CN108897286B - Fault detection method based on distributed nonlinear dynamic relation model - Google Patents

Fault detection method based on distributed nonlinear dynamic relation model Download PDF

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CN108897286B
CN108897286B CN201810658917.9A CN201810658917A CN108897286B CN 108897286 B CN108897286 B CN 108897286B CN 201810658917 A CN201810658917 A CN 201810658917A CN 108897286 B CN108897286 B CN 108897286B
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CN108897286A (en
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宋励嘉
童楚东
俞海珍
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Hefei Jiuzhou Longteng Scientific And Technological Achievement Transformation Co ltd
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Ningbo University
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    • G05B19/41885—Total factory control, i.e. centrally controlling a plurality of machines, e.g. direct or distributed numerical control [DNC], flexible manufacturing systems [FMS], integrated manufacturing systems [IMS], computer integrated manufacturing [CIM] characterised by modeling, simulation of the manufacturing system
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    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
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Abstract

The invention discloses a fault detection method based on a distributed nonlinear dynamic relation model, and aims to establish a distributed nonlinear dynamic relation model for each measurement variable and implement fault detection based on the distributed model. The method mainly comprises the steps of establishing respective nonlinear dynamic relation models for various measured variables by using the RBF neural network, and considering the autocorrelation of the variable body at different sampling moments and the cross correlation of the variable body and other variables at different sampling moments. Compared with the traditional method, the method utilizes the RBF neural network algorithm to serve as the nonlinear dynamic relation model of each measured variable construction body at different sampling moments, and embodies the advantages and characteristics of distributed modeling. Secondly, the method takes the error as the monitored object, and is very beneficial to establishing a fault detection model by utilizing a principal component analysis algorithm subsequently. Therefore, the method of the invention is more suitable for fault detection of dynamic processes.

Description

Fault detection method based on distributed nonlinear dynamic relation model
Technical Field
The invention relates to a data-driven fault detection method, in particular to a fault detection method based on a distributed nonlinear dynamic relation model.
Background
Under the industrial big data stream, the utilization degree of the industrial big data represents a high level degree of industrial management. As an important component of the whole production automation, a fault detection system occupies a significant position, the fault detection system aims at timely alarming the fault state occurring in the production process, and the realized technical means is converted into a data-driven strategy from an implementation method based on a mechanism model. Due to the development of advanced instrument technology, sampling time intervals are greatly shortened, the time sequence autocorrelation among sampling data is a problem which must be considered in a data-driven process monitoring method, and the correlation among measurement variables is reflected not only among different measurement variables but also at different sampling moments. For such problems, a widely used fault detection method is similar to a Dynamic Principal Component Analysis (DPCA) method based on an amplification matrix, and the basic idea is to introduce a delay measurement value into each training sample data to form an amplification matrix, so that the amplification matrix can simultaneously consider the cross correlation between the sample data timing autocorrelation and the variables.
In addition, researchers have proposed using an autoregressive model to mine the sequence autocorrelation between sampled data, where the input of the autoregressive model is typically time-delayed measurement data and the output is new time measurement data, and the determination of the model parameters can be generally estimated by a partial least squares algorithm. However, these methods are all to build a linear autoregressive model, and there are few studies related to non-linear autoregressive models. In the field of nonlinear modeling methods, neural network technology has been widely studied and applied. The most common neural network models generally include a BP neural network and an RBF neural network, the BP neural network can fit any problem with any precision through error back propagation, but the BP neural network is easy to generate an over-fitting phenomenon. In contrast, the nonlinear fitting capability of the RBF neural network is not inferior to that of the BP neural network, and the RBF neural network generally does not generate an overfitting phenomenon.
It is worth mentioning that, for each measured variable, in addition to the autocorrelation, the measured variable is also cross-correlated with the sampled data of other variables at different time instants, and this complex relationship embodied at different sampling time instants may be referred to as a dynamic relationship. And a corresponding dynamic relation model is independently established for each measured variable, so that the complex dynamic relation can be better mined. The idea of multiple models can also be referred to as decentralized modeling, compared to a single model, which has the advantages that multiple models not only can reduce the complexity of problem analysis, but also the generalization capability is generally superior to that of a single model.
