CN112180893B - Construction method of fault-related distributed orthogonal neighborhood preserving embedded model in CSTR process and fault monitoring method thereof - Google Patents

Abstract

The invention discloses a method for constructing a fault-related distributed orthogonal neighborhood preserving embedded model in a CSTR process, which comprises the following steps: n historical normal samples of the physical quantity monitored by m physical quantity monitoring points in the CSTR process are obtainedUsing SNR algorithm to pick out the variable related to each fault to form B +1 sub-blocks [ X ]₁,…,X_B+1]Calculating the historical normal sample of each sub-block

Statistic of (2)

And statistics SPE_b,i(i-1, …, n) and its control limits

SPE_b,lim(ii) a Acquiring physical quantity data of m physical quantity monitoring points in the CSTR process on line, corresponding the data to B +1 sub-blocks, and calculating X sub-block of each sub-block_b,newX of the ith (i ═ 1,2, …, n1) measurement sample of (a)_b,newiStatistics

Statistics SPE_b,newi(ii) a Constructing statistics using Bayesian inference

And

statistics

Exceeding its control limit indicates that a fault has occurred. The method considers local information of CSTR process data, establishes a distributed monitoring model and improves the detection rate of faults.

Description

Construction method of fault-related distributed orthogonal neighborhood preserving embedded model in CSTR process and fault monitoring method thereof

Technical Field

The invention belongs to the technical field of fault monitoring in a chemical production process, and particularly relates to a construction method of a fault-related distributed orthogonal neighborhood preserving embedded model in a CSTR process and a fault monitoring method thereof, which are used for improving the fault monitoring accuracy in the chemical process.

Background

Continuous Stirred Tank Reactors (CSTRs) are important in the industrial chemical process facilities and are widely used in the chemical reactions. It is widely used in pharmaceutical and synthetic food industries, and in semiconductor manufacturing industries. Along with diversification of chemical industrial production equipment and raw materials and increasingly complicated process flow, various production safety accidents also enter a peak period of easy occurrence and multiple occurrence; therefore, fault monitoring in CSTR processes is also becoming increasingly important.

Multivariate Statistical Process Monitoring (MSPM) technology represented by principal component analysis has become a research hotspot for fault monitoring of chemical process due to the strong capability of extracting useful information. Modern increasingly complex chemical processes typically involve large numbers of production equipment and control systems whose measurement data have high-dimensional, strong correlations, especially strong non-linearities that are prevalent among variables. The MSPM technique does not effectively account for non-linear fluctuations in the data and therefore cannot be used to monitor non-linear chemical processes.

Due to the complex correlation between CSTR process variables, the existing fault monitoring model is usually a global model, it is difficult to fully adapt it as a global monitoring model for the whole process, since it ignores the local behavior of the physicochemical data, and the monitoring results are often difficult to interpret.

Disclosure of Invention

The invention aims to solve the technical problem of providing a CSTR process Fault monitoring method based on a Fault-dependent distributed orthogonal neighborhood preserving embedding (FDONPE) model, so as to solve the technical problem of low Fault detection rate caused by neglecting of physicochemical parameters or local behaviors of data in the existing global model.

In order to solve the technical problems, the inventor establishes an FDONPE model based on an ONPE method based on long-term practical research in the field, and applies the FDONPE model to CSTR process fault monitoring so as to maintain local characteristics of process physical parameters or data and better extract distribution characteristics and essential information of each physical parameter.

Among them, the Neighborhood Orthogonal Preserving Embedding (ONPE) algorithm (Liu X M, Yin J W, Feng Z L, et al. organic New born Embedding for Face Recognition [ C ]// Proceedings of 2007 IEEE International reference on Image, ICIP 2007.New York,2007: 133-.

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

a construction method of a fault-related distributed orthogonal neighborhood preserving embedded model in a CSTR process is designed, and comprises the following steps:

(1) obtaining n historical normal samples of the physical quantity monitored by m physical quantity monitoring points in the CSTR process, and constructing a matrix X' belonging to the R^m×nSubtracting the mean value of all sample data in the row from each row of X', and dividing the mean value by the standard deviation of all sample data in the row to obtain a matrix X e R^m×n。

(2) Using SNR algorithm to pick out the variable related to each fault to form B sub-blocks [ X ]₁,X₂,…,X_B]And the global variable X is considered as a new block, constituting in total B +1 sub-blocks [ X₁,…,X_B+1]Sub-block

Sub-block samples

d_b(B-1, 2, …, B +1) is the subblock X_b(B-1, 2, …, B +1), where B is the number of known failure types.

