CN112149054B

CN112149054B - Construction and application of orthogonal neighborhood preserving embedding model based on time sequence expansion

Info

Publication number: CN112149054B
Application number: CN202010969184.8A
Authority: CN
Inventors: 王妍; 凌丹; 韩帅帅; 王延峰; 顾晓光; 孙军伟; 王英聪; 朱传迁
Original assignee: Zhengzhou University of Light Industry
Current assignee: Zhengzhou University of Light Industry
Priority date: 2020-09-15
Filing date: 2020-09-15
Publication date: 2023-08-04
Anticipated expiration: 2040-09-15
Also published as: CN112149054A

Abstract

The invention discloses construction and application of a time sequence expansion-based orthogonal neighborhood preserving embedding (TONPE) model, which comprises the following steps: n historical normal samples of physical quantities monitored by m physical quantity monitoring points in the CSTR process are obtained, and a fault monitoring method of TONPE model is applied to calculate x of each normal historical sample _i (i＝1,...,n)∈R ^m Statistics T of _i ² (i=1, 2, …, n) and statistics SPE _i (i=1, 2, … n) and calculating T using a kernel density estimation function _i ² Control limits of (i=1, 2, …, n)Sum statistics SPE _i Control limit SPE of (i=1, 2, … n) _lim The method comprises the steps of carrying out a first treatment on the surface of the Physical quantity data of m physical quantity monitoring points in the CSTR process are collected on line, and test data x is calculated _newi (i＝1,...,n1)∈R ^m Is a monitoring index of (2)And SPE _newi (i=1, 2, …, n 1), statistics are to be obtainedSPE _newi (i=1, 2, …, n 1) and control limitsSPE _lim And respectively comparing the parts which are larger than the control limit, namely, considering that the sample point has faults. The method considers the dynamic characteristics of CSTR process data, fully extracts the space structure information and the time structure information of physicochemical data, and improves the accuracy of fault monitoring.

Description

Construction and application of orthogonal neighborhood preserving embedding model based on time sequence expansion

Technical Field

The invention belongs to the technical field of fault monitoring in a chemical production process, and particularly relates to construction and application of an orthogonal neighborhood preserving embedding model based on time sequence expansion, which can improve the fault monitoring accuracy of the chemical process.

Background

The continuous stirring reaction kettle (Continuous Stirred Tank Reactor, CSTR) is a chemical reactor commonly used in industrial production processes of chemical industry, fermentation, petroleum production and the like. Due to the aging of equipment and the influence of external environmental factors, the CSTR process can have faults, thereby leading to the occurrence of industrial production safety accidents. In recent years, industrial production safety problems are increasingly concerned, and importance of process fault monitoring is highlighted. The multi-element statistical process monitoring (MSPM) method can convert high-dimensional data into low-dimensional data, and effective characteristic information is obtained in the low-dimensional data and is commonly used for fault monitoring of industrial processes.

MSPM is mainly used for processing gaussian and linear data, but a large amount of nonlinear physicochemical data exists in actual production and life. In order to solve the problem of dimension reduction of nonlinear physicochemical data, a learner proposes a neighborhood preserving embedding (Neighborhood Preserving Embedding, NPE) algorithm which well preserves manifold structure information of a physicochemical data set. Liu X.M. et al, based on NPE, have added an orthogonal constraint, and proposed an orthogonal neighborhood preserving embedding (Orthogonal Neighborhood Preserving Em bedding, ONPE) algorithm (Liu X M, yin J W, feng Z L, et al, orthomonal Neig hborhood Preserving Embedding for Face Recognition [ C ]// procedures of 2007IEEE International Conference on Image,ICIP 2007.New York,2007:133-136) that greatly improves the problem of suppressing useful information in the NPE algorithm, showing great superiority in the studies of the graphical image processing and fault monitoring fields, but often ignoring the dynamics of physicochemical data and the typical characteristics of multiple modes.

