CN112180893A - Construction and application of fault-related distributed orthogonal neighborhood preserving embedded model in CSTR (continuous stirred tank reactor) process - Google Patents

Abstract

Translated fromChinese

本发明公开了一种CSTR过程中故障相关分布式正交邻域保持嵌入模型的构建方法，包括：获取CSTR过程中m个物理量监测点监测的物理量的n个历史正常样本，应用信噪比算法挑选出与每个故障相关的变量,构成B+1个子块[X₁,…,X_B+1]，计算每个子块历史正常样本

的统计量

和统计量SPE_b,i(i＝1,…,n)及其控制限

SPE_b,lim；在线采集CSTR过程中m个物理量监测点的物理量数据，把数据对应到B+1个子块内，计算每一个子块X_b,new的第i(i＝1,2,…,n1)个测量样本的x_b,newi统计量

统计量SPE_b,newi；采用贝叶斯推理构造统计量

和

统计量

超出其控制限时表示有故障发生。该方法考虑了CSTR过程数据的局部信息，建立分布式监控模型，提高了故障的检测率。

The invention discloses a method for constructing a fault-related distributed orthogonal neighborhood maintenance embedded model in a CSTR process, comprising: acquiring n historical normal samples of physical quantities monitored by m physical quantity monitoring points in the CSTR process, and applying a signal-to-noise ratio algorithm Select the variables related to each fault, form B+1 sub-blocks [X₁ ,...,X_B+1 ], and calculate the historical normal samples of each sub-block

statistic

and statistic SPE_b,i (i=1,...,n) and its control limits

SPE_b,lim ; collect the physical quantity data of m physical quantity monitoring points in the CSTR process, map the data to B+1 sub-blocks, and calculate the i-th (i=1,2,… ,n1) x_b,newi statistics of measurement samples

Statistics SPE_b,newi ; statistics are constructed using Bayesian inference

and

Statistics

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

Description

Construction and application of fault-related distributed orthogonal neighborhood preserving embedded model in CSTR (continuous stirred tank reactor) process

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 a fault-related distributed orthogonal neighborhood preserving embedded model in a CSTR (continuous stirred tank reactor) process, 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 2007IEEE 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 sub-blocks X are divided for the historical normal data_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 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 constraint to solve the optimization problem, and the formula (6) can be converted into the following generalized eigenvalue solutionThe problems are as follows:

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×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) inclaim 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(xb_,newi)＝P_SPE(xb_,newi|N)P_SPE(N)+P_SPE(xb_,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 thefault 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 thefault 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 theCSTR 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 is generated by a CSTR model built by 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 each fault is introduced from 201 th test sample. 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_f7 is the number 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 thei 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]。

We can find all a by equation (22)_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.

Thefault 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 thefailure 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 thesubblocks 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 thefault 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 thefault 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 the specific application of a chemical production process fault monitoring method based on a distributed ONPE model (FDONPE), the table 1 lists the physical quantities acquired by 7 physical quantity monitoring points in the CSTR process, the table 2 lists 10 faults highly related to the physical quantity data acquired by the 7 physical quantity monitoring points, the table 3 lists the blocking results of the process physical quantities through an SNR algorithm, and the table 4 shows the fault monitoring accuracy rate (the fault monitoring accuracy rate is) when the 10 faults are monitored by respectively adopting PCA, NMF, NPE, ONPE and FDONPE

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

Fault number	Block number	Variables of
			1	1	3,5
2	2	7,5
			3	3	3,7
4	4	1,2
			5	5	2,5
6	6	6,5
			7	7	3,2
8	8	4,2
			9	9	7,6
10	10	5,1

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 offaults 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 (4)

