CN104777830B - A kind of multiple operating modes process monitoring method based on KPCA mixed models - Google Patents

Abstract

The invention discloses a kind of multiple operating modes process monitoring method based on KPCA mixed models, belong to industrial process monitoring and diagnostic techniques field.The present invention combines gauss hybrid models and core pivot element analysis model, using superior function of the core pivot element analysis the problems such as advantage and gauss hybrid models in terms of handling industrial process nonlinear, reduction data dimension are handling non-gaussian, multi-state, industrial process is monitored.Compared to existing other method, due to the non-gaussian for having taken into full account industrial process, non-linear, multi-state complex characteristics, the inventive method can more accurately estimate the statistical property of each operating mode, so as to more accurately and timely detect the various failures of multiple operating modes process.

Description

A kind of multiple operating modes process monitoring method based on KPCA mixed models

Technical field

It is more particularly to a kind of based on many of KPCA mixed models the invention belongs to industrial process monitoring and fault diagnosis field Operating mode course monitoring method.

Background technology

With the growth of industrial process complexity, the Usefulness Pair of Industrial Process Monitoring and diagnosis is in guarantee production process peace Entirely, maintaining product quality and optimization product interests becomes to become more and more important.

For process monitoring and troubleshooting issue, traditional method uses multivariate statistical process monitoring technology mostly (Multivariable Statistical Process Monitoring, MSPM), wherein with pivot analysis (Principal Component Analysis, PCA) and offset minimum binary (Partial Least Squares, PLS) be the method such as representative It is successfully applied in industrial process monitoring.Traditional MSPM methods assume process data Gaussian distributed, become Be between amount linear relationship and data under single operation operating mode, but measurement data is difficult to meet these hypothesis in practice Condition, is often presented the characteristics such as non-gaussian, non-linear and multi-state.Although some improved methods are such as directed to non-gaussian ICA, core PCA (KPCA) etc. is also suggested.But, when the characteristics such as above-mentioned non-gaussian, non-linear and multi-state are simultaneous, these sides Method still can not be solved well.

In recent years, the multiple operating modes process monitoring method based on PCA mixed models is proposed for solving the above problems.Will be mixed Close Gauss model and PCA is combined, the operating mode number of model and the distributed constant and pivot number of operating mode are estimated with EM algorithms, and it is right Each submodel builds T², SPE statistics multiple operating modes process when realizing monitoring.Such a method is to each gauss component model A pca model is established, but tradition PCA can only handle the linear relationship between variable, can not extract the non-thread between variable Property information, and the non-linear relation between industrial process, variable is generally existing.Thus, there are strong nonlinearity feelings in operating mode Under condition, fault detect may be caused to make a mistake.

The content of the invention

The purpose of the present invention is there is provided a kind of multiple operating modes process based on KPCA mixed models in view of the shortcomings of the prior art Monitoring method, it is mixed using advantage of the core pivot element analysis in terms of processing industrial process nonlinear, reduction data dimension and Gauss Superior function of matched moulds type the problems such as non-gaussian, multi-state is handled, is monitored to industrial process, so that more accurately and timely Detect the various failures of multiple operating modes process.

The step of a kind of multiple operating modes process monitoring method based on KPCA mixed models, this method, is as follows：

Step one：Off-line modeling, collects the data that multiple operating modes process is normally run, and gauss hybrid models is built, in Gauss On the basis of mixed model, KPCA conversion and dimensionality reduction are carried out to each Gauss member space, the mixed model based on KPCA is established.Adopt Model parameter is estimated with EM algorithms, and the control for building each operating mode according to traditional KPCA methods is limited；

Step 2：On-line checking, gathers on-line operation data, is pressed using the mixed model described in step one by sample is monitored Its posterior probability magnitude classification is into corresponding operating mode, and according to traditional KPCA method Counting statistics amounts, if the statistic The corresponding control limit set up beyond step one, then failure judgement generation.