(3) Obtaining each sub-block X based on ONPE model_b(B-1, 2, …, B +1) projection matrix

And calculating the historical normal sample of each sub-block

Statistic of (2)

And statistics SPE_b,i(i＝1,…,n)。

Wherein, a_b,i(i＝1,…,g_b) Is the projection vector, g_bIs dimension reduction, Λ_b＝Y_bY_b ^T/(n-1)，Y_b＝A_b ^TX_b，y_b,i＝A_b ^Tx_b,i(i＝1,2,…,n)。

(4) Computing each sub-block X using a kernel density estimation function_b(B-1, 2, …, B) control limit

And control limit SPE_b,lim。

Further, in the step (2), the history is normalizedData partitioning sub-block X_bThe method of (B ═ 1,2, …, B) is:

consider a set of fault data sets

X_fThe data in (1) is collected in an operation mode in which a certain failure occurs in the system; wherein m is_fIs the number of variables, n_fIs the number of samples.

SNR is the ratio of signal s to noise e in a system, and each variable i (i ═ 1, …, m)_f) SNR of (1)_iThe calculation is as follows:

wherein

X_f(i, j) is X_fValue in ith row and jth column, X_f(i,: means X)_fThe vector of row i; SNR_iIt is the signal-to-noise ratio of the ith variable in a certain failure operation mode, which reflects the change degree of the ith variable after failure, and is higher than each variable i (i is 1, …, m)_f) SNR of (1)_iThe magnitude of (c) indicates that it has changed significantly since the failure occurred, the selection and { SNR }_i，i＝1,…,m_fAnd the variables corresponding to the first C maximum values in the sequence are taken as relevant variables of the fault.

Further, in the step (3), each sub-block X is calculated based on the ONPE model_b(B-1, 2, …, B +1) projection matrix

Comprises the following steps:

(3a) construction of neighborhood set S_b: for some normal history sample point x_b,i(i ═ 1,2, …, n), calculating Euclidean distances to other sample points, and then selecting k with the minimum Euclidean distance to the sample point_bPoints constitute a neighborhood set

(3b) Determining a weight coefficient matrix W_b：

By a minimization function

Obtaining a spatial neighborhood set S_bIs given by the weight coefficient matrix W_b：

Wherein

Represents a sample x_b,iThe j-th proximity point, W_bijIs a matrix W_bRow i and column j of (1), representing a sample

For reconstructed sample x_b,iThe weight coefficient of (a); the constraint condition is

If sample

Is not x_b,iNeighborhood of (1), then W_bij＝0。

(3c) Establishing an objective function J (y)_b)：

Wherein y is_b,iIs x_b,iThe vector of the projection of (a) is,

denotes y_b,iOf the neighboring points.

(3d) Computing projectionsMatrix array

Will be provided with

Substituting equation (5) yields:

J(A_b)＝minA_b ^TX_bM_bX_b ^TA_b (6)

wherein M is_b＝(I_b-W_b)^T(I_b-W_b)。

Adding constraint conditions on the basis of the formula (6): a. the_b ^TX_bX_b ^TA_b＝I_b，

The lagrange multiplier method is utilized to contain constraints to solve the optimization problem, and the formula (6) can be converted into the following generalized eigenvalue solving problem, namely:

X_bM_bX_b ^TA_b＝λ_bX_bX_b ^TA_b (7)

solving equation (7) yields:

1)a_b,1is (X)_bX_b ^T)^-1X_bM_bX_b ^TThe feature vector corresponding to the minimum feature value of (1);

2)a_b,i(i＝2,…,g_b) Is Q_b ⁽ⁱ⁾The feature vector corresponding to the minimum feature value of (1);

Q_b ⁽ⁱ⁾＝{I_b-(X_bX_b ^T)^-1a_b ^(i-1)[G_b ^(i-1)]^T}(X_bX_b ^T)^-1X_bM_bX_b ^T (8)

in the formula, G_b ^(i-1)＝[a_b ^(i-1)]^T(X_bX_b ^T)^-1a_b ^(i-1)；a_b ^(i-1)＝[a_b,1,a_b,2,…a_b,i-1]。

Determining all a from the formula (8)_b,i(i＝1,…,g_b) To obtain a projection matrix A_b。