Disclosure of Invention
The invention aims to solve the main technical problems that: how to build a distributed nonlinear dynamic relation model for each measurement variable and implement fault detection based on the distributed model. Specifically, the method mainly comprises the step of establishing respective nonlinear dynamic relation models for each measured variable by using the RBF neural network, wherein the dynamic relation models not only consider the autocorrelation of the variable body at different sampling moments, but also reflect the cross correlation reflected at different sampling moments. Then, the error which is obtained by eliminating the influence of the nonlinear dynamic relation from each variable is used as a new monitored object to implement fault modeling and online fault detection.
The technical scheme adopted by the invention for solving the technical problems is as follows: a fault detection method based on a distributed nonlinear dynamic relation model comprises the following steps:
(1) collecting samples in normal operation state of production process to form training data set X belonging to Rn×mAnd constructing the augmented matrix X as followsa∈R(n-d)×m(d+1)：
Figure GSB0000185891310000021
Wherein n is the number of training samples, m is the number of process measurement variables, R is the set of real numbers, R is the number of training samplesn×mRepresenting a matrix of real numbers in dimensions n x m, xi∈R1×mFor the sample data at the ith sampling time, the subscript i is 1, 2, …, and n, d is the number of the introduced delay measurement values (generally, d is 1 or 2).
(2) For the augmented matrix X according to the formulaaVector x of each columnaCarrying out standardization to obtain a matrix Z epsilon R with a mean value of 0 and a standard deviation of 1(n-d)×m(d+1)And Z is ═ Z1，z2，…，zd(m+1)]。
z＝(xa-μ)/δ (2)
Wherein mu and delta are vectors x respectivelyaZ is the column vector xaNormalized result, Z corresponding to each column vector in the matrix Z, Zj∈RN×1In the j-th column of the matrix Z, N-d, j-1, 2, …, m (d + 1).
(3) And setting the number gamma of hidden nodes of the RBF neural network, and initializing k to be 1.
(4) The k column Z in the matrix ZkTaking out as output of RBF neural network, input Y of RBF neural networkkThen the following is shown:
Yk＝[z1，z2，…，zk-1，zk+1，…，zd(m+1)](3)
(5) using input YkAnd an output zkTraining the RBF neural network to obtain a non-linear motion corresponding to the kth measured variableThe state relation model is as follows:
Figure GSB0000185891310000022
in the above-mentioned formula (4),
Figure GSB0000185891310000023
utilizing input Y for RBF neural networkskThe resulting output zkThe function f () is a nonlinear functional relation obtained by RBF neural network fitting. The specific implementation process for training the RBF neural network is as follows:
① random slave input YkAnd randomly selecting gamma row vectors as initial central point vectors of each cluster.
② calculating input YkAnd dividing each row vector into corresponding cluster according to the minimum distance value.
③ calculating the mean vector of all the attribution row vectors in each cluster, which is the new central point vector of the cluster.
④ determining whether the central point vectors are converged, if not, returning to step ②, if yes, recording the converged central point vectors as the central point vectors
Figure GSB0000185891310000031
And step ⑤ is performed.
⑤ calculating RBF parameters according to the formula
Figure GSB0000185891310000032
Figure GSB0000185891310000033
In the above formula, p is 1, 2, …, γ, q is 1, 2, …, γ, and the symbol | | | | | represents the length of the calculation vector.