Off-line modeling process described in step one is as follows：

1) the multi-state Monitoring Data gathered using industrial process constitutes X=[x₁,x₂,…,x_n]^T∈R^n×m, wherein m represents The number of variable is monitored, n represents number of samples, x_i∈R^m, i=1 ..., n represents i-th of sample；

2) its probability density function under limited GMM model is expressed asWherein K represents GMM Middle mixed Gaussian component number, w_iThe mixed coefficint of i-th of single gauss component is represented, and is met With θ={ θ₁,…,θ_KLocal and global Gauss model parameter set, i.e. mean vector μ are represented respectively_iWith covariance matrix Σ_i.Phase The multivariate Gaussian density function for i-th of the component answered is represented by

3) i-th of single gauss component sample set is expressed asθ_i={ μ_i,Σ_i}.It is right Data set X_iCarry out KPCA projections.

3.1) kernel function φ is introduced by data set X_iHigh-dimensional feature space F is projected to, is expressed as

Φ:R^m→F (1)

3.2) nuclear matrix K is calculated

K_ij=＜ Φ (x_i),Φ(x_j) ＞=K (x_i,x_j) (2)

Wherein use Radial basis kernel functionσ=rm, r are constant.

3.3) centralization processing is carried out to nuclear matrix K

Wherein

3.4) principal component t is calculated_k

4) model parameter is estimated using EM algorithms

4.1)E-step

Wherein p^(s)(C_i|x_j) represent that j-th of training sample belongs to the posterior probability of i-th of gauss component after the s times iteration.

4.2)M-step

Wherein,And α_i,jRepresent respectively after (s+1) secondary iteration, i-th gauss component Average, covariance, prior probability and KPCA characteristic vectors.

5) T is determined²Count and limit with SPE

On-line checking process described in step 2 is as follows：

1) online acquisition measurement data y ∈ R^m；

2) the operating mode classification that collecting sample belongs to is judged.CalculateThen x_tAffiliated operating mode For

3) T of collecting sample is calculated²With SPE statistics.

T²=[t₁,…,t_p]Λ^-1[t₁,…,t_p]^T (12)

4) T is compared², the detection control limit T that is set up in SPE and formula (10), (11)² _lim、SPE_limBetween size, if Statistic is limited beyond control, then failure judgement occurs；If statistic is limited less than control, declarative procedure is normally run.

A kind of method described in basis is used for blast furnace ironmaking process fault diagnosis.

The present invention has following advantage：

1. present invention firstly provides a kind of multiple operating modes process monitoring method based on KPCA mixed models, realize to complicated mistake The monitoring of journey；

2. the present invention can solve the problem that process data exist non-gaussian, it is non-linear and multi-modal the problems such as, so as to more Effectively monitor.

Embodiment

A kind of multiple operating modes process monitoring method based on KPCA mixed models proposed by the present invention, including following steps：

Step one：Off-line modeling

1) the multi-state Monitoring Data gathered using industrial process constitutes X=[x₁,x₂,…,x_n]^T∈R^n×m, wherein m represents The number of variable is monitored, n represents number of samples, x_i∈R^m, i=1 ..., n represents i-th of sample；

2) its probability density function under limited GMM model is expressed asWherein K is represented in GMM Mixed Gaussian component number, w_iThe mixed coefficint of i-th of single gauss component is represented, and is metWith θ= {θ₁,…,θ_KLocal and global Gauss model parameter set, i.e. mean vector μ are represented respectively_iWith covariance matrix Σ_i.Accordingly The multivariate Gaussian density function of i-th of component is represented by

3) i-th of single gauss component sample set is expressed asθ_i={ μ_i,Σ_i}.It is right Data set X_iCarry out KPCA projections.

3.1) kernel function φ is introduced by data set X_iHigh-dimensional feature space F is projected to, is expressed as

Φ:R^m→F (1)

3.2) nuclear matrix K is calculated

K_ij=＜ Φ (x_i),Φ(x_j) ＞=K (x_i,x_j) (2)

Wherein use Radial basis kernel functionσ=rm, r are constant.