Disclosure of Invention

The invention aims to solve the technical problem that based on the existing fault monitoring method, the dynamic property and the autocorrelation property of various physical and chemical parameters and data are not considered, the characteristic information of the physical and chemical parameters or the data, which changes with time, is ignored, and the situation that the fault detection rate of a CSTR process is low is often caused, and provides a CSTR process monitoring method based on time sequence expansion and orthogonal neighborhood preserving embedding (Temporal Extension Orthogonal Neighborhood Preserving embedding, TONPE).

In order to solve the technical problems, the inventor establishes a TONPE model based on an ONPE method based on long-term practical research in the field and applies the TONPE model to CSTR process fault monitoring so as to consider the dynamic performance of process physicochemical parameters or data.

The specific technical scheme adopted by the invention is as follows:

the construction method of the orthogonal neighborhood preserving embedding model based on time sequence expansion comprises the following steps:

(1) N normal history samples of m physical quantity monitoring points in the CSTR process are obtained to form a matrix X ₁ ＝[x ₁₁ ,x ₁₂ ,…x _1n ]∈R ^m×n Subtracting the average value of the line of sample data from each line of data, and dividing the average value by the standard deviation of the line of sample data to obtain a matrix X= [ X ] ₁ ,x ₂ ,…x _n ]∈R ^m×n 。

(2) Fault monitoring method using TONPE model, projection matrix A (a ₁ ,…,a _b )∈R ^m×b (b.ltoreq.m), and calculates each normal history sample x _i (i＝1,...,n)∈R ^m Statistics T of _i ² (i=1, 2, …, n) and statistics SPE _i (i＝1,2,…n)。

wherein ,a_i (i=1, …, b) is the projection vector, b is the dimension of dimension reduction, Λ=yy ^T /(n-1)，Y＝A ^T X，y _i ＝A ^T x _i (i＝1,2,…,n)。

(3) Calculating T using a kernel density estimation function (KDE) _i ² Control limits of (i=1, 2, …, n)Sum statistics SPE _i Control limit SPE of (i=1, 2, … n) _lim 。

Further, in the step (2), the method for calculating the projection matrix a is as follows:

(2a) Construction of a spatial neighborhood set S

For a certain normal history sample point x _i (i＝1,...,n)∈R ^m Calculating Euclidean distance d between the sample point and other sample points, and then selecting k points with minimum Euclidean distance d from the sample point to form a space neighborhood set Representing sample x _i Is the kth near point of (c).

(2b) Constructing a time neighborhood set Q

For x _i Sample point construction time neighborhood set Q epsilon { x } _i-m ,...,x _i-1 ,x _i+1 ,...,x _i+m And k=2m in value.

(2c) Determining a weight coefficient matrix W

By minimizing a functionObtaining a weight coefficient matrix W of the space neighborhood set S _s ：

wherein ,representing sample x _i W is the j-th nearest point of _Sij As a matrix W _s The j-th column element of the i-th row of (2) represents sample +.>For reconstructed sample x _i Weight coefficient of (2); constraint is->If sample->Not x _i Is a neighborhood of (2), W _Sij ＝0。

Again by a minimization functionObtaining a time coefficient weight matrix W _Q ：

wherein ,W_Qij As a matrix W _Q The ith row and jth column element of (2) represents sample x _j For reconstructed sample x _i Weight coefficient of (2); the constraint condition is thatIf x _j Not x _i W is equal to the time neighborhood point of _Qij ＝0。

(2d) Establishing an objective function J (y):

wherein ,y _i is x _i Is> and y_j Respectively represent y _i The weight coefficient eta of the spatial characteristic information is equal to or more than 0 and equal to or less than 1.

