CN108037668A - A kind of new Chemical Batch Process modeling and monitoring method - Google Patents
A kind of new Chemical Batch Process modeling and monitoring method Download PDFInfo
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- G05B13/042—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators in which a parameter or coefficient is automatically adjusted to optimise the performance
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Abstract
The invention discloses a kind of new Chemical Batch Process modeling and monitoring method.The present invention is by gathering the data in chemical process, obtained after handling data comprising the most data of procedural information, then process model is established with the data after processing, finally proposes the monitoring method for the model to ensure the stable operation of Chemical Batch Process.The process status that reactor can be tracked well using the present invention is changed, and be compensate for the uncertainty of model to a certain extent, is improved the performance of system.
Description
Technical field
The invention belongs to technical field of automation, is related to a kind of new Chemical Batch Process modeling and monitoring method.
Background technology
With the quickening of globalization process, the industrial technology in China enters an all-round developing stage.Chemical industry interval
Process plays an increasingly important role in the industrial process in China, of increased attention.Chemical industry interval mistake
Cheng Zhonghui produces substantial amounts of data, and it is unpractical that all data are carried out with processing, it is, therefore, desirable to provide a kind of method is come
These data are handled, to obtain the valid data that can be modeled to Chemical Batch Process.
System control is a ring important in Chemical Batch Process, system whether stablize the quality that directly determines product and
The height of yield.Therefore, appropriate modeling is carried out to Chemical Batch Process, the change for carrying out tracking system state is necessary.
There are many scholars to propose many modeling methods at present, such as PID modelings, PCA modelings, PLS modelings etc., these models all rise
Certain effect has been arrived, but also there are some limitations.
The content of the invention
The present invention proposes a kind of new modeling method for Chemical Batch Process, and proposes and this model is carried out
The means of monitoring.
The step of the method for the present invention, includes：
Step 1. establishes the system model of Chemical Batch Process.Concretely comprise the following steps：
1.1 obtain the data matrix of batch process, are expressed as：
vm=[x1m x2m…xNm]T(m=1,2 ..., M)
In formula, the data that obtain during X is represented, the number of data sample during N is represented, M represents process variable
Number, m-th of process variable during m is represented, x1x2…xNThe 1st, 2 is represented respectively ..., N number of sample data vector, v1v2…vM
The 1,2nd is represented respectively ... M process variable.T represents transposition symbol.
Data in 1.2 pairs of steps 1.1 carry out centralization processing：
In formula,Represent n-th of sample data of m-th of variable of system after centralization is handled,
xnmThe initial data of n-th of sample of m-th of variable in expression system,Represent variable vmAverage.
1.3 due to widely different between process variable measurement, and therefore, it is necessary to carry out nondimensionalization processing to data：
smRepresent variable vmStandard deviation, after nondimensionalization, the variance of each variable of system becomes 1.
1.4 after standardization, and the data of system are expressed as：
Xs=[x1 x2…xP]T
=[v1 v2…vJ]
vj=[x1j x2j…xPj] (j=1,2 ..., J)
In formula, XsRepresent the data of the system after standardization, v1v2…vJRepresent respectively after standardization
The 1st, 2 of system ..., J process variable, x1x2…xPThe 1,2nd is represented respectively ..., P sample data vector.
1.5 for the data matrix X after the processing of step 1.4 Playsizations∈RP×J, it is necessary to obtain generalized variable a t, t
Represent data matrix XsMiddle variable v1v2…vJLinear combination., in order to ensure that the generalized variable calculated has uniqueness
It is normalized, is expressed as：
T=XsL=[v1 v2…vJ] l s.t. | | l | |=1
In order to ensure that t includes most information, then the variance of t should get maximum, be expressed as：
In formula, l represents the corresponding coefficient matrixes of generalized variable t.
It is expressed as with mathematical formulae：
1.6 in order in settlement steps to deal 1.5 the problem of, introduce the object function of system：
Local derviation is asked to l and λ respectively, and it is zero to make it, is had：
It can obtain
In formula, λ represents a pull-type coefficient.As can be seen that l isA standardized feature vector, it institute it is right
The characteristic value answered is exactly λ.