3.3) centralization processing is carried out to nuclear matrix K

Wherein

3.4) principal component t is calculated_k

4) model parameter is estimated using EM algorithms

4.1)E-step

Wherein p^(s)(C_i|x_j) represent that j-th of training sample belongs to the posterior probability of i-th of gauss component after the s times iteration.

4.2)M-step

Wherein,And α_i,jRepresent respectively after (s+1) secondary iteration, i-th gauss component Average, covariance, prior probability and KPCA characteristic vectors.

5) T is determined²Count and limit with SPE

Step 2：On-line monitoring

1) online acquisition measurement data y ∈ R^m；

2) the operating mode classification that collecting sample belongs to is judged.CalculateThen x_tIt is affiliated Operating mode is

3) T of collecting sample is calculated²With SPE statistics.

T²=[t₁,…,t_p]Λ^-1[t₁,…,t_p]^T (12)

4) T is compared², the detection control limit T that is set up in SPE and formula (10), (11)² _lim、SPE_limBetween size, if Statistic is limited beyond control, then failure judgement occurs；If statistic is limited less than control, declarative procedure is normally run.

Embodiment

Smelting iron and steel as one of most important basic industry in national economy, be weigh national economic level and The important indicator of overall national strength.And blast furnace ironmaking is most important link in steel and iron industry production procedure, so to large blast furnace Damage is diagnosed to carry out studying significant with method for safe operation.

Blast furnace is a huge closed reaction vessel, and its internal smelting process is under high temperature, condition of high voltage, by one Serial complicated physical chemistry and heat transfer are reacted, and are a typical "black box" operations.Just because of the complexity inside blast furnace, So that its monitoring process has non-linear, non-Gaussian system and the characteristic such as multi-modal.Therefore, it is proposed that method to blast furnace therefore Barrier monitoring has adaptability.Illustrate the validity of the inventive method with reference to No. 2 blast furnaces of Liu Gang.

Be found in the Liu Gang iron-smelters of 1958, be one have that the equipment of 56 years brilliant history is advanced, equipment compared with High large-scale smelting enterprise, major product is the pig iron, and byproduct has stove dirt, slag, blast furnace gas etc..It possesses 7 modernizations Blast furnace, blast furnace entirety dischargeable capacity is 11750 cubic metres, wherein No. 2 blast furnace dischargeable capacitys are 2000 cubic metres, it is current Guangxi Maximum blast furnace.After new blast furnace is gone into operation, iron-smelter will be provided with producing per year the integration capability of more than 10,000,000 tons of the pig iron.

Next the implementation steps of the present invention are set forth in reference to the detailed process：

Step one：Off-line modeling

1) assume sensor collection Research for Feeding Raw Materials System, injection system, hot-blast stove supply air system, gas recovery and dedusting, 6 kinds of Monitoring Datas of feeding system and slag water treatment system, and every kind of Monitoring Data constitutes X=[x₁,x₂,…,x_n]^T∈R^n×m, its Middle m represents the number of monitoring variable, and n represents number of samples x_i∈R^m, i=1 ..., n represents i-th of sample；

2) its probability density function under limited GMM model is expressed asWherein K is represented Mixed Gaussian component number in GMM, w_iThe mixed coefficint of i-th of single gauss component is represented, and it is full

Footθ_i={ μ_i,Σ_iAnd θ={ θ₁,…,θ_KLocal and global Gauss model parameter is represented respectively Collection, i.e. mean vector μ_iWith covariance matrix Σ_i.The multivariate Gaussian density function of corresponding i-th of component is represented by

3) i-th of single gauss component sample set is expressed asθ_i={ μ_i,Σ_i}.It is right Data set X_iCarry out KPCA projections.

3.1) kernel function φ is introduced by data set X_iHigh-dimensional feature space F is projected to, is expressed as

Φ:R^m→F (1)

3.2) nuclear matrix K is calculated

K_ij=＜ Φ (x_i),Φ(x_j) ＞=K (x_i,x_j) (2)

Wherein use Radial basis kernel functionσ=rm, r are constant.