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

firstly, acquiring n1 measurement samples of physical quantities of m physical quantity monitoring points in the chemical production process on line, and constructing a measurement matrix X'_new∈R^m×n1Will be

Subtracting the average value of all sample data in the ith row of the matrix X' from each value in the ith (i-1, …, n1) row in (a), and dividing the average value by the standard deviation of all sample data in the ith row to obtain preprocessed X_new. Handle X_newCorresponds to the sub-block of step (2) in claim 1, forming B +1 sub-blocks

Sub-blocks

Sub-block samples

② calculating each sub-block X by using fault monitoring method of ONPE model_b,newX of the ith (i ═ 1,2, …, n1) measurement sample of (a)_b,newiStatistics

Statistics SPE_b,newi：

SPE_b,newi＝x_b,newi(I_b-A_b ^TA_b)[x_b,newi(I_b-A_b ^TA_b)]^T (10)

Wherein, Λ_b＝(A_b ^TX_b,new)(A_b ^TX_b,new)^T/(n1-1)，y_b,newi＝A_b ^Tx_b,newi(i＝1,2,…,n1)。

Constructing the ith measurement sample x based on Bayesian inference_newi(i＝1,...,n1)∈R^mBayes statistic of (d):

n and F represent normal and fault conditions, statistics, respectively

And statistics SPE_b,newiThe probabilities under normal and fault conditions are respectively:

statistics

And statistics SPE_b,newiThe corresponding failure probabilities are respectively:

P_SPE(x_b,newi)＝P_SPE(x_b,newi|N)P_SPE(N)+P_SPE(x_b,newi|F)P_SPE(F) (14)

wherein

As confidence level alpha (0 < alpha < 1),

is 1-alpha.

Fourthly, the Bayes statistic

And

comparing with the control limit 1-alpha respectively, the part exceeding the control limit indicates the ith sample x_newiA fault occurs.

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 FDONPE model considers the local information of the process data, divides the process physical quantity into a plurality of sub-physical quantity modules through an SNR algorithm, then models each sub-physical quantity space by adopting the ONPE method, and finally constructs new statistic by adopting Bayesian inference to realize the monitoring of the CSTR process data; the method fully utilizes the intra-block local physicochemical data information and the overall global physicochemical data information, and improves the accuracy of fault monitoring.

2. According to the method, the fault information is utilized, the variable set strongly related to the fault is selected and used for model development, the monitoring model is established, and more meaningful directions can be extracted for monitoring, so that the accuracy of fault detection is improved.

The ONPE model has certain processing capacity on the nonlinear data, and the improved FDONPE model can effectively explain the nonlinear fluctuation in the physicochemical data; therefore, the process monitoring model established based on the nonlinear algorithm can also judge whether the online physicochemical data really deviate from the normal working condition.

Drawings

FIG. 1 is a flow chart of an off-line modeling process of a CSTR process monitoring method based on an FDONPE model according to the present invention.

FIG. 2 is a flow chart of the on-line monitoring process of the CSTR process monitoring method based on the FDONPE model of the present invention.

Fig. 3 is a monitoring result of the fault 10 in the CSTR monitoring process by using the ONPE method in the embodiment of the present invention, in which the abscissa is a sample and the ordinate is a statistic.

Fig. 4 is a monitoring result of the fault 10 in the CSTR monitoring process by using the fdonfe method in the embodiment of the present invention, in which the abscissa in the figure is a sample and the ordinate is a statistic.

Fig. 5 shows the 10 sub-block monitoring results of the CSTR fault 10 monitored by using the fdonne method in the embodiment of the present invention, where the abscissa in the figure is a sample and the ordinate is a statistic.

Detailed Description

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

The following embodiments are explained based on a CSTR system, data are generated through a CSTR model built by a Simulink module of matlab, the simulation system can set a plurality of physical measuring point positions corresponding to 10 basic faults and 7 physical quantities to be monitored, and each fault is obtained from the following stepsThe 201 st test sample was introduced. 1200 measurement data were collected, of which the first 200 were normal data and the last 1000 were failure data. Reactor solute concentration Q in example one at 10 failures_CThe description will be given with reference to variations as examples.

The first embodiment of the CSTR process monitoring method based on the FDONPE model is used for processing physical quantity data acquired at a plurality of physical quantity monitoring points in the CSTR process so as to monitor the physical quantity data which fails, and therefore production maintenance personnel can find problems in production as soon as possible and perform corresponding processing conveniently. The physical quantity monitoring points and the corresponding monitored physical quantities of the CSTR process are shown in Table 1.

