CN103309347A - Multi-working-condition process monitoring method based on sparse representation - Google Patents

Abstract

The invention discloses a multi-working-condition process monitoring method based on sparse representation and belongs to the technical field of industrial process monitoring and diagnosing. According to the method, process data are not required to obey normal distribution, and only normal operating data of a process in a certain working condition are supposed to be identical to historical data of the working condition in distribution. The method includes: firstly, building a dictionary according to historical data of each working condition; and secondly, computing sparse representation of on-line data in the dictionary, and then judging whether a process is abnormal or not according to the concentration ratio of presentation coefficients. In addition, the process can be identified to be in a certain single working condition or transition process currently according to normal data, and accordingly products are guaranteed to meet production requirements. The concept of sparse representation is used for multi-working-condition process monitoring; the method does not require the process data to obey normal distribution, thereby being wider in application range and higher in interpretability.

Description

A kind of multi-state course monitoring method based on rarefaction representation

Technical field

The invention belongs to process flow industry process monitoring and fault diagnosis field, particularly a kind of multi-state course monitoring method based on rarefaction representation.

Background technology

For process monitoring and troubleshooting issue, traditional method adopts multivariate statistics process control technology (Multivariable Statistical Process Control mostly, MSPC), wherein with pivot analysis (Principal Component Analysis, PCA) and offset minimum binary (Partial Least Squares PLS) has obtained successful application for method such as representative in the industrial process monitoring.Traditional MSPC method is all supposed process operation under single operation operating mode, but in fact owing to the switching frequently in a plurality of operating modes of being everlasting of reason processes such as product changes, production capacity adjustment.

At the multi-state problem, classic method or adopt single MSPC model to cover all operation operating modes, or adopt the method for multi-model respectively operating mode to be set up sub-MSPC model, perhaps utilize the variation of model iteration method for updating adaptation condition.The most hypothetical process variable of above method satisfies the normal distribution hypothesis, and such hypothesis might not tally with the actual situation, and can cause a little less than the method applicability.

Summary of the invention

Purpose of the present invention provides a kind of multi-state course monitoring method based on rarefaction representation at the deficiencies in the prior art.

The multi-state course monitoring method based on rarefaction representation that the present invention proposes comprises following each step:

1) utilize the data of each nominal situation of multi-sensor data collection systematic collection process to constitute dictionary Wherein, k represents the number of process nominal situation,

The data matrix (sub-dictionary) of expression corresponding process operating mode i, m is the process variable number.

2) to dictionary

Carry out normalized, make

In the l of each columns certificate ₂Norm is equal to 1, obtains new dictionary matrix to be

3) gatherer process on-line operation data

4) to process on-line operation data

Calculate its rarefaction representation on dictionary A, sparse concentration index SCI monitors according to expression.

5) operating mode identification.For being judged to be normal service data, can further carry out the operating mode identification with current certain steady working condition or the operating mode transition stage of being in of deterministic process according to it in the rarefaction representation residual error of dictionary A.

The invention has the beneficial effects as follows: the present invention is used for the multi-state process monitoring with the thought of rarefaction representation, and this method does not also require the process data Normal Distribution, and its scope of application is wider and interpretation is stronger.In addition, at the normal processes data, but also the residing operating mode of the current operation of identification process meets the requirements to guarantee to produce.

Description of drawings

Fig. 1 is the FB(flow block) of the inventive method.

Embodiment

A kind of multi-state course monitoring method based on rarefaction representation that the present invention proposes, its FB(flow block) comprises following each step as shown in Figure 1:

1) utilize the data of each nominal situation of multi-sensor data collection systematic collection process to constitute dictionary (representing database here)

Wherein, k represents the number of process nominal situation,

The data matrix (sub-dictionary) of expression corresponding process operating mode i, m is the process variable number.

2) to dictionary

Carry out normalized, make

In the l of each columns certificate ₂The norm i.e. length of this column vector length is equal to 1, obtains new normalized dictionary matrix to be

3) process on-line operation utilizes the multi-sensor data collection system that m process variable data gathered equally, and the process on-line operation data that at every turn collect are

T represents sampling instant.Through type (1) is found the solution and is obtained $\hat{x}={[x_1,...,x_j,...,x_n]}^T$

$\hat{x}=\underset{x}{\arg \min }{\left|\right|x\left|\right|}_1=\underset{x}{\arg \min }\underset{j=1}{\overset{n}{\mathrm{\Σ}}}\left|x_j\right|---\left(1\right)$

Constraint condition is

Ax=y _tOr || Ax-y _t|| ₂≤ ε (2)

Wherein, || || ₂The l that represents vector in this symbol ₂Norm i.e. the length of vector, The expression error upper limit.

4) whether deterministic process is normally moved.At first, the coefficient that obtains according to step (3) Calculate

Sparse intensity (Sparse Concentration Index, SCI)

$\mathrm{SCI}\left(\hat{x}\right)=\frac{k\·\frac{\underset{i,j}{\max }\left[{\left|\right|{\mathrm{\δ}}_j\left(\hat{x}\right)\left|\right|}_1{\left|\right|{\mathrm{\δ}}_i\left(\hat{x}\right)\left|\right|}_1\right]}{{\left|\right|\hat{x}\left|\right|}_1}-1}{k-1}\∈\left[\mathrm{0,1}\right]---\left(3\right)$

Wherein, It is fundamental function.

Effect be with

In at indexed set

Element on the correspondence position is constant to be set to 0 with other locational element, indexed set I simultaneously _iRepresent the column index of i floor data in the dictionary matrix A.

If Then decision process takes place unusual.Otherwise needing further deterministic process is the transient process that is between certain steady working condition or the operating mode.