3.3) centralization processing is carried out to nuclear matrix K

Wherein

3.4) principal component t is calculated_k

4) model parameter is estimated using EM algorithms

4.1)E-step

Wherein p^(s)(C_i|x_j) represent that j-th of training sample belongs to the posterior probability of i-th of gauss component after the s times iteration.

4.2)M-step

Wherein,And α_i,jRepresent respectively after (s+1) secondary iteration, i-th gauss component Average, covariance, prior probability and KPCA characteristic vectors.

5) T is determined²Count and limit with SPE

Step 2：On-line monitoring

1) online acquisition measurement data y ∈ R^m；

2) the operating mode classification that collecting sample belongs to is judged.CalculateThen x_tIt is affiliated Operating mode is

3) T of collecting sample is calculated²With SPE statistics.

T²=[t₁,…,t_p]Λ^-1[t₁,…,t_p]^T (12)

4) T is compared², the detection control limit T that is set up in SPE and formula (10), (11)² _lim、SPE_limBetween size, if Statistic is limited beyond control, then failure judgement occurs；If statistic is limited less than control, declarative procedure is normally run.

Above-described embodiment is used for illustrating the present invention, rather than limits the invention, the present invention spirit and In scope of the claims, any modifications and changes made to the present invention both fall within protection scope of the present invention.

Claims (1)

1. a kind of multiple operating modes process monitoring method based on KPCA mixed models, it is characterised in that as follows the step of this method：

Step one：Off-line modeling, collects the data that multiple operating modes process is normally run, and gauss hybrid models is built, in Gaussian Mixture On the basis of model, KPCA conversion and dimensionality reduction are carried out to each Gauss member space, the mixed model based on KPCA is established, using EM Algorithm limits to estimate model parameter according to the control of each operating mode of KPCA methods structure；

Step 2：On-line checking, gathers on-line operation data, and sample will be monitored by thereafter using the mixed model described in step one Probability magnitude classification is tested into corresponding operating mode, and according to KPCA method Counting statistics amounts, if the statistic exceeds step one The corresponding control limit set up, then failure judgement generation；

Off-line modeling process described in step one is as follows：

1) the multi-state Monitoring Data gathered using industrial process constitutes X=[x₁,x₂,…,x_n]^T∈R^n×m, wherein m represent monitoring The number of variable, n represents number of samples, x_i∈R^m, i=1 ..., n represents i-th of sample；

2) probability density function under limited GMM model is expressed asWherein K represents to mix in GMM Gauss component number, w_iThe mixed coefficint of i-th of single gauss component is represented, and is metθ_i={ μ_i,∑_iAnd θ= {θ₁,…,θ_KLocal and global Gauss model parameter set, i.e. mean vector μ are represented respectively_iWith covariance matrix ∑_i, accordingly The multivariate Gaussian density function of i-th of component is represented by

3) i-th of single gauss component sample set is expressed asθ_i={ μ_i,∑_i, to data Collect X_iCarry out KPCA projections；

3.1) kernel function φ is introduced by data set X_iHigh-dimensional feature space F is projected to, is expressed as

Φ:R^m→F (1)；

3.2) nuclear matrix K is calculated

K_ij=<Φ(x_i),Φ(x_j)>=K (x_i,x_j) (2)；

Wherein use Radial basis kernel functionσ=rm, r are constant；

3.3) centralization processing is carried out to nuclear matrix K

$\tilde{K}=K-1_{n_i}K-K{1}_{n_i}+1_{n_i}K{1}_{n_i}---\left(3\right);$

Wherein

3.4) principal component t is calculated_k

$t_k=<v_k,\mathrm{\&Phi;}\left(x\right)>=\underset{i=1}{\overset{n_i}{\mathrm{\&Sigma;}}}{\mathrm{\&alpha;}}_i^k<\mathrm{\&Phi;}\left(x_i\right),\mathrm{\&Phi;}\left(x\right)>=\underset{i=1}{\overset{n_i}{\mathrm{\&Sigma;}}}{\mathrm{\&alpha;}}_i^{k}K\left(x_i,x\right)---\left(4\right);$