(2e) Calculate projection matrix A (a ₁ ,…,a _b )∈R ^m×b

Will y _i ＝A ^T x _i The formula (5) is carried out:

wherein ,M_s ＝(I-W _s ) ^T (I-W _S )，M _Q ＝(I-W _Q ) ^T (I-W _Q )，M＝ηM _S +(1-η)M _Q 。

Adding constraint A based on formula (6) ^T XX ^T A＝I，Solving the above optimization problem by using the Lagrangian multiplier method containing constraints, equation (6) can be converted into a generalized eigenvalue solution problem as follows:

XMX ^T A＝λXX ^T A (7)

solving the formula (7) to obtain:

1)a ₁ is (XX) ^T ) ^-1 XMX ^T A feature vector corresponding to the minimum feature value of (a);

2)a _i (i=2, …, b) is Q ⁽ⁱ⁾ A feature vector corresponding to the minimum feature value of (a);

Q ⁽ⁱ⁾ ＝{I-(XX ^T ) ^-1 a ^(i-1) [G ^(i-1) ] ^T }(XX ^T ) ^-1 XMX ^T (8)

in the formula ,G^(i-1) ＝[a ^(i-1) ] ^T (XX ^T ) ^-1 a ^(i-1) ；a ^(i-1) ＝[a ₁ ,a ₂ ,…a _i-1 ]。

All a are obtained by the formula (8) _i The values of (i=1, …, b) result in projection matrix a.

On the other hand, a CSTR process fault monitoring method based on TONPE is designed, which comprises the following steps:

(1) n1 test sample data of m physical quantity monitoring points in the CSTR process are collected on line to form a matrix X _new1 ＝[x _new11 ,x _new12 ,…x _new1n1 ]∈R ^m×n1 X is taken as _new1 Subtracting the normal history sample matrix X from each row ₁ Dividing the data mean value of the corresponding row by the standard deviation of the corresponding row data to obtain a matrix X _new ＝[x _new1 ,x _new2 ,…x _newn1 ]∈R ^m×n1 。

(2) Fault monitoring method using TONPE model to calculate test data x _newi (i＝1,...,n1)∈R ^m Is a monitoring index of (2) and SPE_newi (i＝1,2,…,n1)。

SPE _newi ＝x _newi (I-A ^T A)[x _newi (I-A ^T A)] ^T (10)

Wherein Λ= (a) ^T X _new )(A ^T X _new ) ^T /(n1-1)，y _newi ＝A ^T x _newi (i＝1,2,…,n1)。

(3) Will statisticsSPE _newi (i=1, 2, …, n 1) and control limit +.>SPE _lim Comparing the two parts, namely, considering that the sample point has faults, wherein the parts are larger than the control limit; and then summarizing all fault sample points, and solving the detection rate and the false alarm rate.

Compared with the prior art, the invention has the main beneficial technical effects that:

1. compared with the traditional CSTR process monitoring method based on the ONPE model, the CSTR process monitoring method based on the TONPE model considers the dynamic performance of process physical and chemical quantities, models various historical physical and chemical data by the TONPE method, and finally calculates statistics by the KDE method to realize the monitoring of various physical and chemical data in the CSTR process; the method fully extracts the space structure information and the time structure information of the physicochemical data, and improves the accuracy of fault monitoring.

The 2TONPE algorithm is a linear algorithm, the data processing and calculation are simple and convenient, and the calculated amount is small; the method solves the actual calculation problem of the projection matrix, realizes the direct conversion relation between the input variable and the projection space, can establish common statistics in the aspect of fault diagnosis to realize fault diagnosis, and is easier, more convenient and effective.

3. The TONPE algorithm of the invention is convenient and simple when constructing the neighborhood set, well solves the problem that extremum appears in local, and greatly reduces the related calculated amount.

Drawings

FIG. 1 is a flow chart of a TONPE model building method for CSTR process monitoring based on time-series expansion.

FIG. 2 is a flow chart of an on-line monitoring process of the CSTR process monitoring method of the present invention based on a time-series expansion orthogonal neighborhood preserving embedding.

FIG. 3 is a graph of the monitoring results of fault 9 during CSTR monitoring using PCA, with the abscissa being the sample and the ordinate being the statistic.

