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

Multi-working-condition process monitoring method based on sparse representation

Technical Field

The invention belongs to the field of process industrial process monitoring and fault diagnosis, and particularly relates to a multi-working-condition process monitoring method based on sparse representation.

Background

For Process monitoring and fault diagnosis, the conventional methods mostly adopt a Multivariate Statistical Process Control (MSPC) technique, wherein methods represented by Principal Component Analysis (PCA) and Partial Least Squares (PLS) have been successfully applied in industrial Process monitoring. The conventional MSPC method assumes that the process is operated under a single operating condition, but in practice, the process is frequently switched among a plurality of operating conditions due to product changes, capacity adjustment and the like.

Aiming at the problem of multiple working conditions, the traditional method adopts a single MSPC model to cover all the operating conditions, or adopts a multi-model method to respectively establish sub MSPC models for the working conditions, or adopts a model iteration updating method to adapt to the change of the working conditions. Most of the above methods assume that the process variables satisfy the assumption of normal distribution, and such assumption does not necessarily conform to the actual situation, which may result in poor applicability of the method.

Disclosure of Invention

Aiming at the defects of the prior art, the invention provides a multi-working-condition process monitoring method based on sparse representation.

The invention provides a multi-working-condition process monitoring method based on sparse representation, which comprises the following steps of:

1) dictionary formed by collecting data of all normal working conditions in process by using multi-sensor data acquisition systemWherein k represents the number of normal working conditions in the process,

and (3) representing a data matrix (sub dictionary) corresponding to the process working condition i, wherein m is the number of process variables.

2) For dictionary

A normalization process is performed so that

Of each column of data₂Norm equals to 1, and a new dictionary matrix is obtained

3) Collecting process on-line operational data

4) On-line operation data to process

And calculating the sparse representation of the dictionary A, and monitoring according to the index SCI in the representation sparse set.

5) And identifying the working condition. For the operation data judged to be normal, the working condition identification can be further carried out according to the sparse representation residual error of the operation data in the dictionary A so as to determine that the process is in a certain stable working condition or working condition transition stage at present.

The invention has the beneficial effects that: the method uses the idea of sparse representation for multi-working-condition process monitoring, does not require process data to obey normal distribution, and has wider application range and stronger interpretability. In addition, aiming at normal process data, the working condition of the current operation of the process can be identified so as to ensure that the production meets the requirements.

Drawings

FIG. 1 is a block flow diagram of the method of the present invention.

Detailed Description

The invention provides a multi-working-condition process monitoring method based on sparse representation, a flow chart of which is shown in figure 1, and the method comprises the following steps:

1) using a multisensor data collection system to collect data for each normal condition of the process to form a dictionary (here the database is represented)

Wherein k represents the number of normal working conditions in the process,

and (3) representing a data matrix (sub dictionary) corresponding to the process working condition i, wherein m is the number of process variables.

2) For dictionary

A normalization process is performed so that

Of each column of data₂The norm, i.e., the length of the column vector length, is equal to 1, and a new normalized dictionary matrix is obtained as

3) The process runs on-line and is equally advantageousThe multi-sensor data acquisition system is used for acquiring m process variable data, and the process online operation data acquired each time is

t denotes the sampling instant. Obtained by solving the formula (1) $\hat{x}={[x_1,...,x_j,...,x_n]}^T$

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

The constraint condition is

Ax=y_tOr | | Ax-y_t||₂≤ε (2)

Wherein | · | purple sweet₂Representing the vector in the symbol by₂The norm is the length of the vector,the upper error limit is indicated.

4) And judging whether the process normally runs or not. Firstly, the coefficient obtained from step (3)Computing

Degree of Sparse Concentration (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,is a characteristic function.

Has the functions of

Middle ropeGuiding and collecting device

The elements in the corresponding positions are not changed, and the elements in other positions are set to be 0, so that the index set I_iAnd the column index of the ith working condition data in the dictionary matrix A is represented.

If it isIt is determined that an abnormality has occurred in the process. Otherwise, it is necessary to further determine whether the process is in a stable condition or a transition between conditions.

5) And judging the working condition of the process. And (4) if the process is judged to be not abnormal according to the step (4), further judging whether the process is currently in a stable single working condition or a transition process between two working conditions. First, the online data y is calculated_tResidual under dictionary A sparse 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,

is a characteristic function.

Has the functions of

Middle index set

The elements in the corresponding positions are not changed, and the elements in other positions are set to be 0, so that the index set I_p,qAnd the column indexes of the p and q working condition data in the dictionary matrix A are represented.

Then, the minimum residual error is obtained and the working condition of the online monitoring data is identified according to the value

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

When in use

When the determination process is operated at the second

Working conditions; when in use $a=\underset{p,q}{\min }{\stackrel{\‾}{\mathrm{\γ}}}_{p,q}\left(y_t\right)$ When the judging process is in working condition $\stackrel{\‾}{p},\stackrel{\‾}{q}(\left[\begin{array}{c}\stackrel{\‾}{p}\\ \stackrel{\‾}{q}\end{array}\right]=\underset{p,q}{\arg \min }{\stackrel{\‾}{\mathrm{\γ}}}_{p,q}\left(y_t\right))$ The transition phase of (2).

Claims (1)

1. A multi-working-condition process monitoring method based on sparse representation is characterized by comprising the following steps:

1) dictionary formed by collecting data of all normal working conditions in process by using multi-sensor data acquisition system

Wherein k represents the number of normal working conditions in the process,a sub-dictionary representing a corresponding process condition i, m being the number of process variables, n_iThe number of data in each working condition is n, and the n is the total number of the data;

2) for dictionary

A normalization process is performed so that

Of each column of data₂Norm is equal to 1, and normalized dictionary matrix is obtained

3) Collecting process on-line operational datat represents a sampling instant; obtained by solving the formula (1) $\hat{x}={[x_1,...,x_j,...,x_n]}^T$

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

The constraint condition is

Ax=y_tOr | | Ax-y_t||₂≤ε (2)

Wherein | · | purple sweet₂Representing the vector in the symbol by₂The norm of the number of the first-order-of-arrival,

representing an upper error limit;

4) judging whether the process normally runs or not; first, the coefficients are calculated

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,

is a characteristic function;

has the functions of

Middle index setThe elements in the corresponding positions are not changed, and the elements in other positions are set to be 0, so that the index set I_iRepresenting the column index of the ith working condition data in the normalized dictionary matrix A;

if it is

Judging that the process is abnormal; on the contrary, the process needs to be further judged to be in a certain stable working condition or a transition process between the working conditions;

5) judging the working condition of the process; first, the online data y is calculated_tResidual under sparse representation of normalized dictionary matrix A

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

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

Wherein,

is a characteristic function;

has the functions ofMiddle index set

The elements in the corresponding positions are not changed, and the elements in other positions are set to be 0, so that the index set I_p,qRepresenting column indexes of the p and q working condition data in the normalized dictionary matrix A;

then, the minimum residual error is obtained and the working condition of the online monitoring data is identified according to the value

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

Then, when

When the determination process is operated at the second

Working conditions; when in use $a=\underset{p,q}{\min }{\stackrel{\‾}{\mathrm{\γ}}}_{p,q}\left(y_t\right)$ When the judging process is in working condition $\stackrel{\‾}{p},\stackrel{\‾}{q}\left(\left[\begin{array}{c}\stackrel{\‾}{p}\\ \stackrel{\‾}{q}\end{array}\right]=\underset{p,q}{\arg \min }{\stackrel{\‾}{\mathrm{\γ}}}_{p,q}\left(y_t\right)\right)$ The transition phase of (2).

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