1.7 can obtain according to step 1.5 and step 1.6
Var (t)=λ
So to make the variance of t reach maximum, the characteristic root λ corresponding to l has to get maximum.Here t=Xl
It is referred to as principal component.
1.8 t that will be obtained for the first time in above-mentioned steps, λ, l are denoted as t respectively1, λ1, l1, the then t in judgment step 1.7
Whether restrain, if with convergence, by the data X in step 1.4sReplace with dataRepeat step 1.4
To step 1.8, continue to calculate a-th of principal component.I represents i-th of principal component.The procedural information that current A principal component includes reaches
During to required standard, stop circulation.A represents the total number of principal component.
1.9 store the data of above-mentioned acquisition in a matrix, can be expressed as：
C=[t1 t2…ta]
L=[l1 l2…la]
In formula, C represents the principal component matrix of system, and L represents the coefficient matrix of system.
1.9 in conclusion the model finally established can be expressed as：
C=XaL
In formula,Represent the information of initial data X being back-calculated to obtain by model.E represents the residual information of model.A is represented
The number of the principal component retained in model.
Step 2, monitors Chemical Batch Process on-line using a kind of obtained system model of step.Specific steps
For：
2.1 processing Jing Guo step 1, original data space are broken down into two orthogonal subspaces, by vector [l1,
l2,…lA] composition principal component subspace and by [lA+1,lA+2,…lJ] composition residual error subspace.The measurement number that will newly obtain
It can be obtained according to principal component subspace is projected to：
T=LTx
2.2 introduce first monitoring index of system, T2Statistic：
T2Statistic represents the changeable figureofmerit collectively formed by A principal component.By monitoring T2The change of statistic
It can realize and monitoring is carried out at the same time to multiple principal components, so as to judge whether the operating status of whole process is normal.
2.3 introduce another monitoring index of system, Q statistical magnitude：
Measured value deviates the distance of principal component model during Q statistical magnitude represents.
2.4 may determine that process during process operation by the two indices in monitoring step 2.2 and step 2.3
Whether operate under normal operation operating mode.When process is under normal operating condition, pass through the mould of the data foundation of collection
Type can obtain controlled T2With Q indexs；Process is caused to deviate normal operating when very big disturbance or maloperation occurs in process
During state, the correlation between process variable can also deviate normal dependency structure, then cause the T increased extremely2Refer to Q
Mark.
The present invention proposes a kind of new Chemical Batch Process modeling and monitoring method, and this method is by gathering chemical industry mistake
Data in journey, obtain, comprising the most data of procedural information, then being established with the data after processing after handling data
Process model, finally proposes the monitoring method for the model to ensure the stable operation of Chemical Batch Process.
The process status that reactor can be tracked well using the present invention is changed, and compensate for model to a certain extent not
Certainty, improves the performance of system.
Embodiment
By taking garbage disposal gasification furnace as an example：
Garbage disposal gasification furnace is a kind of common chemical industry Batch reaction processes, is become during reacting comprising many processes
Amount, can be efficiently used model proposed by the present invention.
Step 1. establishes the system model of garbage disposal gasification furnace reaction process.Concretely comprise the following steps：
1.1 obtain the measurement data of garbage processing procedure, are expressed as：
vm=[x1m x2m…xNm]T(m=1,2 ..., M)
In formula, the data matrix that obtains during X is represented, the number of data sample during N is represented, M represents process variable
Number, m represent during m-th of process variable, x1x2…xNThe 1st, 2 is represented respectively ..., N number of sample data vector, v1v2…
vMThe 1,2nd is represented respectively ... M process variable.T represents transposition symbol.
Data in 1.2 pairs of steps 1.1 carry out centralization processing：
In formula,Represent n-th of sample data of m-th of variable of system after centralization is handled,
xnmThe initial data of n-th of sample of m-th of variable in expression system,Represent variable vmAverage.
1.3 due to widely different between process variable measurement, and therefore, it is necessary to carry out nondimensionalization processing to data：
smRepresent variable vmStandard deviation, after nondimensionalization, the variance of each variable of system becomes 1.
