance matrix, Θ={ θ1,
θ2,...,θCBe global Gauss model parameter set, θ1,θ2,...,θCRespectively represent the 1st, the 2nd ..., the C part
Gauss component；For k-th of gauss component, its probability density function g (d θk) be expressed as
If Z={ z1,z2,…,zNIndicate the missing data of classification, and zi∈ { 1,2 ..., C }, ziIndicate the i-th sample category
In classification；If zi=k, then it represents that the i-th sample belongs to k-th of gauss component, then latent variable zki=1, otherwise zki=0；M is sample
The parameter Θ of this dimension, the relevant gauss hybrid models of quality is solved by maximizing following likelihood function:
In formula, L (ω, Θ；D, Z) it is likelihood function, ω is posterior probability；
Step b, the principle being still close to based on the similar sample in rarefaction representation and manifold structure in embedded space,
The geometry knowledge of fusion conditions probability distribution, constructs sparse GMM in GMM objective function；To gaussian probability distribution at
Similar constraint is realized and minimizes sparse regular terms, bound term indicates are as follows:
Wherein, γn=p (zn|dn), indicate n-th of sample dnBelong to znThe probability of classification, γj=p (zj|dj), indicate jth
A sample djBelong to zjThe probability of classification, H (| |) two kinds of similarity degrees being distributed have been measured, it is minimum using KL distance metric
After changing bound term, data will be along manifold geometry ranging smooth distribution；The sparse regular terms is merged with the likelihood function of GMM,
Obtain the objective function J of sparse GMM:
Wherein, δ > 0 is regularization parameter；The parameter of sparse GMM is solved using desired value maximization approach；
Step c, according to original GMM and bayes rule, latent variable z is calculatedki:
Wherein, ωlIt is the posterior probability of gauss component l, g (di|θk) it is sample diIn gauss component θkDensity probability, g
(di|θl) it is sample diIn gauss component θlDensity probability；
Step d, model parameter is updated:
In formula,It is the classification summation of the sample of k-th of gauss component, Ωnk=(dn-μk)(dn-μk)T,
It is the sample covariance of k-th of gauss component.
(3) sparse GMM monitoring index is constructed, the output result of entire model and the local mahalanobis distance of each mode are utilized
Reasonable fault detection and diagnosis index, the output of the fusion process overall situation and local message are designed, the operation of multi-modal process is assessed
State.The sub-step for solving sparse GMM monitoring index indicates are as follows:
Step 1., for each monitoring sample dt, the output of global structure information is characterized according to sparse GMM as a result, utilizing
Model exports JoutMeasurement monitoring sample deviates the degree of controlled trained baseline, and measurement monitoring sample deviates controlled trained baseline
Degree JoutIt indicates are as follows:
Jout=-ln p (dt|Θ) (12)
In formula, p (dt| Θ) indicate monitoring sample dtProbability density based on training pattern；
The output valve of the monitoring sample probability smaller than training sample output valve is counted, L is designedotQuantification of targets process shape
State:
Lot(dt)=Pr (Jout(dt)≤Jout(dtrain)) (13)
In formula, Jout(dtrain) indicate training set output, Jout(dt) indicate test sample output, Lot(dt) it is the overall situation
Information index；Pr(Jout(dt)≤Jout(dtrain)) indicate probability of the test sample output lower than training set output；
Mahalanobis distance is used to measure the relevant fault detection of quality in single mode, calculates monitoring sample dtTo each mould
State CkMahalanobis distance MD are as follows:
Mahalanobis distance follows the χ approached2Distribution, i.e.,And
Pass through amalgamation of global information index Lot(dt) and local information index MD(k)(dt|dt∈ k), one synthesis failure of design
Testing index GL, reduces monitoring cost and operating burden, and GL is indicated are as follows:
Given control limit ηα(α=0.05), when monitoring sample GL beyond the control limit, then detect relevant to quality
Otherwise failure illustrates fault-free；
Step 2., after the relevant failure of detection mass, further determine that the root variable that failure occurs；Process is become
The contribution degree of amount is defined as fault sample the distance between to controlled neighbour, passes through the virtual controlled neighbour for solving failure, obtains
Failure deviates the direction of normal operating, determines the root variable that failure generates；
The majorized function of the controlled neighbour of failure definition are as follows:
Wherein, dfaultIt is the fault sample detected, dnicnIt is virtual controlled neighbour's sample of failure, from training sample
Initialization input of the sample as Nonlinear Programming Technique is randomly choosed, solves controlled neighbour's sample, then fault sample is into one
Step indicates are as follows:
dfault=dnicn+f (17)
In formula, f indicates the fault vectors estimated, the minimum value for being adjusted to normal condition for evaluating fault sample；
The contribution degree of each variable is defined as dfaultAnd dnicnBetween Euclidean distance CONq:
In formula,And fqRespectively indicate dnicn, dfaultWith q-th of element of f；
The contribution degree CONMD of variable is redefined using mahalanobis distanceq:
In formula, ξqIt is the unit vector that q-th of element is 1, there will be maximum CONMDqThe variables set of value is isolated, and threshold is arranged
Value τ are as follows:
If the variable of failure has exceeded this threshold tau, it is determined that the variation of the variable causes process exception, triggering event
Barrier.