Translated fromChinese

1.一种CSTR过程中故障相关分布式正交邻域保持嵌入模型的构建方法，其特征在于，包括以下步骤：1. a method for constructing a fault-related distributed orthogonal neighborhood to maintain an embedded model in a CSTR process, is characterized in that, comprises the following steps:(1)获取CSTR过程中m个物理量监测点监测的物理量的n个历史正常样本，并构建矩阵X′∈R^m×n,将X′的每一行减去这一行所有样本数据的均值，然后除以这一行所有样本数据的标准差，得到矩阵X∈R^m×n；(1) Obtain n historical normal samples of physical quantities monitored by m physical quantity monitoring points in the CSTR process, and construct a matrix X′∈R^m×n , subtract the mean value of all sample data in this row from each row of X′, and then Divide by the standard deviation of all sample data in this row to get the matrix X∈Rm^×n ;(2)应用信噪比算法挑选出与每个故障相关的变量，构成B个子块[X₁,X₂,…,X_B]，且将全局变量X看成是一个新块，总计构成B+1个子块[X₁,…,X_B+1]，子块

子块样本

d_b(b＝1,2,…,B+1)是子块X_b(b＝1,2,…,B+1)内物理量的个数，B是已知故障类型的个数；(2) Apply the signal-to-noise ratio algorithm to select the variables related to each fault to form B sub-blocks [X₁ , X₂ ,..., X_B ], and regard the global variable X as a new block, which constitutes B in total +1 sub-block [X₁ ,...,X_B+1 ], sub-block

sub-block samples

d_b (b=1,2,...,B+1) is the number of physical quantities in the sub-block X_b (b=1,2,...,B+1), and B is the number of known fault types;(3)基于ONPE模型获得每个子块X_b(b＝1,2,…,B+1)的投影矩阵

并计算每个子块历史正常样本

的统计量

和统计量SPE_b,i(i＝1,…,n)；(3) Obtain the projection matrix of each sub-block X_b (b=1,2,...,B+1) based on the ONPE model

and calculate the historical normal samples of each sub-block

statistic

and statistic SPE_b,i (i=1,...,n);

其中，a_i(i＝1,…,g_b)是第b个子块的投影向量，g_b是第b个子块的降维维度，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)；Among them, a_i (i=1,...,g_b ) is the projection vector of the b-th sub-block, g_b is the dimension reduction dimension of the b-th sub-block, Λ_b =Y_b Y_b^T /(n-1), Y_b =A_b^T X_b , y_b,i =A_b^T x_b,i (i=1,2,...,n);(4)应用核密度估计函数计算每个子块X_b(b＝1,2,…,B)的控制限

和控制限SPE_b,lim。(4) Apply the kernel density estimation function to calculate the control limits of each sub-block X_b (b=1,2,...,B)

and the control limit SPE_b,lim .2.根据权利要求1所述CSTR过程中故障相关分布式正交邻域保持嵌入模型的构建方法，其特征在于，在所述步骤(2)中，对历史正常数据划分子块X_b(b＝1,2,…,B)的方法为：2. in the described CSTR process according to claim 1, fault-related distributed orthogonal neighborhood maintains the construction method of embedded model, it is characterized in that, in described step (2), to historical normal data division sub-block X_b (b =1,2,...,B) method is:采集一组历史故障数据集

X_f中的数据是在系统发生某种故障的操作模式下收集的；其中m_f是变量的个数，n_f是样本数；Collect a set of historical failure data sets

The data in X_f are collected in the operating mode where the system has some kind of failure; where m_f is the number of variables and n_f is the number of samples;SNR为一个系统中信号s与噪声e的比例，每一个变量i(i＝1,…,m_f)的SNR_i计算如下：SNR is the ratio of signal s to noise e in a system. The SNR_i of each variable i (i=1,...,m_f ) is calculated as follows:

其中

X_f(i,j)为X_f中第i行，第j列的值，X_f(i,：)指的是X_f中第i行的向量；SNR_i是指在某个故障操作模式下，第i个变量的信噪比，其反应发生故障后第i个变量的变化程度，比每一个变量i(i＝1,…,m_f)的SNR_i的大小，选择与{SNR_i，i＝1,…,m_f}中的前C个最大值相对应的变量作为该故障的相关变量。in

