CN103309347A

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

Info

Publication number: CN103309347A
Application number: CN2013102213296A
Authority: CN
Inventors: 杨春节; 周哲; 文成林
Original assignee: Zhejiang University ZJU
Current assignee: Zhejiang University ZJU
Priority date: 2013-06-05
Filing date: 2013-06-05
Publication date: 2013-09-18
Anticipated expiration: 2033-06-05
Also published as: CN103309347B

Abstract

The invention discloses a multi-working-condition process monitoring method based on sparse representation, which belongs to the technical field of industrial process monitoring and diagnosis. This method does not require the process data to obey the normal distribution, but only assumes that the normal operating data under a certain working condition of the process has the same distribution as the historical data of the working condition. Firstly, construct a dictionary based on the historical data of each working condition; then, calculate the sparse representation of the online data on the dictionary, and then judge whether the process is abnormal according to the concentration degree of the representation coefficient. In addition, for normal data, it can also be identified that the process is currently in a single working condition or a transitional process, so as to ensure that the product meets the production requirements. The invention uses the idea of sparse representation for multi-working-condition process monitoring, and the method does not require process data to obey normal distribution, and has wider application range and stronger interpretability.

Description

A Method for Multi-working Condition Process Monitoring Based on Sparse Representation

技术领域technical field

本发明属于流程工业过程监控与故障诊断领域，特别涉及一种基于稀疏表示的多工况过程监控方法。The invention belongs to the field of flow industry process monitoring and fault diagnosis, in particular to a multi-working-condition process monitoring method based on sparse representation.

背景技术Background technique

对于过程监控和故障诊断问题，传统的方法大多采用多元统计过程控制技术（Multivariable Statistical Process Control,MSPC），其中以主元分析（PrincipalComponent Analysis,PCA）和偏最小二乘（Partial Least Squares,PLS）为代表等方法已在工业过程监控中得到了成功的应用。传统的MSPC方法均假设过程运行在单一的操作工况下，但是实际上由于产品改变、产能调整等原因过程常在多个工况中频繁的切换。For process monitoring and fault diagnosis problems, most traditional methods use multivariable statistical process control technology (Multivariable Statistical Process Control, MSPC), in which principal component analysis (Principal Component Analysis, PCA) and partial least squares (Partial Least Squares, PLS) The representative methods have been successfully applied in industrial process monitoring. The traditional MSPC method assumes that the process runs under a single operating condition, but in fact, due to product changes, capacity adjustments, etc., the process often switches frequently among multiple operating conditions.

针对多工况问题，传统方法要么采用单一的MSPC模型覆盖所有的操作工况，要么采用多模型的方法分别对工况建立子MSPC模型，或者利用模型迭代更新的方法适应工况的变化。以上方法大多假设过程变量满足正态分布假设，这样的假设并不一定符合实际情况，会导致方法适用性弱。For the problem of multiple operating conditions, the traditional method either uses a single MSPC model to cover all operating conditions, or uses a multi-model method to establish sub-MSPC models for each operating condition, or uses the iterative update method of the model to adapt to changes in operating conditions. Most of the above methods assume that the process variable satisfies the assumption of normal distribution. Such an assumption does not necessarily meet the actual situation, which will lead to weak applicability of the method.

发明内容Contents of the invention

本发明的目的在针对现有技术的不足，提供一种基于稀疏表示的多工况过程监控方法。The purpose of the present invention is to provide a multi-working-condition process monitoring method based on sparse representation to address the deficiencies of the prior art.

本发明提出的基于稀疏表示的多工况过程监控方法，包括以下各步骤：The multi-working-condition process monitoring method based on sparse representation proposed by the present invention includes the following steps:

1)利用多传感器数据采集系统收集过程各个正常工况的数据构成字典其中，k表示过程正常工况的个数，

表示对应过程工况i的数据矩阵（子字典），m为过程变量个数。1) Use the multi-sensor data acquisition system to collect the data of each normal working condition in the process to form a dictionary Among them, k represents the number of normal working conditions of the process,

Indicates the data matrix (sub-dictionary) corresponding to the process condition i, and m is the number of process variables.

2)对字典

进行归一化处理，使得

中每一列数据的l₂范数均等于1，得到新的字典矩阵为

2) For dictionaries

normalized so that

The l ₂ norm of each column of data in is equal to 1, and the new dictionary matrix is obtained as

3）采集过程在线运行数据 3) Collection process online operation data

4)对过程在线运行数据

计算它在字典A上的稀疏表示，根据表示稀疏集中指数SCI进行监控。4) Online operation data for the process

Calculate its sparse representation on the dictionary A, and monitor it according to the representation sparse concentration index SCI.