4) model parameter is estimated using EM algorithms

4.1)E-step

$p^{\left(s\right)}\left(C_i\right|x_j)=\frac{w_i^{\left(s\right)}g\left(x_j\right|{\mathrm{\&mu;}}_i^{\left(s\right)},{\mathrm{\&Sigma;}}_i^{\left(s\right)})}{\underset{k=1}{\overset{K}{\&Sigma;}}{w}_k^{\left(s\right)}g\left(x_j\right|{\mathrm{\&mu;}}_k^{\left(s\right)},{\mathrm{\&Sigma;}}_k^{\left(s\right)})}---\left(5\right);$

Wherein p^(s)(C_i|x_j) represent that j-th of training sample belongs to the posterior probability of i-th of gauss component after the s times iteration；

4.2)M-step

${\mathrm{\&mu;}}_i^{(s+1)}=\frac{\underset{j=1}{\overset{n_i}{\&Sigma;}}{p}^{\left(s\right)}\left(C_i\right|x_j)x_j}{\underset{j=1}{\overset{n_i}{\&Sigma;}}{p}^{\left(s\right)}\left(C_i\right|x_j)}---\left(6\right);$

${\mathrm{\&Sigma;}}_i^{\left(s+1\right)}=\frac{\underset{j=1}{\overset{n_i}{\mathrm{\&Sigma;}}}{p}^{\left(s\right)}\left(C_i|x_j\right)\left(x_j-{\mathrm{\&mu;}}_i^{\left(s+1\right)}\right){\left(x_j-{\mathrm{\&mu;}}_i^{\left(s+1\right)}\right)}^T}{\underset{j=1}{\overset{n_i}{\mathrm{\&Sigma;}}}{p}^{\left(s\right)}\left(C_i|x_j\right)}---\left(7\right);$

$w_i^{(s+1)}=\frac{\underset{j=1}{\overset{n_i}{\&Sigma;}}{p}^{\left(s\right)}\left(C_i\right|x_j)}{N}---\left(8\right);$

${\mathrm{\&lambda;}}_{i,j}^{s+1}{\mathrm{\&alpha;}}_{i,j}={\tilde{K}}_i^{(s+1)}{\mathrm{\&alpha;}}_{i,j}---\left(9\right);$

Wherein,And α_i,jRepresent respectively after (s+1) secondary iteration, the average of i-th of gauss component, Covariance, prior probability and KPCA characteristic vectors；

5) T is determined²Count and limit with SPE

${T^2}_{\lim }=\frac{p\left(n_i-1\right)}{n_i\left(n_i-p\right)}{F}_{\mathrm{\&alpha;}}(p,n_i-p)---\left(10\right);$

${\mathrm{SPE}}_{\lim }={\mathrm{g\&chi;}}_h^2---\left(11\right);$

On-line checking process described in step 2 is as follows：

A) online acquisition measurement data y ∈ R^m；

B) judge the operating mode classification that collecting sample belongs to, calculateThen x_tAffiliated operating mode For

C) T of collecting sample is calculated²With SPE statistics,

T²=[t₁,…,t_p]Λ^-1[t₁,…,t_p]^T(12)；

$SPE=\left|\right|\mathrm{\&phi;}\left(x\right)-{\mathrm{\&phi;}}_p\left(x\right)|{|}^2=\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}{t}_i^2-\underset{i=1}{\overset{P}{\&Sigma;}}{t}_i^2---\left(13\right);$

D) T is compared², the detection control limit T that is set up in SPE and formula (10), (11)² _lim、SPE_limBetween size, if statistics Amount occurs beyond control limit, then failure judgement；If statistic is limited less than control, declarative procedure is normally run；Described event Hinder for blast furnace ironmaking process failure.