1.4 after standardization, and the data of system are expressed as：
Xs=[x1 x2…xP]T
=[v1 v2…vJ]
vj=[x1j x2j…xPj] (j=1,2 ..., J)
In formula, XsRepresent the data of the system after standardization, v1 v2…vJRepresent to pass through standardization respectively
The 1st, 2 of system ... afterwards, J process variable, x1 x2…xPThe 1,2nd is represented respectively ..., P sample data vector.
1.5 for the data matrix X after the processing of step 1.4 Playsizations∈RP×J, it is necessary to obtain generalized variable a t, t
Represent data matrix XsMiddle variable v1 v2…vJLinear combination.In order to ensure that the generalized variable calculated has uniqueness,
It is normalized, is expressed as：
T=XsL=[v1 v2…vJ] l s.t. | | l | |=1
In order to ensure that t includes most information, then the variance of t should get maximum, be expressed as：
In formula, l represents the corresponding coefficient matrixes of generalized variable t.
It is expressed as with mathematical formulae：
1.6 in order in settlement steps to deal 1.5 the problem of, introduce the object function of system：
Local derviation is asked to l and λ respectively, and it is zero to make it, is had：
It can obtain
In formula, λ represents a pull-type coefficient.As can be seen that l isA standardized feature vector, it institute it is right
The characteristic value answered is exactly λ.
1.7 can obtain according to step 1.5 and step 1.6
Var (t)=λ
So to make the variance of t reach maximum, the characteristic root λ corresponding to l has to get maximum.Here t=Xl
It is referred to as principal component.
1.8 t that will be obtained for the first time in above-mentioned steps, λ, l are denoted as t respectively1, λ1, l1, the then t in judgment step 1.7
Whether restrain, if with convergence, by the data X in step 1.4sReplace with dataRepeat step 1.4
To step 1.8, continue to calculate a-th of principal component.I represents i-th of principal component.The procedural information that current A principal component includes reaches
During to required standard, stop circulation.A represents the total number of principal component.
1.9 store the data of above-mentioned acquisition in a matrix, can be expressed as：
C=[t1 t2…ta]
L=[l1 l2…la]
In formula, C represents the principal component matrix of system, and L represents the coefficient matrix of system.
1.9 in conclusion the model finally established can be expressed as：
C=XaL
In formula,Represent the information of initial data X being back-calculated to obtain by model.E represents the residual information of model.A is represented
The number of the principal component retained in model.
Step 2, monitors garbage processing procedure on-line using a kind of obtained system model of step.Specific steps
For：
2.1 processing Jing Guo step 1, original data space are broken down into two orthogonal subspaces, by vector [l1,
l2,…lA] composition principal component subspace and by [lA+1,lA+2,…lJ] composition residual error subspace.The measurement number that will newly obtain
It can be obtained according to principal component subspace is projected to：
T=LTx
2.2 introduce first monitoring index of system, T2Statistic：
T2Statistic represents the changeable figureofmerit collectively formed by A principal component.By monitoring T2The change of statistic
It can realize and monitoring is carried out at the same time to multiple principal components, so as to judge whether the operating status of whole process is normal.
2.3 introduce another monitoring index of system, Q statistical magnitude：
Measured value deviates the distance of principal component model during Q statistical magnitude represents.
2.4 may determine that process in garbage processing procedure by the two indices in monitoring step 2.2 and step 2.3
Whether operate under normal operation operating mode.When process is under normal operating condition, pass through the mould of the data foundation of collection
Type can obtain controlled T2With Q indexs；Process is caused to deviate normal operating when very big disturbance or maloperation occurs in process
During state, the correlation between process variable can also deviate normal dependency structure, then cause the T increased extremely2Refer to Q
Mark.