5)工况辨识。对于判定为正常的运行数据，可进一步根据它在字典A的稀疏表示残差进行工况辨识以确定过程当前处于某稳定工况或工况过度阶段。5) Working condition identification. For the operation data judged to be normal, the working condition identification can be further carried out according to its sparse representation residual in the dictionary A to determine that the process is currently in a stable working condition or an excessive working condition.

本发明的有益效果是：本发明将稀疏表示的思想用于多工况过程监控，该方法并不要求过程数据服从正态分布，其适用范围更广且可解释性更强。另外，针对正常过程数据，也可辨识过程当前运行所处的工况以确保生产符合要求。The beneficial effects of the present invention are: the present invention uses the idea of sparse representation for multi-working condition process monitoring, and the method does not require process data to obey normal distribution, and has wider application range and stronger interpretability. In addition, for normal process data, it is also possible to identify the working conditions in which the process is currently running to ensure that production meets requirements.

附图说明Description of drawings

图1是本发明方法的流程框图。Fig. 1 is a block flow diagram of the method of the present invention.

具体实施方式Detailed ways

本发明提出的一种基于稀疏表示的多工况过程监控方法，其流程框图如图1所示，包括以下各步骤：A multi-working-condition process monitoring method based on sparse representation proposed by the present invention has a flow chart as shown in Figure 1, including the following steps:

1)利用多传感器数据采集系统收集过程各个正常工况的数据构成字典（这里表示数据库）

其中，k表示过程正常工况的个数，

表示对应过程工况i的数据矩阵（子字典），m为过程变量个数。1) Use the multi-sensor data acquisition system to collect the data of each normal working condition in the process to form a dictionary (here represents the database)

Among them, k represents the number of normal working conditions of the process,

2)对字典

进行归一化处理，使得

中每一列数据的l₂范数即该列向量长度的长度均等于1，得到新的归一化的字典矩阵为

2) For dictionaries

normalized so that

The l ₂ norm of each column of data in , that is, the length of the column vector length is equal to 1, and the new normalized dictionary matrix is obtained as

3)过程在线运行，同样利用多传感器数据采集系统对m个过程变量数据进行采集，每次采集得到的过程在线运行数据为

t表示采样时刻。通过式(1)求解得到

\hat{x} = {[x_{1}, . . ., x_{j}, . . ., x_{n}]}^{T}

3) The process is running online. The multi-sensor data acquisition system is also used to collect m process variable data. The online running data of the process obtained each time is

t represents the sampling time. By solving formula (1), we get

\hat{x} = {[x_{1}, . . ., x_{j}, . . ., x_{no}]}^{T}

$\overset{^^}{x x} = = \underset{x x}{arg arg min min} {| | | | x x | | | |}_{11} = = \underset{x x}{arg arg min min} {Σ Σ}_{j j = = 11}^{n no} | | {x x}_{j j} | | - - - - - - ((11))$

约束条件为The constraints are

Ax=y_t或||Ax-y_t||₂≤ε (2)Ax=y _t or ||Ax-y _t || ₂ ≤ε (2)

其中，||·||₂表示该符号中向量的l₂范数即向量的长度，表示误差上限。Among them, ||·|| ₂ represents the l ₂ norm of the vector in the symbol, that is, the length of the vector, Indicates the upper limit of error.

4)判断过程是否正常运行。首先，根据步骤（3）得到的系数计算

的稀疏集中程度（Sparse Concentration Index,SCI）4) Determine whether the process is running normally. First, according to the coefficient obtained in step (3) calculate

Sparse Concentration Index (SCI)

$SCI SCI ((\overset{^^}{x x})) = = \frac{k k \cdot &Center Dot; \frac{\underset{i i,, j j}{max max} [[{| | | | {δ δ}_{j j} ((\overset{^^}{x x})) | | | |}_{11} {| | | | {δ δ}_{i i} ((\overset{^^}{x x})) | | | |}_{11}]]}{{| | | | \overset{^^}{x x} | | | |}_{11}} - - 11}{k k - - 11} &Element; &Element; [[0,1 0,1]] - - - - - - ((33))$

其中，是特征函数。

的作用是将

中在索引集

对应位置上的元素不变同时将其它位置上的元素置为0，索引集I_i表示第i个工况数据在字典矩阵A中的列索引。in, is the characteristic function.

The role of the

in the index set

The elements at the corresponding positions remain unchanged while the elements at other positions are set to 0. The index set I _i represents the column index of the i-th working condition data in the dictionary matrix A.

若则判定过程发生异常。反之，需要进一步判断过程是处于某稳定工况或是工况之间的过渡过程。like An exception occurs in the judgment process. On the contrary, it is necessary to further judge whether the process is in a stable working condition or a transition process between working conditions.