The method mainly comprises the following steps:

step (I): establishing an offline FDONPE model

(1) Obtaining n historical normal samples of the physical quantity monitored by m physical quantity monitoring points in the CSTR process, and constructing a matrix X' belonging to the R^m×nSubtracting the mean value of all sample data in the row from each row of X' (the mean function of Matlab software can be used), and dividing the mean value by the standard deviation of all sample data in the row (the std function of Matlab software can be used) to obtain a matrix X epsilon R^m×nWhere m is 7 and n is 1200.

(2) The Signal-to-Noise Ratio (SNR) algorithm is applied to pick out the variables related to each fault to form 10 subblocks, namely [ X ]₁,X₂,…,X₁₀]Sub-block

d_b(b-1, 2, …,10) is the sub-block X_b(b is 1,2, …,10) the number of physical quantities, where d is_b＝2。

Partitioning sub-blocks [ X ] according to failure data₁,X₂,…,X₁₀]The algorithm is as follows:

collecting a set of historical failure data sets

X_fThe data in (1) is collected in an operation mode in which a certain failure occurs in the system; wherein m is_fIs 7 isNumber of variables, n _f800 is the number of samples.

SNR refers to the ratio of signal s to noise e in a system, and the SNR of each variable i_iThe following can be calculated:

wherein

(the mean function of Matlab software can be used),

(e_ie_i ^Tobtained by var function of Matlab software), X_f(i, j) means X_fThe value in the ith and jth columns, X_f(i,: means X)_fThe vector of row i.

SNR_iThe signal-to-noise ratio of the ith variable in a certain fault operation mode; it can reflect the change degree of the ith variable after the fault occurs; each variable i (i ═ 1, …, m)_f) SNR of (1)_iThe size of (d); selection and { SNR_iAnd the variable corresponding to the first 2 maximum values in the i 1, …,7 is used as the related variable of the fault.

The variables corresponding to the first 2 maximum values of 10 faults in the CSTR process are found out as the related variables of the faults according to the method, and a sub-block is formed.

The global variable X is considered as a new block, taking into account the global nature of the data. The proposed algorithm therefore comprises 11 subblocks [ X ]₁,…,X₁₁]。

(3) Obtaining each sub-block X by applying fault monitoring method of ONPE model_b(b 1,2, …,11) projection matrix

And calculating historical normal sample x of each sub-block_b,i(i＝1,2,…,1200)∈R²Statistic of (2)

And statistics SPE_b,i(i＝1,…,1200)。

Wherein, a_i(i＝1,…,g_b) Is the projection vector, g_bIs the dimension of dimension reduction, here g_bIs generally equal to pair sub-block X_b(b is 1,2, …,11) the contribution rate of PCA (principal component analysis) decomposition is 85% (PCA function of Matlab software can be used). Lambda_b＝Y_bY_b ^T/(1200-1)，Y_b＝A_b ^TX_b，y_b,i＝A_b ^Tx_b,i(i＝1,2,…,1200)。

Calculating each sub-block X by applying ONPE model_b(b 1,2, …,11) projection matrix a_bMainly comprises the following steps:

(3a) construction of neighborhood set S_b：

For some normal history sample point x_b,i(i ═ 1,2, …,1200), the Euclidean distances to other sample points are calculated (using matlab function EuDist2), and then k is chosen that is the minimum Euclidean distance from this sample point_bPoints constitute a neighborhood set

Where k is_b＝K_b+1，K_bIs sub-block X_b(b is 1,2, …,11) the contribution rate of PCA (principal component analysis) decomposition is 85% (PCA function of Matlab software can be used).

(3b) Determining a weight coefficient matrix W_b：

First, by minimizing a function

Obtaining a spatial neighborhood set S_bIs given by the weight coefficient matrix W_b:

Wherein

Represents a sample x_b,iThe j-th proximity point, W_bijIs a matrix W_bRow i and column j of (1), representing a sample

For reconstructed sample x_b,iThe weight coefficient of (a); the constraint condition is

If the sample

Is not x_b,iNeighborhood of (1), then W_bij＝0。

(3c) Establishing an objective function J (y)_b)：

Wherein y is_b,iIs x_b,iThe vector of the projection of (a) is,

denotes y_b,iOf the neighboring points.