FIG. 4 is a graph of the monitoring results of fault 9 during CSTR monitoring using NPE method, with the abscissa being the sample and the ordinate being the statistic.

FIG. 5 is a graph of the monitoring results of fault 9 during CSTR monitoring using the ONPE method, with the abscissa being the sample and the ordinate being the statistic.

FIG. 6 is a graph of the monitoring results of faults 9 during CSTR monitoring using the TONPE method, with the abscissa being samples and the ordinate being statistics.

Detailed Description

The following examples are given to illustrate the invention in detail, but are not intended to limit the scope of the invention in any way.

The continuous stirred tank reactor plays an important role in chemical industrial production process equipment, and is a reactor widely used in chemical reaction. Accordingly, the following examples are presented based on a continuous stirred tank reactor system.

The data of the following embodiments are generated by a CSTR model built by a Simulink module of matlab, the simulation system can set a plurality of physical measurement point positions corresponding to 10 basic faults and 7 physical quantities to be monitored, and the CSTR process simulation system is widely applied to various fields, such as: fault detection field, fault diagnosis field, model predictive control field, etc.; in the example, the fault 9 is taken as the cooling water temperature T _C The variation will be described as an example.

In the first embodiment, a CSTR process monitoring method based on time-series expansion orthogonal neighborhood preserving embedding (TONPE) is used for processing physical quantity data acquired at a plurality of physical quantity monitoring points in a CSTR process to monitor physical quantity data with faults, so that production maintenance personnel can find problems of the CSTR process as soon as possible and perform corresponding processing, and the physical quantity monitoring points of the CSTR process and the corresponding monitored physical quantities are shown in table 1.

Mainly comprises the following steps:

step one, TONPE model building, see FIG. 1:

(1) M physical quantity monitoring in CSTR acquisition processN normal history samples of the measuring point form a matrix X ₁ ＝[x ₁₁ ,x ₁₂ ,…x _1n ]∈R ^m×n X is firstly taken ₁ Performing normalization processing, namely subtracting the mean value of the line of sample data from each line of normal history data (the mean function of Matlab software can be utilized), and dividing the mean value by the standard deviation of the line of sample data (the std function of Matlab software can be utilized) to obtain a matrix X= [ X ] ₁ ,x ₂ ,…x _n ]∈R ^m×n Here m=7, n=1200.

(2) Fault monitoring method using TONPE model, projection matrix A (a ₁ ,…,a _b )∈R ^7×b And calculate each normal history sample x _i (i＝1,...,1200)∈R ⁷ Statistics T of _i ² (i=1, 2, …, 1200) and statistics SPE _i (i=1, 2, … 1200), where b=4.

(2a) Construction of a spatial neighborhood set S

For a certain normal history sample point x _i Calculating Euclidean distance d (using matlab function EuDist 2) with other sample points, and selecting k points with minimum Euclidean distance d to the sample point to form a space neighborhood set Representing sample x _i Where k=6.

(2b) Constructing a time neighborhood set Q

For x _i Sample point construction time neighborhood set Q epsilon { x } _i-m1 ,...,x _i-1 ,x _i+1 ,...,x _i+m1 M1=3 here.

(2c) Determining an optimal reconstruction coefficient matrix W:

first, by minimizing the functionObtaining a weight coefficient matrix W of the space neighborhood set S _s ：

Then, by minimizing the functionObtaining a time coefficient weight matrix W _Q ：

wherein ,W_Qij As a matrix W _Q The ith row and jth column element of (2) represents sample x _j For reconstructed sample x _i Weight coefficient of (2); the constraint condition is thatWhen x is _j Not x _i W is equal to the time neighborhood point of _Qij ＝0。

(2d) Establishing an objective function J (y):

wherein ,y _i is x _i Is> and y_j Respectively represent y _i The weight coefficient eta of the spatial characteristic information is as follows: η=0.5.