5)判断过程所处工况。如果根据步骤（4）判定过程运行未发生异常，那么需进一步判断过程当前是处于某稳定单一工况下或是两个工况之间的过渡过程。首先，计算在线数据y_t在字典A稀疏表示下的残差5) Judging the working condition of the process. If it is judged according to step (4) that there is no abnormality in the operation of the process, it is necessary to further judge whether the process is currently in a stable single working condition or a transition process between two working conditions. First, calculate the residual of the online data y _t under the sparse representation of the dictionary A

${γ γ}_{i i} (({y the y}_{t t})) = = | | | | {{y the y}_{t t} - - A A \cdot \cdot {δ δ}_{i i} ((\overset{^^}{x x})) | | | |}_{22},, i i = = 11,, . . . . . .,, k k - - - - - - ((44))$

${\overset{&OverBar; &OverBar;}{γ γ}}_{p p,, q q} (({y the y}_{t t})) = = | | | | {{y the y}_{t t} - - A A \cdot &Center Dot; {σ σ}_{p p,, q q} ((\overset{^^}{x x})) | | | |}_{22},, p p = = 11,, . . . . . . k k,, q q = = 11,, . . . . . .,, k k,, q q &NotEqual; &NotEqual; p p - - - - - - ((55))$

其中，

是特征函数。

的作用是将

中在索引集

对应位置上的元素不变同时将其它位置上的元素置为0，索引集I_p,q表示p、q两个工况数据在字典矩阵A中的列索引。in,

is the characteristic function.

The role of the

in the index set

The elements at the corresponding positions remain unchanged and the elements at other positions are set to 0. The index set I _{p, q} represents the column index of the two working condition data of p and q in the dictionary matrix A.

然后，求取最小残差并根据该值辨识在线监测数据所处工况Then, calculate the minimum residual error and identify the working condition of the online monitoring data according to the value

$a a = = min min [[\underset{i i}{min min} {γ γ}_{i i} (({y the y}_{t t})),, \underset{p p,, q q}{min min} {\overset{&OverBar; &OverBar;}{γ γ}}_{p p,, q q} (({y the y}_{t t}))]] - - - - - - ((66))$

当

时，判定过程运行处于第

工况；当

a = \min_{p, q} {\overset{&OverBar;}{γ}}_{p, q} (y_{t})

时，判定过程运行处于工况

\overset{&OverBar;}{p}, \overset{&OverBar;}{q} ([\begin{matrix} \overset{&OverBar;}{p} \\ \overset{&OverBar;}{q} \end{matrix}] = \underset{p, q}{\arg \min} {\overset{&OverBar;}{γ}}_{p, q} (y_{t}))

的过渡阶段。when

When , the judgment process is running at the first

Working condition; when

a = \min_{p, q} {\overset{&OverBar;}{γ}}_{p, q} ({the y}_{t})

When , it is determined that the process is running in the working condition

\overset{&OverBar;}{p}, \overset{&OverBar;}{q} ([\begin{matrix} \overset{&OverBar;}{p} \\ \overset{&OverBar;}{q} \end{matrix}] = \underset{p, q}{\arg \min} {\overset{&OverBar;}{γ}}_{p, q} ({the y}_{t}))

transitional stage.

Claims

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} {| | x | |}_{1} = \underset{x}{\arg \min} Σ_{j = 1}^{n} | x_{j} | - - - (1)

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

SCI (\hat{x}) = \frac{k \cdot \frac{\max_{i, j} [{| | δ_{j} (\hat{x}) | |}_{1} + {| | δ_{i} (\hat{x}) | |}_{1}]}{{| | \hat{x} | |}_{1}} - 1}{k - 1} &Element; [0,1] - - - (3)

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

γ_{i} (y_{t}) = {| | y_{t} - A \cdot δ_{i} (\hat{x}) | |}_{2}, i = 1, . . ., k - - - (4)

{\overset{&OverBar;}{γ}}_{p, q} (y_{t}) = {| | y_{t} - A \cdot σ_{p, q} (\hat{x}) | |}_{2}, p = 1, . . . k, q = 1, . . ., k, q &NotEqual; p - - - (5)

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 [\min_{i} γ_{i} (y_{t}), \min_{p, q} {\overset{&OverBar;}{γ}}_{p, q} (y_{t})] - - - (6)

Then, when

When the determination process is operated at the second

Working conditions; when in use

a = \min_{p, q} {\overset{&OverBar;}{γ}}_{p, q} (y_{t})

When the judging process is in working condition

\overset{&OverBar;}{p}, \overset{&OverBar;}{q} ([\begin{matrix} \overset{&OverBar;}{p} \\ \overset{&OverBar;}{q} \end{matrix}] = \underset{p, q}{\arg \min} {\overset{&OverBar;}{γ}}_{p, q} (y_{t}))

The transition phase of (2).