Claims (1)
1. a kind of new Chemical Batch Process modeling and monitoring method, it is characterised in that this method is specifically：
Step 1. establishes the system model of Chemical Batch Process：
1.1 obtain the data matrix of batch process, are expressed as：
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vm=[x1m x2m … xNm]T(m=1,2 ..., M)
In formula, the data matrix that obtains during X is represented, the number of data sample during N is represented, M represents of process variable
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… vMThe 1,2nd is represented respectively ... M process variable；T represents transposition symbol；
Data in 1.2 pairs of steps 1.1 carry out centralization processing：
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The initial data of n-th of sample of m variable,Represent variable vmAverage；
1.3 pairs of data carry out nondimensionalization processing：
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1.5 are directed to the data matrix X after being handled in step 1.4s∈RP×J, it is necessary to obtaining generalized variable a t, t represents data square
Battle array XsMiddle variable v1 v2 … vJLinear combination；In order to ensure that the generalized variable calculated has uniqueness, to be returned
One change is handled, and is expressed as：
T=XsL=[v1 v2 … vJ] l s.t. | | l | |=1
In order to ensure that t includes most information, then the variance of t should get maximum, be expressed as：
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1.6 introduce the object function of system：
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</msub>
<mo>-</mo>
<mn>2</mn>
<msubsup>
<mi>&lambda;X</mi>
<mi>s</mi>
<mi>T</mi>
</msubsup>
<msub>
<mi>X</mi>
<mi>s</mi>
</msub>
<mo>=</mo>
<mn>0</mn>
</mrow>
<mrow>
<mfrac>
<mrow>
<mo>&part;</mo>
<mi>G</mi>
</mrow>
<mrow>
<mo>&part;</mo>
<mi>&lambda;</mi>
</mrow>
</mfrac>
<mo>=</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<msubsup>
<mi>X</mi>
<mi>s</mi>
<mi>T</mi>
</msubsup>
<msub>
<mi>X</mi>
<mi>s</mi>
</msub>
<mo>-</mo>
<mn>1</mn>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mn>0</mn>
</mrow>
Obtain
<mrow>
<msubsup>
<mi>X</mi>
<mi>s</mi>
<mi>T</mi>
</msubsup>
<msub>
<mi>X</mi>
<mi>s</mi>
</msub>
<mi>l</mi>
<mo>=</mo>
<msubsup>
<mi>&lambda;X</mi>
<mi>s</mi>
<mi>T</mi>
</msubsup>
<msub>
<mi>X</mi>
<mi>s</mi>
</msub>
</mrow>
In formula, λ represents a pull-type coefficient；As can be seen that l isA standardized feature vector, corresponding to it
Characteristic value is exactly λ；
1.7 obtain according to step 1.5 and step 1.6
Var (t)=λ
So to make the variance of t reach maximum, the characteristic root λ corresponding to l has to get maximum；Here t=Xl is claimed
For principal component；
1.8 t that will be obtained for the first time in above-mentioned steps, λ, l are denoted as t respectively1, λ1, l1, then whether the t in judgment step 1.7
Convergence, if convergence, by the data X in step 1.4sReplace with dataRepeat step 1.4 is to step
1.8, continue to calculate a-th of principal component；I represents i-th of principal component；The procedural information that current A principal component includes, which reaches, to be wanted
During the standard asked, stop circulation, A represents the total number of principal component；
1.9 store the data of above-mentioned acquisition in a matrix, are expressed as：
C=[t1 t2 … ta]
L=[l1 l2 … la]
In formula, C represents the principal component matrix of system, and L represents the coefficient matrix of system；