⑥ calculate the input Y according to the formula shown belowkRow vector of the middle τ th row
Figure GSB0000185891310000034
Output s converted by p-th neuron node of hidden layerτ，p：
Figure GSB0000185891310000035
In the above formula, τ is 1, 2, …, N, and the corresponding hidden layer output vector is
Figure GSB0000185891310000036
⑦ repeat step ⑥ until Y is obtainedkHidden layer output corresponding to all N line vectors
Figure GSB0000185891310000037
⑧ according to formula bk＝(Sk TSk)-1Sk TzkComputing hidden layer output SkTo the output layer output zkRegression coefficient vector b betweenk。
⑨ output estimation value calculated by RBF neural network obtained by training
Figure GSB0000185891310000038
(6) According to the formula
Figure GSB0000185891310000039
Calculating an error vector e after eliminating the influence of the nonlinear dynamic relationshipkAnd judging whether the condition k is less than m; if yes, returning to the step (4) after k is set to k + 1; if not, obtaining an error matrix E ═ E1，e2，…，em]。
(7) Standardizing each column in the error matrix E to obtain a new data matrix with a mean value of 0 and a standard deviation of 1
Figure GSB00001858913100000310
(8) Using a masterEstablishing a fault detection model by a component analysis algorithm, and reserving a model parameter set theta ═ P, Lambda and Dlim，QlimP is a projective transformation matrix, Λ is a covariance matrix of principal components, DlimAnd QlimThe specific implementation processes are as follows:
① calculation
Figure GSB00001858913100000311
Covariance matrix of
Figure GSB00001858913100000312
② solving all the eigenvalues λ of C1≥λ2≥…≥λmCorresponding feature vector α1，α2…，αm。
③, setting the reserved main component number η as the minimum value satisfying the following conditions, and combining the corresponding η eigenvectors into a load matrix P [ α ]1，α2…，αη]。
Figure GSB00001858913100000313
④ dividing the characteristic value lambda1，λ2，…，ληInto a diagonal matrix Λ ∈ Rη×ηAnd Λ is the covariance matrix of the principal component.
⑤ calculating the upper control limit D of the monitoring statistical indexes D and Q according to the formulalimAnd Qlim：
Figure GSB0000185891310000041
In the above formula, F (β, N- η) represents the value of F distribution with the degree of freedom of η and N- η under the confidence of β (generally 99 percent),
Figure GSB0000185891310000042
Represents a degree of freedom of h-2 a2Chi-square distribution of/v inThe value under the confidence β, the weighting coefficient g ═ v/(2a), a, and v represent the estimated mean and the estimated variance of the monitored statistical indicator Q, respectively.
The steps (1) to (8) are offline modeling stages of the method of the present invention, and the steps (9) to (14) shown below are online dynamic process monitoring implementation processes of the method of the present invention.
(9) Collecting data samples x at a new sampling instantt∈R1×mThe samples of the previous d sampling moments are introduced to obtain an augmented vector xa＝[xt，xt-1，…，xt-d]Where t represents the current sampling instant.
(10) For xaPerforming the same normalization process as the step (2)
Figure GSB0000185891310000043
Memo
Figure GSB0000185891310000044
(11) Will vector
Figure GSB0000185891310000045
The k element of (1)
Figure GSB0000185891310000046
Taking out, the rest elements constitute input vector ykAnd input vector ykInputting the k-th measured variable obtained in the step (5) into a nonlinear dynamic relation model, and calculating to obtain an output estimation value
Figure GSB0000185891310000047
(12) Repeating the step (11) until all output estimated values are obtained
Figure GSB0000185891310000048
And constructs an error vector epsilon according to the formula:
Figure GSB0000185891310000049
(13) the error vector epsilon is subjected to the same normalization processing as in the step (7), and a data vector is obtained
Figure GSB00001858913100000410
(14) Calling the model parameter set reserved in the step (8) to implement online fault detection, wherein the specific implementation process comprises the following steps:
① the specific values of the monitoring statistics D and Q are calculated according to the following formula:
Figure GSB00001858913100000411
② according to the specific values of D and Q and the corresponding control upper limit DlimAnd QlimAnd (3) deciding whether the fault occurs or not, namely judging whether the condition is met: d is less than or equal to DlimAnd Q is less than or equal to Qlim(ii) a If yes, the current sample is sampled under normal working conditions, and the step (9) is returned to continue to monitor the next new sample data; if not, the current sampling data comes from the fault working condition.