5) deterministic process operating mode of living in.If take place according to step (4) decision process operation unusual, need so further deterministic process current be in certain stablize under the single operating mode or two operating modes between transient process.At first, calculate online data y _tResidual error under dictionary A rarefaction representation

${\mathrm{\γ}}_i\left(y_t\right)=\left|\right|{y_t-A\·{\mathrm{\δ}}_i\left(\hat{x}\right)\left|\right|}_2,i=1,...,k---\left(4\right)$

${\stackrel{\‾}{\mathrm{\γ}}}_{p,q}\left(y_t\right)=\left|\right|{y_t-A\·{\mathrm{\σ}}_{p,q}\left(\hat{x}\right)\left|\right|}_2,p=1,...k,q=1,...,k,q\≠p---\left(5\right)$

Wherein,

It is fundamental function.

Effect be with

In at indexed set

Element on the correspondence position is constant to be set to 0 with other locational element, indexed set I simultaneously _{P, q}The column index of expression two floor datas of p, q in the dictionary matrix A.

Then, ask for least residual and according to this value identification online monitoring data operating mode of living in

$a=\min [\underset{i}{\min }{\mathrm{\γ}}_i\left(y_t\right),\underset{p,q}{\min }{\stackrel{\‾}{\mathrm{\γ}}}_{p,q}\left(y_t\right)]---\left(6\right)$

When

The time, decision process operation is in the

Operating mode; When $a=\underset{p,q}{\min }{\stackrel{\‾}{\mathrm{\γ}}}_{p,q}\left(y_t\right)$ The time, the decision process operation is in operating mode $\stackrel{\‾}{p},\stackrel{\‾}{q}(\left[\begin{array}{c}\stackrel{\‾}{p}\\ \stackrel{\‾}{q}\end{array}\right]=\underset{p,q}{\arg \min }{\stackrel{\‾}{\mathrm{\γ}}}_{p,q}\left(y_t\right))$ Transition period.

Claims (1)

1. multi-state course monitoring method based on rarefaction representation is characterized in that this method comprises following each step:

1) utilize the data of each nominal situation of multi-sensor data collection systematic collection process to constitute dictionary

Wherein, k represents the number of process nominal situation, The sub-dictionary of expression corresponding process operating mode i, m is the process variable number, n _iBe each floor data number, n is the total numbers of data;

2) to dictionary

Carry out normalized, make

In the l of each columns certificate ₂Norm is equal to 1, and the dictionary matrix that obtains after the normalization is

3) gatherer process on-line operation data T represents sampling instant; Through type (1) is found the solution and is obtained $\hat{x}={[x_1,...,x_j,...,x_n]}^T$

$\hat{x}=\underset{x}{\arg \min }{\left|\right|x\left|\right|}_1=\underset{x}{\arg \min }\underset{j=1}{\overset{n}{\mathrm{\Σ}}}\left|x_j\right|---\left(1\right)$

Constraint condition is

Ax=y _tOr || Ax-y _t|| ₂≤ ε (2)

Wherein, || || ₂The l that represents vector in this symbol ₂Norm,

The expression error upper limit;

4) whether deterministic process is normally moved; At first, design factor

Sparse concentration index SCI

$\mathrm{SCI}\left(\hat{x}\right)=\frac{k\·\frac{\underset{i,j}{\max }[{\left|\right|{\mathrm{\δ}}_j\left(\hat{x}\right)\left|\right|}_1+{\left|\right|{\mathrm{\δ}}_i\left(\hat{x}\right)\left|\right|}_1]}{{\left|\right|\hat{x}\left|\right|}_1}-1}{k-1}\∈\left[\mathrm{0,1}\right]---\left(3\right)$

Wherein,

It is fundamental function;

Effect be with

In at indexed set Element on the correspondence position is constant to be set to 0 with other locational element, indexed set I simultaneously _iRepresent the column index in the dictionary matrix A of i floor data after normalization;

If

Then decision process takes place unusual; Otherwise needing further deterministic process is the transient process that is between certain steady working condition or the operating mode;

5) deterministic process operating mode of living in; At first, calculate online data y _tResidual error under the dictionary matrix A rarefaction representation after the normalization

${\mathrm{\γ}}_i\left(y_t\right)={\left|\right|y_t-A\·{\mathrm{\δ}}_i\left(\hat{x}\right)\left|\right|}_2,i=1,...,k---\left(4\right)$

${\stackrel{\‾}{\mathrm{\γ}}}_{p,q}\left(y_t\right)={\left|\right|y_t-A\·{\mathrm{\σ}}_{p,q}\left(\hat{x}\right)\left|\right|}_2,p=1,...k,q=1,...,k,q\≠p---\left(5\right)$

Wherein,

It is fundamental function;

Effect be with In at indexed set

Element on the correspondence position is constant to be set to 0 with other locational element, indexed set I simultaneously _{P, q}Column index in the dictionary matrix A of expression two floor datas of p, q after normalization;

Then, ask for least residual and according to this value identification online monitoring data operating mode of living in

$a=\min [\underset{i}{\min }{\mathrm{\γ}}_i\left(y_t\right),\underset{p,q}{\min }{\stackrel{\‾}{\mathrm{\γ}}}_{p,q}\left(y_t\right)]---\left(6\right)$

So, when

The time, decision process operation is in the

Operating mode; When $a=\underset{p,q}{\min }{\stackrel{\‾}{\mathrm{\γ}}}_{p,q}\left(y_t\right)$ The time, the decision process operation is in operating mode $\stackrel{\‾}{p},\stackrel{\‾}{q}\left(\left[\begin{array}{c}\stackrel{\‾}{p}\\ \stackrel{\‾}{q}\end{array}\right]=\underset{p,q}{\arg \min }{\stackrel{\‾}{\mathrm{\γ}}}_{p,q}\left(y_t\right)\right)$ Transition period.

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