1.9 models finally established are expressed as：
C=XaL
<mrow>
<msub>
<mover>
<mi>X</mi>
<mo>^</mo>
</mover>
<mi>a</mi>
</msub>
<mo>=</mo>
<msup>
<mi>CL</mi>
<mi>T</mi>
</msup>
<mo>=</mo>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>a</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>A</mi>
</munderover>
<msub>
<mi>t</mi>
<mi>a</mi>
</msub>
<msubsup>
<mi>l</mi>
<mi>a</mi>
<mi>T</mi>
</msubsup>
</mrow>
<mrow>
<mi>E</mi>
<mo>=</mo>
<msub>
<mi>X</mi>
<mi>a</mi>
</msub>
<mo>-</mo>
<msub>
<mover>
<mi>X</mi>
<mo>^</mo>
</mover>
<mi>a</mi>
</msub>
</mrow>
In formula,Represent the information of initial data X being back-calculated to obtain by model；E represents the residual information of model；A represents model
The number of the principal component of middle reservation；
Step 2, monitors Chemical Batch Process on-line using obtained system model：
2.1 processing Jing Guo step 1, original data space are broken down into two orthogonal subspaces, by vector [l1,l2,…
lA] composition principal component subspace and by [lA+1,lA+2,…lJ] composition residual error subspace, by the measurement data newly obtained project
It can be obtained to principal component subspace：
T=LTx
<mrow>
<mover>
<mi>x</mi>
<mo>^</mo>
</mover>
<mo>=</mo>
<mi>L</mi>
<mi>t</mi>
<mo>=</mo>
<msup>
<mi>LL</mi>
<mi>T</mi>
</msup>
<mi>x</mi>
</mrow>
<mrow>
<mi>e</mi>
<mo>=</mo>
<mi>x</mi>
<mo>-</mo>
<mover>
<mi>x</mi>
<mo>^</mo>
</mover>
<mo>=</mo>
<mrow>
<mo>(</mo>
<mn>1</mn>
<mo>-</mo>
<msup>
<mi>LL</mi>
<mi>T</mi>
</msup>
<mo>)</mo>
</mrow>
<mi>x</mi>
</mrow>
2.2 introduce first monitoring index of system, T2Statistic：
<mrow>
<msup>
<mi>T</mi>
<mn>2</mn>
</msup>
<mo>=</mo>
<msup>
<mi>t</mi>
<mi>T</mi>
</msup>
<msup>
<mi>S</mi>
<mrow>
<mo>-</mo>
<mn>1</mn>
</mrow>
</msup>
<mi>t</mi>
<mo>=</mo>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>a</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>A</mi>
</munderover>
<mfrac>
<msubsup>
<mi>t</mi>
<mi>a</mi>
<mn>2</mn>
</msubsup>
<msub>
<mi>&lambda;</mi>
<mi>a</mi>
</msub>
</mfrac>
</mrow>
T2Statistic represents the changeable figureofmerit collectively formed by A principal component；By monitoring T2The change of statistic is realized
Monitoring is carried out at the same time to multiple principal components, so as to judge whether the operating status of whole process is normal；
2.3 introduce another monitoring index of system, Q statistical magnitude：
<mrow>
<mi>Q</mi>
<mo>=</mo>
<msup>
<mi>e</mi>
<mi>T</mi>
</msup>
<mi>e</mi>
<mo>=</mo>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>j</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>J</mi>
</munderover>
<msup>
<mrow>
<mo>(</mo>
<msub>
<mi>x</mi>
<mi>j</mi>
</msub>
<mo>-</mo>
<msub>
<mover>
<mi>x</mi>
<mo>^</mo>
</mover>
<mi>j</mi>
</msub>
<mo>)</mo>
</mrow>
<mn>2</mn>
</msup>
</mrow>
Measured value deviates the distance of principal component model during Q statistical magnitude represents；
Whether 2.4 may determine that process during process operation by the two indices in monitoring step 2.2 and step 2.3
Operate under normal operation operating mode；When process is under normal operating condition, the model established by the data of collection can
To obtain controlled T2With Q indexs；Process is caused to deviate normal operating state when very big disturbance or maloperation occurs in process
When, the correlation between process variable can also deviate normal dependency structure, then cause the T increased extremely2With Q indexs.