The present invention keeps the part of data manifold in gauss component using the weight matrix of rarefaction representation characterization manifold structure
Geometry feature, automatically obtain gauss component quantity, in the process noise and outlier have robustness.This method exists
On the basis of GMM, the sparsity and locality of manifold geometry are merged, constructs sparse GMM, is grabbed relevant to quality variable
Process variable characteristic reflects the state change situation of multimode process, and according to the controlled neighbour for having detected that failure, identifies event
The root variable of barrier.Therefore, the method for the present invention is suitble to the relevant fault detection and diagnosis of quality during multimode.
The above description is merely a specific embodiment, but scope of protection of the present invention is not limited thereto, any
In the technical scope disclosed by the present invention, any changes or substitutions that can be easily thought of by those familiar with the art, all answers
It is included within the scope of protection of the present invention.
Claims (5)
1. a kind of relevant method for diagnosing faults of multimode procedure quality based on sparse GMM, which is characterized in that including following step
It is rapid:
Step A, the sparse representation model between establishment process variable and quality variable obtains the sparse reconstruction weights matrix of sample
S；
Step B, sparse gauss hybrid models are constructed: dilute in the sparse reconstruction weights matrix S obtained according to sparse representation model
Sparse coefficient, formed gauss component around neighbour's sample similarity constraint condition, the contiguous range of adaptively selected training sample,
The similar conditional probability distribution of gauss component is obtained, the locality and sparsity of data manifold structure is maintained, automatically knows
Other gauss component number；
Step C, sparse GMM monitoring index is constructed, the output result of sparse gauss hybrid models and the part of each mode are utilized
The detection of mahalanobis distance design error failure and diagnosis index, the output of the fusion process overall situation and local message, assess the fortune of multi-modal process
Row state.
2. a kind of relevant method for diagnosing faults of multimode procedure quality based on sparse GMM according to claim 1, special
Sign is that the step A is specific as follows:
Given N number of sample from multimode process, each sample include process variable x ∈ RmWith quality variable y ∈ R, then history number
It is indicated according to collection D are as follows:
Wherein, RmIndicate that m ties up variable, R indicates 1 dimension variable, [y (1) x (1)]TIndicate quality variable and the 1st process variable, letter
Write as d1, and so on, [y (1) x (N)]TIt indicates quality variable and n-th process variable, writes a Chinese character in simplified form into dN, subscript T is transposition；
Rarefaction representation calculates the rarefaction representation amount of training sample by following equation combined optimization objective function:
In formula, the sum of the absolute value of L1- normal form representing matrix element, λ is regularization parameter positive value, and E is sparse error, and e is member
The column vector that element is 1；Sparse reconstruction weights matrix S=[s is solved using convex optimization method1,s2,…,sN]∈RN×N, RN×NTable
Show that row and column is the memory space of N, wherein sn=[sn1,sn2,…,snn-1,0,snn+1,…,snN]T, n=1,2..., N, snFor
N-th of sample data dnSparse coefficient variable, its each element snjIndicate dnTo j-th of sample d of reconstructjContribution degree.