X_f (i,j) is the value of the i-th row and j-th column in X_f , X_f (i,:) refers to the vector of the i-th row in X_f ; SNR_i refers to a fault operating mode Next, the signal-to-noise ratio of the i-th variable, which reflects the degree of change of the i-th variable after the failure, is greater than the size of the SNR_i of each variable i (i=1,...,m_f ), which is chosen to be the same as {SNR_i ,_i =1, .3.根据权利要求1所述CSTR过程中故障相关分布式正交邻域保持嵌入模型的构建方法，其特征在于，在所述步骤(3)中，基于ONPE模型计算出每个子块X_b(b＝1,2,…,B+1)的投影矩阵

包含以下步骤：3. in the described CSTR process according to claim 1, fault-related distributed orthogonal neighborhood maintains the construction method of embedded model, it is characterized in that, in described step (3), calculates each sub-block X based on_ONPE model ( b=1,2,...,B+1) projection matrix

Contains the following steps:(3a)构建邻域集S_b：针对某个正常历史样本点x_b,i(i＝1,2,…,n)，计算与其它样本点的欧式距离，然后选取距离此样本点欧氏距离最小的k_b个点组成邻域集

(3a) Construct a neighborhood set S_b : for a certain normal historical sample point x_b,i (i=1,2,...,n), calculate the Euclidean distance with other sample points, and then select the Euclidean distance from this sample point The k_b points with the smallest distance form a neighborhood set

(3b)确定权重系数矩阵W_b：(3b) Determine the weight coefficient matrix W_b :由最小化函数

得到空间邻域集S_b的权重系数矩阵W_b：by the minimization function

The weight coefficient matrix W_b of the spatial neighborhood set S_b is obtained:

其中

表示样本x_b,i的第j个临近点，W_bij为矩阵W_b的第i行第j列元素，代表样本

对重构样本x_b,i的权重系数；约束条件为

若样本

不是x_b,i的邻域，则W_bij＝0；in

Represents the j-th adjacent point of the sample x_{b, i} , W_bij is the i-th row and j-th column element of the matrix W_b , representing the sample

The weight coefficient of the reconstructed sample x_b,i ; the constraints are

If the sample

is not the neighborhood of x_b,i , then W_bij =0;(3c)建立目标函数J(y_b)：(3c) Establish the objective function J(y_b ):

其中y_b,i为x_b,i的投影向量，

表示y_b,i的邻近点；where y_b,i is the projection vector of x_b,i ,

Represents the adjacent points of y_{b, i} ;(3d)计算投影矩阵

(3d) Calculate the projection matrix

将

带入公式(5)得：Will

Bring in formula (5) to get:J(A_b)＝minA_b^TX_bM_bX_b^TA_b (6)J(A_b )=minA_b^T X_b M_b X_b^T A_b (6)其中M_b＝(I_b-W_b)^T(I_b-W_b)；where M_b =(I_b -W_b )^T (I_b -W_b );在式(6)的基础上加入约束条件：A_b^TX_bX_b^TA_b＝I_b，

利用拉格朗日乘子法包含约束来求解以上优化问题，式(6)可以转化为如下的广义特征值求解问题，即:Add constraints on the basis of formula (6): A_b^T X_b X_b^T A_b =I_b ,