(3d) Computing a projection matrix A_bThis can be obtained by solving equation (19):

will be provided with

Substituting into equation (19), the reduction can be:

J(A_b)＝minA_b ^TX_bM_bX_b ^TA_b (20)

wherein M is_b＝(I_b-W_b)^T(I_b-W_b)。

Adding a constraint condition on the basis of the formula (20): a. the_b ^TX_bX_b ^TA_b＝I_b，

By solving the above optimization problem using lagrange multiplier method including constraints, equation (20) can be converted into the following generalized eigenvalue solution problem, namely:

X_bM_bX_b ^TA_b＝λ_bX_bX_b ^TA_b (21)

solving equation (21) yields:

1)a_b,1is (X)_bX_b ^T)^-1X_bM_bX_b ^TThe minimum eigenvalue of (matlab function eigs).

2)a_b,i(i＝2,…,g_b) Is Q_b ⁽ⁱ⁾The minimum eigenvalue of (matlab function eigs).

Q_b ⁽ⁱ⁾＝{I_b-(X_bX_b ^T)^-1a_b ^(i-1)[G_b ^(i-1)]^T}(X_bX_b ^T)^-1X_bM_bX_b ^T (22)

In the formula: g_b ^(i-1)＝[a_b ^(i-1)]^T(X_bX_b ^T)^-1a_b ^(i-1)；a_b ^(i-1)＝[a_b,1,a_b,2,…a_b,i-1]。

Through (22) formulaWe can find out all a_b,i(i＝1,…,g_b) To obtain a projection matrix A_b。

(4) Computing each sub-block X using Kernel Density Estimation (KDE)_bControl limit of (B ═ 1,2, …, B)

And control limit SPE_b,lim(using the fitsist and icdf functions of matlab software).

Step (II): online process monitoring

(5) 1200 measurement samples of the physical quantity of 7 physical quantity monitoring points in the CSTR process are acquired on line, and a measurement matrix X 'is constructed'_new∈R^7×1200To measurement matrix X'_newPretreatment is carried out, namely X'_newSubtracting the average value of all sample data in ith row of the matrix X' from each value in ith (i-1, 2, …,7) row in (a), and dividing by the standard deviation of all sample data in ith row to obtain preprocessed X_new(ii) a Handle X_newCorresponding the data in step (2) to the sub-blocks to form 11 sub-blocks [ X ]_1,new,…,X_11,new]。

(6) Each sub-block X is calculated according to equations (3) to (4)_b,newX of the ith (i ═ 1,2, …,1200) measurement sample of (a)_b,newiStatistics

Statistics SPE_b,newi。

(7) Constructing the ith measurement sample x according to equations (5) - (8) and Bayesian inference_newi(i＝1,...,n1)∈R^mBayesian statistics of

And

(8) bayesian statistics

And

the part exceeding the control limit indicates the ith sample x, compared with the control limit 1-alpha (alpha is 0.99), respectively_newiA fault occurs.

Specific monitoring results are shown in fig. 3 and table 4.

The monitoring result of the faults in the chemical production process can be obtained through the circulation of the two steps.

The fault 10 is caused by the volume concentration Q_CFaults caused by changes are introduced into 201 th to 1200 th sample points, and the physical quantity of the faults is 5. The detection results based on the ONPE and FDONPE methods are shown in fig. 3, 4, and 5, where the dotted line indicates the control limit and the solid line indicates the value of the statistic.

From the detection result of the failure 10, it can be seen that N is passed²Statistics shows that the detection result of FDONPE reaches 86 percent, while N of ONPE²The statistic was only 58% detected, it is evident that FDONPE is in

The detection result of the statistic is obviously improved, so that the FDONPE method is superior to the ONPE method, and the subblock results of the FDONPE method are analyzed, wherein the detection results of the subblocks 1,2,5,6 and 10 are shown in

And BIC_SPEThe detection rate of the statistic is ideal, the 5 sub-blocks all contain the variable 5, and the detection results of the remaining sub-blocks without the variable 5 are not ideal, so that the variable 5 is a responsible variable of the fault 10, and the variable 5 corresponds to the cooling water temperature Q_CThis verifies the feasibility of the method of the invention.

Through the analysis, in the fault 10, the FDONPE method is superior to the ONPE method, and more accurate information can be provided for monitoring personnel.