(2e) Calculate projection matrix A (a ₁ ,…,a ₄ )∈R ^7×4 Can be obtained by solving equation (13):

will y _i ＝A ^T x _i Bringing into equation (13), the reduction can be obtained as:

wherein ,M_s ＝(I-W _s ) ^T (I-W _S )，M _Q ＝(I-W _Q ) ^T (I-W _Q )，M＝0.5M _S +0.5M _Q 。

Adding constraint A based on equation (14) ^T XX ^T A＝I，Solving the above optimization problem using the Lagrangian multiplier method involving constraints, equation (14) can be converted into a generalized eigenvalue solution problem as follows:

XMX ^T A＝λXX ^T A (15)

solving equation (15) yields:

1)a ₁ is (XX) ^T ) ^-1 XMX ^T Feature vectors (matlab functions eigs) corresponding to the minimum feature values of (a);

2)a _i (i=2, …, b) is Q ⁽ⁱ⁾ Feature vector (matlab function) corresponding to minimum feature value of (a)Number eigs).

Q ⁽ⁱ⁾ ＝{I-(XX ^T ) ^-1 a ^(i-1) [S ^(i-1) ] ^T }(XX ^T ) ^-1 XMX ^T (16)

in the formula ,S^(i-1) ＝[a ^(i-1) ] ^T (XX ^T ) ^-1 a ^(i-1) ；a ^(i-1) ＝[a ₁ ,a ₂ ,…a _i-1 ]。

All a can be found by the expression (16) _i The value of (i=1, …, 4) gives the projection matrix a.

(2f) Calculate each normal history sample x _i (i＝1,...,1200)∈R ⁷ Statistics T of _i ² (i=1, 2, …, 1200) and statistics SPE _i (i＝1,2,…1200)：

Wherein Λ=yy ^T /(1200-1)，Y＝A ^T X，y _i ＝A ^T x _i (i＝1,2,…,1200)。

(3) Calculating T using a kernel density estimation function (KDE) _i ² Control limits of (i=1, 2, …, n)Sum statistics SPE _i Control limit SPE of (i=1, 2, … n) _lim (Fitdist and icdf functions using matlab software).

Step two, online process monitoring, see fig. 2:

(4) N1 test sample data of m physical quantity monitoring points in the process of continuously stirring kettle type reactor are collected on line to form a matrix X _1new ＝[x ₁ ,x ₂ ,...,x _n1 ]∈R ^m×n1 Handle X _1new ∈R ^m×n1 Standardized treatment, i.e. X _1new ∈R ^m×n1 Subtracting the mean value of the line of sample data (which may be using the mean function of Matlab software) and dividing by the standard deviation of the line of sample data (which may be using the std function of Matlab software) to obtain a matrix X _new ＝[x _new1 ,x _new2 ,…,x _newn ]∈R ^m×n ，m＝7，n1＝1200。

(5) Fault monitoring method using TONPE model to calculate test data x _newi (i＝1,...,1200)∈R ^m Is a monitoring index of (2) and SPE_newi (i＝1,2,…,1200)；

SPE _newi ＝x _newi (I-A ^T A)[x _newi (I-A ^T A)] ^T (20)

Wherein Λ= (a) ^T X _new )(A ^T X _new ) ^T /(1200-1)，y _newi ＝A ^T x _newi (i＝1,2,…,1200)。

(6) Will statisticsSPE _newi And control limit->SPE _lim Respectively comparing the sample points x to the control points x _newi A fault occurs.

Fault 9: the fault is caused by the temperature T of the cooling water _C The faults caused by the change are introduced into the 201 st to 1200 th sample points, the detection results based on the PCA, NPE, ONPE and TONPE methods are shown in figures 3, 4, 5 and 6, the red dotted line represents the control limit, and the blue solid line represents the value of the statistic. Figure 3 is a view of the detection of PCA,T ² the detection rates of the statistic and SPE statistic are 0.74 and 0.93 respectively; FIG. 4 is a diagram of NPE detection, T ² The detection rates of the statistic and SPE statistic are 0.64 and 0.91 respectively; FIG. 5 is a view of an ONPE detection, statistics T ² And the detection rate of the statistic SPE is 0.62 and 0.91 respectively; FIG. 6 is a diagram of TONPE detection, statistics T ² And the detection rates of the statistics SPE are 0.98 and 0.72 respectively. Although SPE has low detection rate, T ² And the comprehensive detection rate is far higher than that of other three methods. The method has overall detection effect superior to that of PCA method, NPE method and ONPE method, wherein T is ² The detection effect is more obvious, and the method is proved to be effective.