Compared with the traditional method, the method has the advantages that:
firstly, the method utilizes the RBF neural network algorithm to represent the nonlinear dynamic relationship model of each measured variable construction body at different sampling moments, and embodies the advantages and characteristics of distributed modeling. Secondly, the method takes the error as the monitored object, and because the error not only can reflect the change condition of the nonlinear dynamic relation of each variable, but also the nonlinear dynamic relation characteristic of the original measured variable does not appear in the error data any more, the method is greatly beneficial to establishing a fault detection model by utilizing a principal component analysis algorithm subsequently. Therefore, the method is more suitable for dynamic process modeling and fault detection.
Drawings
FIG. 1 is a flow chart of an embodiment of the method of the present invention.
FIG. 2 is a comparison graph of the monitoring details of the inlet temperature fault of the cooling water of the condenser of the TE process.
Detailed Description
The method of the present invention is described in detail below with reference to the accompanying drawings and specific embodiments.
As shown in fig. 1, the present invention discloses a fault detection method based on a distributed nonlinear dynamical relationship model. The following description is given with reference to a specific industrial process example to illustrate the practice of the method of the present invention and its advantages over the prior art methods.
The application object is from the U.S. Tennessee-Ismann (TE) chemical process experiment, and the prototype is a practical process flow of an Ismann chemical production workshop. At present, the TE process has been widely used as a standard experimental platform for fault detection research due to the complexity of the process. The entire TE process includes 22 measured variables, 12 manipulated variables, and 19 constituent measured variables. The TE process object may simulate a variety of different fault types, such as material inlet temperature step changes, cooling water fault changes, and so forth. To monitor the process, 33 process variables were selected as shown in table 1. Due to the short sampling interval time, the TE process sampling data inevitably has sequence autocorrelation. Moreover, due to the complex characteristics of the TE process, the non-linear characteristics between the sampled data are significant, and therefore non-linear modeling should be implemented. The following describes the detailed implementation steps of the present invention in conjunction with the TE process.
Table 1: the TE process monitors variables.
Serial number Description of variables Serial number Description of variables Serial number Description of variables
1 Flow rate of material A 12 Liquid level of separator 23 D feed valve position
2 Flow rate of material D 13 Pressure of separator 24 E feed valve position
3 Flow rate of material E 14 Bottom flow of separator 25 A feed valve position
4 Total feed flow 15 Stripper grade 26 A and C feed valve position
5 Flow rate of circulation 16 Stripping column pressureForce of 27 Compressor cycling valve position
6 Reactor feed 17 Bottom flow of stripping tower 28 Evacuation valve position
7 Reactor pressure 18 Stripper temperature 29 Separator liquid phase valve position
8 Reactor grade 19 Stripping tower overhead steam 30 Stripper liquid phase valve position
9 Reactor temperature 20 Compressor power 31 Stripper steam valve position
10 Rate of emptying 21 Reactor cooling water outlet temperature 32 Reactor condensate flow
11 Separator temperature 22 Separator cooling water outlet temperature 33 Flow rate of cooling water of condenser
Firstly, establishing a dynamic process monitoring model by using 960 sampling data under the normal working condition of the TE process, and comprising the following steps of:
step (1): collecting samples in normal operation state in production process, and forming training data set X e R according to sampling time960×33And introducing 2 delay measurement values d to construct an amplification matrix Xa∈R958×99：
Figure GSB0000185891310000061
Step (2): for the augmented matrix XaIn the formula (I), each column is subjected to normalization treatment, and is recorded as Z ═ Z1，z2，…，zd(m+1)]。
And (3): and setting the number gamma of hidden nodes of the RBF neural network, and initializing k to be 1.