3. a kind of relevant method for diagnosing faults of multimode procedure quality based on sparse GMM according to claim 1, special
Sign is that constructing sparse gauss hybrid models, specific step is as follows:
Step a, the probability density function p (d | Θ) of building gauss hybrid models relevant to quality, each sample is indicated are as follows:
Wherein, d is sample data, and C is gauss component number, ωkIt is the posterior probability of k-th of gauss component, meetsGaussian parameter θk={ μk,Σk, μkIt is kth class mean value, ΣkIt is kth class covariance matrix, Θ={ θ1,
θ2,...,θCBe global Gauss model parameter set, θ1,θ2,...,θCRespectively represent the 1st, the 2nd ..., the C part
Gauss component；For k-th of gauss component, it probability density function g (d | θk) be expressed as
If Z={ z1,z2,…,zNIndicate the missing data of classification, and zi∈ { 1,2 ..., C }, ziIndicate what the i-th sample belonged to
Classification；If zi=k, then it represents that the i-th sample belongs to k-th of gauss component, then latent variable zki=1, otherwise zki=0；M is sample
The parameter Θ of dimension, the relevant gauss hybrid models of quality is solved by maximizing following likelihood function:
In formula, L (ω, Θ；D, Z) it is likelihood function, ω is posterior probability；
Step b, the principle being still close to based on the similar sample in rarefaction representation and manifold structure in embedded space, in GMM mesh
The geometry knowledge of fusion conditions probability distribution, constructs sparse GMM in scalar functions；To pairs of similar in gaussian probability distribution
Constraint, which is realized, minimizes sparse regular terms, and bound term indicates are as follows:
Wherein, γn=p (zn|dn), indicate n-th of sample dnBelong to znThe probability of classification, γj=p (zj|dj), indicate j-th of sample
This djBelong to zjThe probability of classification, H (| |) two kinds of similarity degrees being distributed have been measured, using KL distance metric, minimize about
Shu Xianghou, data will be along manifold geometry ranging smooth distributions；The sparse regular terms is merged with the likelihood function of GMM, is obtained
The objective function J of sparse GMM:
Wherein, δ > 0 is regularization parameter；The parameter of sparse GMM is solved using desired value maximization approach；
Step c, according to original GMM and bayes rule, latent variable z is calculatedki:
Wherein, ωlIt is the posterior probability of gauss component l, g (di|θk) it is sample diIn gauss component θkDensity probability, g (di|
θl) it is sample diIn gauss component θlDensity probability；
Step d, model parameter is updated:
In formula,It is the classification summation of the sample of k-th of gauss component, Ωnk=(dn-μk)(dn-μk)T, it is
The sample covariance of k gauss component.
4. a kind of relevant method for diagnosing faults of multimode procedure quality based on sparse GMM according to claim 1, special
The step of sign is, constructs sparse GMM monitoring index is specific as follows:
Step 1., for each monitoring sample dt, the output of global structure information is characterized as a result, defeated using model according to sparse GMM
J outoutMeasurement monitoring sample deviates the degree of controlled trained baseline, and measurement monitoring sample deviates the degree J of controlled trained baselineout
It indicates are as follows:
Jout=-lnp (dt|Θ) (12)
In formula, p (dt| Θ) indicate monitoring sample dtProbability density based on training pattern；
The output valve of the monitoring sample probability smaller than training sample output valve is counted, L is designedotQuantification of targets process status:
Lot(dt)=Pr (Jout(dt)≤Jout(dtrain)) (13)
In formula, Jout(dtrain) indicate training set output, Jout(dt) indicate test sample output, Lot(dt) it is global information
Index；Pr(Jout(dt)≤Jout(dtrain)) indicate probability of the test sample output lower than training set output；
Mahalanobis distance is used to measure the relevant fault detection of quality in single mode, calculates monitoring sample dtTo each mode Ck
Mahalanobis distance MD are as follows:
Mahalanobis distance follows the χ approached2Distribution, i.e.,And
Pass through amalgamation of global information index Lot(dt) and local information index MD(k)(dt|dt∈ k), one synthesis fault detection of design
Index GL, reduces monitoring cost and operating burden, and GL is indicated are as follows:
Given control limit ηα, when monitoring sample GL beyond the control limit, then detect failure relevant to quality, otherwise, explanation
Fault-free occurs；
Step 2., after the relevant failure of detection mass, further determine that the root variable that failure occurs；By process variable
Contribution degree is defined as fault sample the distance between to controlled neighbour, passes through the virtual controlled neighbour for solving failure, obtains failure
The direction for deviateing normal operating determines the root variable that failure generates；
The majorized function of the controlled neighbour of failure definition are as follows:
Wherein, dfaultIt is the fault sample detected, dnicnIt is virtual controlled neighbour's sample of failure, it is random from training sample
It selects sample to input as the initialization of Nonlinear Programming Technique, solves controlled neighbour's sample, then the further table of fault sample
It is shown as:
dfault=dnicn+f (17)
In formula, f indicates the fault vectors estimated, the minimum value for being adjusted to normal condition for evaluating fault sample；Each
The contribution degree of variable is defined as dfaultAnd dnicnBetween Euclidean distance CONq:
In formula,And fqRespectively indicate dnicn, dfaultWith q-th of element of f；
The contribution degree CONMD of variable is redefined using mahalanobis distanceq:
In formula, ξqIt is the unit vector that q-th of element is 1, there will be maximum CONMDqThe variables set of value is isolated, and threshold tau is arranged
Are as follows:
If the variable of failure has exceeded this threshold tau, it is determined that the variation of the variable causes process exception, triggers failure.
5. a kind of relevant method for diagnosing faults of multimode procedure quality based on sparse GMM according to claim 4, special
Sign is, α=0.05.
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