From the above analysis, it can be seen that in the fault 9, the TONPE method of the present invention is superior to the PCA method, the NPE method, and the ONPE method, and can provide more accurate information to the monitoring personnel.

Experimental example: a CSTR process system is adopted to simulate a fault monitoring method based on time sequence expansion orthogonal neighborhood preserving embedding (TONPE), the physical quantity collected by 7 physical quantity monitoring points of the CSTR process is listed in table 1, 10 faults highly related to the physical quantity data collected by the 7 physical quantity monitoring points are listed in table 2, and the fault monitoring accuracy and false alarm rate in the process of monitoring the 10 faults by PCA, NPE, ONPE, TONPE are respectively shown in tables 3 and 4

TABLE 1 CSTR System physical quantity information

TABLE 2 CSTR System 1O Process failure

Table 3 fault monitoring accuracy

Table 4 failure monitoring failure report rate

Table 3 shows the fault monitoring results of the PCA process monitoring method, the NPE process monitoring method, the ONPE process monitoring method, and the TONPE process monitoring method for 10 faults of the CSTR process. The detection rate with sharp contrast is marked with bold letters. It can be seen that the TONPE process monitoring method shows the highest failure detection rate in most failure modes and has better performance in the case of failures 1,2, 3, 7, 8, 9, compared to the PCA process monitoring method, the NPE process monitoring method, and the ONPE process monitoring method. From average detection T ² The statistic detection rate and the comprehensive detection are far higher than those of the other three detection methods, and the SPE statistic is higher than PCA but lower than NPE and ONPE.

Table 4 shows the failure monitoring false alarm rate results of the PCA process monitoring method, the NPE process monitoring method, the ONPE process monitoring method and the TONPE process monitoring method for 10 failures of the CSTR process, and it is obvious from the table that the failure false alarm rate of the TONPE is very low.

The invention has been described in detail with reference to the examples; however, it will be understood by those skilled in the art that various specific parameters of the above embodiments may be changed or equivalents may be substituted for corresponding technical means without departing from the spirit of the present invention, so as to form a plurality of specific embodiments, which are common variations of the present invention and will not be described in detail herein.

Claims

1. The construction method of the orthogonal neighborhood preserving embedding model based on time sequence expansion is characterized by comprising the following steps:

(1) N normal history samples of m physical quantity monitoring points in the CSTR process are obtained to form a matrix X ₁ ＝[x ₁₁ ,x ₁₂ ,…x _1n ]∈R ^m×n Subtracting the average value of the line of sample data from each line of data, and dividing the average value by the standard deviation of the line of sample data to obtain a matrix X= [ X ] ₁ ,x ₂ ,…x _n ]∈R ^m×n ；

(2) Fault monitoring method using TONPE model, projection matrix A (a ₁ ，…，a _b )∈R ^m×b Wherein b.ltoreq.m, and calculating each normal history sample x _i ∈R ^m Statistics T of _i ² Sum statistics SPE _i Wherein i=1, 2, … n;

in the formula ,a_i Is the projection vector, and i=1, … b; b is dimension of dimension reduction; Λ=yy ^T /(n-1)；Y＝A ^T X；y _i ＝A ^T x _i Where i=1, 2, … n;

the method for acquiring the projection matrix A comprises the following steps:

(2a) Construction of a spatial neighborhood set S

For a certain normal history sample point x _i ∈R ^m And i=1, 2, … n, calculating Euclidean distance d with other sample points, and then selecting k points with minimum Euclidean distance d from the sample point to form a space neighborhood set Representing sample x _i Is the kth near point of (c);