And (4): the k column Z in the matrix ZkTaking out the output as the output of the RBF neural network, and taking the rest columns in the matrix Z as the input Y of the RBF neural networkk。
And (5): using input YkAnd an output zkAnd training the RBF neural network so as to obtain a nonlinear dynamic relation model corresponding to the kth measured variable.
And (6): according to the formula
Figure GSB0000185891310000062
Calculating an error vector e after eliminating the influence of the nonlinear dynamic relationshipkAnd judges whether or not the condition k < 33? If yes, returning to the step (4) after k is set to k + 1; if not, obtaining an error matrix E ═ E1，e2，…，e33]。
And (7): a normalization process is performed for each column in the error matrix E.
And (8): establishing a fault detection model by using a principal component analysis algorithm, and reserving model parameters theta ═ P, Lambda and Dlim，Qlim}。
Secondly, a test data set under the condition of temperature fault of a cooling water inlet of the condenser in the TE process is collected, and online process monitoring is implemented. It is worth noting that the first 160 sample data of the test data set were collected from normal conditions, and fault conditions were introduced from 161 moments.
And (9): collecting data samples x at the latest sampling instantt∈R1×33And finding out the delay measurement data x thereoft-1，xt-2Thereby obtaining an augmented vector xa＝[xt，xt-1，xt-2]。
Step (10): for xaPerforming the same normalization process as the step (2)
Figure GSB0000185891310000063
Memo
Figure GSB0000185891310000064
Step (11): will vector
Figure GSB0000185891310000065
The k element of (1)
Figure GSB0000185891310000066
Taking out, the rest elements constitute input vector ykAnd will vector ykInputting the k-th measured variable obtained in step (5)In a linear dynamic relation model, thereby obtaining an output estimation value by calculation
Figure GSB0000185891310000067
Step (12): repeating the step (11) until all output estimated values are obtained
Figure GSB0000185891310000068
And constructs an error vector according to the formula shown below
Figure GSB0000185891310000069
Step (13): the error ε is normalized in the same manner as in step (8), and a data vector is obtained
Figure GSB00001858913100000610
Step (14): and (5) calling the parameter set reserved in the step (8) to carry out online fault detection.
Finally, the process monitoring details of the inventive method and the conventional DPCA method are compared in fig. 2. As can be seen from fig. 2, the monitoring effect of the method of the present invention on the fault is superior to that of the conventional DPCA method, and the fault failure rate after the fault occurs is significantly lower than that of the conventional DPCA method.
The above embodiments are merely illustrative of specific implementations of the present invention and are not intended to limit the present invention. Any modification of the present invention within the spirit of the present invention and the scope of the claims will fall within the scope of the present invention.

Claims (3)

1. A fault detection method based on a distributed nonlinear dynamic relation model is characterized by comprising the following steps:
the implementation of the offline modeling phase is as follows:
step (1): collecting samples in normal operation state of production process to form training data set X belonging to Rn×mAnd constructing the augmented matrix X as followsa∈R(n-d)×m(d+1)：
Figure FSB0000185891300000011
Wherein n is the number of training samples, m is the number of process measurement variables, R is the set of real numbers, R is the number of training samplesn×mRepresenting a matrix of real numbers in dimensions n x m, xi∈R1×mFor sample data at the ith sampling moment, the subscript number i is 1, 2, …, n, d is the number of introduced delay measurement values;
step (2): for the augmented matrix XaIn which each column is subjected to a normalization process, i.e. an augmented matrix XaSubtracting the mean value of each column vector and dividing the obtained value by the standard deviation of each column vector to obtain a normalized matrix Z epsilon R(n-d)×m(d+1)And Z is ═ Z1，z2，…，zd(m+1)]Wherein z isj∈RN×1Is the j-th column in the matrix Z, N-d, j-1, 2, …, m (d + 1);
and (3): setting the number gamma of hidden nodes of the RBF neural network, and initializing k to be 1;