Using the Lagrange multiplier method to include constraints to solve the above optimization problem, equation (6) can be transformed into the following generalized eigenvalue solution problem, namely:X_bM_bX_b^TA_b＝λ_bX_bX_b^TA_b (7)X_b M_b X_b^T A_b =λ_b X_b X_b^T A_b (7)求解公式(7)得：Solving Equation (7) we get:1)a_b,1是(X_bX_b^T)^-1X_bM_bX_b^T的最小特征值对应的特征向量；1) a_b,1 is the eigenvector corresponding to the minimum eigenvalue of (X_b X_b^T )^-1 X_b M_b X_b^T ;2)a_b,i(i＝2,…,g_b)是Q_b⁽ⁱ⁾的最小特征值对应的特征向量；2) a_b,i (i=2,...,g_b ) is the eigenvector corresponding to the smallest eigenvalue of Q_b⁽ⁱ⁾ ;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)Q_b⁽ⁱ⁾ = {I_b -(X_b X_b^T )^-1 a_b^(i-1) [G_b^(i-1) ]^T }(X_b X_b^T )^-1 X_b M_b X_b^T (8)式中，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]；In the formula, G_b^(i-1) = [a_b^(i-1) ]^T (X_b X_b^T )^-1 a_b^(i-1) ; a_b^(i-1) = [a_{b, 1} ,a_b,2 ,…a_b,i-1 ];由(8)式求出所有的a_b,i(i＝1,…,g_b)的值，得到投影矩阵A_b。All the values of a_b,i (i=1,...,g_b ) are obtained from equation (8), and the projection matrix A_b is obtained.4.一种基于FDONPE的CSTR过程故障监控方法，包括如下步骤：4. A CSTR process fault monitoring method based on FDONPE, comprising the steps:①在线采集化工生产过程中m个物理量监测点的物理量的n1个测量样本，①On-line collection of n1 measurement samples of physical quantities of m physical quantity monitoring points in the chemical production process,并构建测量矩阵X′_new∈R^m×n1，将X′_new中的第i(i＝1,…,n1)行的每一个值减去矩阵X′第i行所有样本数据的均值，然后除以第i行所有样本数据的标准差，得到预处理后的X_new；And construct the measurement matrix X′_new ∈ R^m×n1 , subtract the mean value of all sample data in the i-th row of the matrix X′ from each value of the i-th row (i=1,...,n1) in X′-_new , and then Divide by the standard deviation of all sample data in row i to get the preprocessed X_new ;把X_new的数据对应到权利要求1中所述步骤(2)的子块内，形成B+1个子块[X_1,new,…,X_B+1,new]，子块

子块样本

Corresponding the data of X_new to the sub-block of the step (2) in claim 1, forming B+1 sub-blocks [X_1,new ,...,X_B+1,new ], the sub-block

sub-block samples

②使用ONPE模型的故障监测方法计算每一个子块X_b,new的第i(i＝1,2,…,n1)个测量样本的x_b,newi统计量

统计量SPE_b,newi；②Use the fault monitoring method of the ONPE model to calculate the x_b,newi statistics of the i-th (i=1,2,...,n1) measurement sample of each sub-block X_b,new

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)SPE_b,newi =x_b,newi (I_b -A_b^T A_b )[x_b,newi (I_b -A_b^T A_b )]^T (10)其中，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)；Among them, Λ_b =(A_b^T X_b,new )(A_b^T X_b,new )^T /(n1-1), y_b,newi =A_b^T x_b,newi (i=1,2, ...,n1);③基于贝叶斯推理构造第i个测量样本x_newi(i＝1,...,n1)∈R^m的贝叶斯统计量：③Construct the Bayesian statistic of the i-th measurement sample x_newi (i=1,...,n1)∈R^m based on Bayesian inference:

N和F分别代表正常状况和故障状况，统计量

和统计量SPE_b,newi对应正常和故障条件下的概率分别为：N and F represent normal and fault conditions, respectively, statistics

and the statistic SPE_{b, newi} corresponding to the probability under normal and fault conditions are:

统计量

和统计量SPE_b,newi对应的故障概率分别为：Statistics

The failure probabilities corresponding to the statistics SPE_{b and newi} are:

P_SPE(x_b,newi)＝P_SPE(x_b,newi|N)P_SPE(N)+P_SPE(x_b,newi|F)P_SPE(F) (14)P_SPE (x_{b, newi} ) = P_SPE (x_{b, newi} |N) P_SPE (N)+P_SPE (x_{b, newi} | F) P_SPE (F) (14)其中

为置信水平α(0＜α＜1)，

为1-α；in

is the confidence level α (0<α<1),

is 1-α;④将贝叶斯统计量

和

分别与控制限1-α相比较，超出控制限的部分即表明第i个样本x_newi有故障发生。④The Bayesian statistic

and

Compared with the control limit 1-α, the part beyond the control limit indicates that the ith sample x_newi has a fault.

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