Experimental example: a CSTR model is adopted to simulate chemical production based on a distributed ONPE model (FDONPE)The specific application of the process fault monitoring method is that table 1 lists physical quantities acquired by 7 physical quantity monitoring points in the CSTR process, table 2 lists 10 faults highly related to the physical quantity data acquired by the 7 physical quantity monitoring points, table 3 lists blocking results of the process physical quantities through the SNR algorithm, and table 4 shows fault monitoring accuracy rates (in the case of monitoring the 10 faults by respectively adopting PCA, NMF, NPE, ONPE and FDONPE) (the fault monitoring accuracy rate is shown in the table

Wherein T is²,N²,SPE,

BIC_SPERespectively, monitoring statistics for different methods.

TABLE 1 CSTR System physical quantity information

TABLE 2 CSTR System 1O Process failures

TABLE 3 variable selection results for faults

Table 4 shows the fault monitoring results of 10 types of faults in the chemical production process using the PCA process monitoring method, the NPE process monitoring method, the ONPE process monitoring method, and the FDONPE process monitoring method in the CSTR simulation system. It can be seen that the fdonne process monitoring method shows the highest fault detection rate in most fault modes and has better performance in the modes of faults 8, 9 and 10, compared to the NPE process monitoring method or the onne process monitoring method.

TABLE 4 Fault detection accuracy comparison

The present invention is described in detail with reference to the examples above; however, it will be understood by those skilled in the art that various changes in the specific parameters of the embodiments described above may be made or equivalents may be substituted for elements thereof without departing from the scope of the present invention, so as to form various embodiments, which are not limited to the specific parameters of the embodiments described above, and the detailed description thereof is omitted here.

Claims (2)

1. A method for constructing a fault-related distributed orthogonal neighborhood preserving embedded model in a CSTR process is characterized by comprising the following steps:

(1) obtaining n historical normal samples of the physical quantity monitored by m physical quantity monitoring points in the CSTR process, and constructing a matrix X' belonging to the R^m×nSubtracting the mean value of all sample data in the row from each row of X', and dividing the mean value by the standard deviation of all sample data in the row to obtain a matrix X e R^m×n；

(2) Using SNR algorithm to pick out the variable related to each fault to form B sub-blocks [ X ]₁,X₂,…,X_B]And the global variable X is considered as a new block, constituting in total B +1 sub-blocks [ X₁,…,X_B+1]Sub-block

Sub-block samples

d_b(B-1, 2, …, B +1) is the subblock X_b(B ═ 1,2, …, B +1) the number of physical quantities, B being the number of known failure types;

in this step, sub-blocks X are divided for historical normal data_bThe method of (B ═ 1,2, …, B) is:

collecting a set of historical failure data sets

X_fThe data in (1) is collected in an operation mode in which a certain failure occurs in the system; wherein m is_fIs the number of variables, n_fIs the number of samples;

SNR is the ratio of signal s to noise e in a system, and each variable i (i ═ 1, …, m)_f) SNR of (1)_iThe calculation is as follows:

in the formula (I), the compound is shown in the specification,

X_f(i, j) is X_fValue in ith row and jth column, X_f(i,: means X)_fThe vector of row i; SNR_iIt is the signal-to-noise ratio of the ith variable in a certain failure operation mode, which reflects the change degree of the ith variable after failure, and is higher than each variable i (i is 1, …, m)_f) SNR of (1)_iIs selected in relation to { SNR }_i，i＝1,…,m_fThe variables corresponding to the first C maximum values in the previous step are taken as the relevant variables of the fault;

(3) obtaining each sub-block X based on ONPE model_b(B-1, 2, …, B +1) projection matrix

And calculating the historical normal sample of each sub-block

Statistic of (2)

And statistics SPE_b,i(i＝1,…,n)；

Wherein, a_i(i＝1,…,g_b) Is the projection vector of the b-th sub-block, g_bIs the dimension reduction, Λ, of the b-th sub-block_b＝Y_bY_b ^T/(n-1)，Y_b＝A_b ^TX_b，y_b,i＝A_b ^Tx_b,i(i＝1,2,…,n)；

In this step, each sub-block X is calculated based on the ONPE model_b(B-1, 2, …, B +1) projection matrix

Comprises the following steps:

(3a) construction of neighborhood set S_b: for some normal history sample point x_b,i(i ═ 1,2, …, n), calculating Euclidean distances to other sample points, and then selecting k with the minimum Euclidean distance to the sample point_bPoints constitute a neighborhood set