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Cited By (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN109085816A (en) * | 2018-09-18 | 2018-12-25 | 兰州理工大学 | A kind of global local batch processing fault detection method orthogonal based on dynamic |
| CN109407640A (en) * | 2018-12-13 | 2019-03-01 | 宁波大学 | A kind of dynamic process monitoring method based on the analysis of dynamic orthogonal component |
Citations (8)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| JP2002108412A (en) * | 2000-10-03 | 2002-04-10 | Mitsubishi Chemicals Corp | Method and system for constructing model |
| CN101872182A (en) * | 2010-05-21 | 2010-10-27 | 杭州电子科技大学 | Batch process monitoring method based on recursive non-linear partial least square |
| CN103207567A (en) * | 2013-03-08 | 2013-07-17 | 华北电力大学 | Low-false-alarm-rate improved principal component analysis process monitoring method and system |
| CN103245759A (en) * | 2013-03-28 | 2013-08-14 | 杭州电子科技大学 | Product quality monitoring method based on autoregression total projection to latent structures (T-PLS) |
| CN103336507A (en) * | 2013-06-24 | 2013-10-02 | 浙江大学 | Statistical modeling and on-line monitoring method based on multimodality collaboration time frame automatic division |
| CN103488091A (en) * | 2013-09-27 | 2014-01-01 | 上海交通大学 | Data-driving control process monitoring method based on dynamic component analysis |
| CN103777627A (en) * | 2014-01-24 | 2014-05-07 | 浙江大学 | Batch process online-monitoring method based on small number of batches |
| CN103853152A (en) * | 2014-03-21 | 2014-06-11 | 北京工业大学 | Batch process failure monitoring method based on AR-PCA (Autoregressive Principal Component Analysis) |
-
2017
- 2017-12-28 CN CN201711458657.2A patent/CN108037668A/en active Pending
Patent Citations (8)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| JP2002108412A (en) * | 2000-10-03 | 2002-04-10 | Mitsubishi Chemicals Corp | Method and system for constructing model |
| CN101872182A (en) * | 2010-05-21 | 2010-10-27 | 杭州电子科技大学 | Batch process monitoring method based on recursive non-linear partial least square |
| CN103207567A (en) * | 2013-03-08 | 2013-07-17 | 华北电力大学 | Low-false-alarm-rate improved principal component analysis process monitoring method and system |
| CN103245759A (en) * | 2013-03-28 | 2013-08-14 | 杭州电子科技大学 | Product quality monitoring method based on autoregression total projection to latent structures (T-PLS) |
| CN103336507A (en) * | 2013-06-24 | 2013-10-02 | 浙江大学 | Statistical modeling and on-line monitoring method based on multimodality collaboration time frame automatic division |
| CN103488091A (en) * | 2013-09-27 | 2014-01-01 | 上海交通大学 | Data-driving control process monitoring method based on dynamic component analysis |
| CN103777627A (en) * | 2014-01-24 | 2014-05-07 | 浙江大学 | Batch process online-monitoring method based on small number of batches |
| CN103853152A (en) * | 2014-03-21 | 2014-06-11 | 北京工业大学 | Batch process failure monitoring method based on AR-PCA (Autoregressive Principal Component Analysis) |
Non-Patent Citations (7)
| Title |
|---|
| JUNGHUI CHEN，等: "On-line batch process monitoring using dynamic PCA and dynamic PLS models", 《CHEMICAL ENGINEERING SCIENCE》 * |
| RIDONG ZHANG，等: "Data-Driven Modeling Using Improved Multi-Objective Optimization Based Neural Network for Coke Furnace System", 《IEEET RANSACTI ON SONINDUSTRIAL ELECTRONICS》 * |
| 刘世成: "面向间歇发酵过程的多元统计监测方法研究", 《中国博士学位论文全文数据库 工程科技Ⅰ辑》 * |
| 曹鹏飞，等: "化工过程软测量建模方法研究进展", 《化工学报》 * |
| 王普，等: "间歇过程子阶段PCA建模和在线监测", 《北京工业大学学报》 * |
| 胡静: "基于多元统计分析的故障诊断与质量监测研究", 《中国博士学位论文全文数据库 基础科学辑》 * |
| 陶二盼: "基于多元统计分析的造纸污水处理故障检测与诊断", 《中国优秀硕士学位论文全文数据库 工程科技I辑》 * |
Cited By (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN109085816A (en) * | 2018-09-18 | 2018-12-25 | 兰州理工大学 | A kind of global local batch processing fault detection method orthogonal based on dynamic |
| CN109407640A (en) * | 2018-12-13 | 2019-03-01 | 宁波大学 | A kind of dynamic process monitoring method based on the analysis of dynamic orthogonal component |
| CN109407640B (en) * | 2018-12-13 | 2021-03-09 | 宁波大学 | Dynamic process monitoring method based on dynamic orthogonal component analysis |
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