(2b) Constructing a time neighborhood set Q

For x _i Sample point construction time neighborhood set Q epsilon { x } _i-m ,...,x _i-1 ,x _i+1 ,...,x _i+m -and k=2m in value;

(2c) Determining a weight coefficient matrix W

wherein ,representing sample x _i W is the j-th nearest point of _Sij As a matrix W _s The j-th column element of the i-th row of (2) represents sample +.>For reconstructed sample x _i Weight coefficient of (2); constraint is->And i=1, 2, … n, if the sample +.>Not x _i Is a neighborhood of (2), W _Sij ＝0；

wherein ,W_Qij As a matrix W _Q The ith row and jth column element of (2) represents sample x _j For reconstructed sample x _i Weight coefficient of (2); the constraint condition is thatAnd i=1, 2, … n if when x _j Not x _i W is equal to the time neighborhood point of _Qij ＝0；

(2d) Establishing an objective function J (y):

wherein ,y _i is x _i Is> and y_j Respectively represent y _i The weight coefficient eta of the spatial characteristic information is equal to or more than 0 and equal to or less than 1;

(2e) Calculate projection matrix A (a ₁ ,…,a _b )∈R ^m×b

Will y _i ＝A ^T x _i The formula (5) is carried out:

wherein ,M_s ＝(I-W _s ) ^T (I-W _S )，M _Q ＝(I-W _Q ) ^T (I-W _Q )，M＝ηM _S +(1-η)M _Q ；

Adding constraint A based on formula (6) ^T XX ^T A＝I，And i=2, …, b, solving the above optimization problem using the lagrangian multiplier method involving constraints, equation (6) translates into a generalized eigenvalue solution problem as follows:

XMX ^T A＝λXX ^T A (7)

solving the formula (7) to obtain:

Q ⁽ⁱ⁾ ＝{I-(XX ^T ) ^-1 a ^(i-1) [G ^(i-1) ] ^T }(XX ^T ) ^-1 XMX ^T (8)

in the formula ,G^(i-1) ＝[a ^(i-1) ] ^T (XX ^T ) ^-1 a ^(i-1) ；a ^(i-1) ＝[a ₁ ,a ₂ ,…a _i-1 ]；

All a are obtained by the formula (8) _i And i=1, …, b, resulting in projection matrix a;

(3) Computing T using a kernel density estimation function _i ² Control limit of (2)Sum statistics SPE _i Control limit SPE _lim Where i=1, 2, … n.

2. A CSTR process fault monitoring method based on the orthogonal neighborhood preserving embedding model constructed according to claim 1, comprising the steps of:

(1) n1 test sample data of m physical quantity monitoring points in the CSTR process are collected on line to form a matrix X _new1 ＝[x _new11 ,x _new12 ,…x _new1n1 ]∈R ^m×n1 X is taken as _new1 Subtracting the normal history sample matrix X from each row ₁ Dividing the data mean value of the corresponding row by the standard deviation of the corresponding row data to obtain a matrix X _new ＝[x _new1 ,x _new2 ,…x _newn1 ]∈R ^m×n1 ；

(2) Calculating test data x by using fault monitoring method of orthogonal neighborhood preserving embedding model constructed in claim 1 _newi ∈R ^m Is a monitoring index of (2) and SPE_newi Wherein i=1, 2, …, n1;

SPE _newi ＝x _newi (I-A ^T A)[x _newi (I-A ^T A)] ^T (10)

wherein Λ= (a) ^T X _new )(A ^T X _new ) ^T /(n1-1)，y _newi ＝A ^T x _newi And i=1, 2, …, n1;

(3) the obtained statistics are used forSPE _newi And control limit->SPE _lim Comparing the two parts, namely, considering that the sample point has faults, wherein the parts are larger than the control limit; and then summarizing all fault sample points, and solving the detection rate and the false alarm rate.