(3b) Determining a weight coefficient matrix W_b：

By a minimization function

Obtaining a spatial neighborhood set S_bIs given by the weight coefficient matrix W_b：

Wherein the content of the first and second substances,

represents a sample x_b,iThe j-th proximity point, W_bijIs a matrix W_bRow i and column j of (1), representing a sample

For reconstructed sample x_b,iThe weight coefficient of (a); the constraint condition is

If sample

Is not x_b,iNeighborhood of (1), then W_bij＝0；

(3c) Establishing an objective function J (y)_b)：

Wherein, y_b,iIs x_b,iThe vector of the projection of (a) is,

denotes y_b,iAdjacent points of (a);

(3d) computing a projection matrix

Will be provided with

Substituting equation (5) yields:

J(A_b)＝minA_b ^TX_bM_bX_b ^TA_b (6)

wherein M is_b＝(I_b-W_b)^T(I_b-W_b)；

Adding constraint conditions on the basis of the formula (6): a. the_b ^TX_bX_b ^TA_b＝I_b，

The lagrange multiplier method is utilized to contain constraints to solve the optimization problem, and the formula (6) can be converted into the following generalized eigenvalue solving problem, namely:

X_bM_bX_b ^TA_b＝λ_bX_bX_b ^TA_b (7)

solving equation (7) yields:

1)a_b,1is (X)_bX_b ^T)^-1X_bM_bX_b ^TThe feature vector corresponding to the minimum feature value of (1);

2)a_b,i(i＝2,…,g_b) Is Q_b ⁽ⁱ⁾The feature vector corresponding to the minimum feature value of (1);

Q_b ⁽ⁱ⁾＝{I_b-(X_bX_b ^T)^-1a_b ^(i-1)[G_b ^(i-1)]^T}(X_bX_b ^T)^-1X_bM_bX_b ^T (8)

in the formula, G_b ^(i-1)＝[a_b ^(i-1)]^T(X_bX_b ^T)^-1a_b ^(i-1)；a_b ^(i-1)＝[a_b,1,a_b,2,…a_b,i-1]；

Determining all a from the formula (8)_b,i(i＝1,…,g_b) To obtain a projection matrix A_b；

(4) Computing each sub-block X using a kernel density estimation function_b(B-1, 2, …, B) control limit

And control limit SPE_b,lim。

2. A CSTR process fault monitoring method based on FDONPE, which adopts the construction method of the model as claimed in claim 1, and comprises the following steps:

firstly, acquiring n1 measurement samples of the physical quantity of m physical quantity monitoring points in the chemical production process on line,

and constructing a measurement matrix X'_new∈R^m×n1Prepared from X'_newSubtracting the average value of all sample data in the ith row of the matrix X' from each value in the ith (i-1, …, n1) row in (a), and dividing the average value by the standard deviation of all sample data in the ith row to obtain preprocessed X_new；

Handle X_newCorresponds to the sub-block of step (2) in claim 1, forming B +1 sub-blocks [ X ]_1,new,…,X_B+1,new]Sub-block

Sub-block samples

② calculating each sub-block X by using fault monitoring method of ONPE model_b,newX of the ith (i ═ 1,2, …, n1) measurement sample of (a)_b,newiStatistics

Statistics SPE_b,newi；

SPE_b,newi＝x_b,newi(I_b-A_b ^TA_b)[x_b,newi(I_b-A_b ^TA_b)]^T (10)

Wherein, Λ_b＝(A_b ^TX_b,new)(A_b ^TX_b,new)^T/(n1-1)，y_b,newi＝A_b ^Tx_b,newi(i＝1,2,…,n1)；

Constructing the ith measurement sample x based on Bayesian inference_newi(i＝1,...,n1)∈R^mBayes statistic of (d):

n and F represent normal and fault conditions, statistics, respectively

And statistics SPE_b,newiThe probabilities under normal and fault conditions are respectively:

statistics

And statistics SPE_b,newiThe corresponding failure probabilities are respectively:

P_SPE(x_b,newi)＝P_SPE(x_b,newi|N)P_SPE(N)+P_SPE(x_b,newi|F)P_SPE(F) (14)

wherein

As confidence level alpha (0 < alpha < 1),

is 1-alpha;

fourthly, the Bayes statistic

And

comparing with the control limit 1-alpha respectively, the part exceeding the control limit indicates the ith sample x_newiA fault occurs.

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