and (4): the k column Z in the matrix ZkTaking out as output of RBF neural network, input Y of RBF neural networkkThen the following is shown:
Yk＝[z1，z2，…，zk-1，zk+1，…，zd(m+1)](2)
and (5): using input YkAnd an output zkTraining the RBF neural network to obtain a nonlinear dynamic relation model corresponding to the kth measured variable:
Figure FSB0000185891300000012
in the above formula, the first and second carbon atoms are,
Figure FSB0000185891300000013
utilizing input Y for RBF neural networkskThe resulting output zkIs obtained by fitting the function f () to the RBF neural networkThe non-linear functional relationship of (a);
and (6): according to the formula
Figure FSB0000185891300000014
Calculating an error vector e after eliminating the influence of the nonlinear dynamic relationshipkAnd judging whether the condition k is less than m; if yes, returning to the step (4) after k is set to k + 1; if not, obtaining an error matrix E ═ E1，e2，…，em]；
And (7): standardizing each column in the error matrix E to obtain a new data matrix with a mean value of 0 and a standard deviation of 1
Figure FSB0000185891300000015
And (8): establishing a fault detection model by using a principal component analysis algorithm, and reserving a model parameter set theta ═ P, Lambda, Dlim，QlimP is a projective transformation matrix, Λ is a covariance matrix of principal components, DlimAnd QlimRespectively monitoring the upper control limits of the statistical indexes D and Q;
the implementation of the on-line process monitoring phase is as follows:
and (9): collecting data samples x at a new sampling instantt∈R1×mThe samples of the previous d sampling moments are introduced to obtain an augmented vector xa＝[xt，xt-1，…，xt-d]Wherein t represents the current sampling instant;
step (10): for the vector x of augmentationaPerforming the same normalization process as the step (2)
Figure FSB0000185891300000021
Memo
Figure FSB0000185891300000022
Step (11): will vector
Figure FSB0000185891300000023
The k element of (1)
Figure FSB0000185891300000024
Taking out, the rest elements constitute input vector ykAnd input vector ykInputting the k-th measured variable obtained in the step (5) into a nonlinear dynamic relation model, and calculating to obtain an output estimation value
Figure FSB0000185891300000025
Step (12): repeating the step (11) until all output estimated values are obtained
Figure FSB0000185891300000026
And constructs an error vector epsilon according to the formula:
Figure FSB0000185891300000027
step (13): the error vector epsilon is subjected to the same normalization processing as in the step (7), and a data vector is obtained
Figure FSB0000185891300000028
Step (14): calling the model parameter set reserved in the step (8) to implement online fault detection, wherein the specific implementation process comprises the following steps:
① the specific values of the monitoring statistics D and Q are calculated according to the following formula:
Figure FSB0000185891300000029
② according to the specific values of D and Q and the corresponding control upper limit DlimAnd QlimAnd (3) deciding whether the fault occurs or not, namely judging whether the condition is met: d is less than or equal to DlimAnd Q is less than or equal to Qlim(ii) a If yes, the current sample is sampled under normal working conditions, and the step (9) is returned to continue to monitor the next new sample data;if not, the current sampling data comes from the fault working condition.
2. The distributed nonlinear dynamical relationship model-based fault detection method as claimed in claim 1, wherein the input Y is utilized in the step (5)kAnd an output zkThe specific implementation process for training the RBF neural network is as follows:
① random slave input YkRandomly selecting gamma row vectors as initial central point vectors of each cluster;
② calculating input YkThe distance between each row vector and the gamma central point vectors is divided into corresponding cluster clusters according to the minimum distance value;
③ calculating the mean vector of all the attribution row vectors in each cluster, wherein the vector is the new central point vector of the cluster;
④ determining whether the central point vectors are converged, if not, returning to step ②, if yes, recording the converged central point vectors as the central point vectors
Figure FSB00001858913000000210
And proceeds to step ⑤;
⑤ calculating RBF parameters according to the formula
Figure FSB00001858913000000211
Figure FSB00001858913000000212
In the above formula, p ═ 1, 2, …, γ, q ═ 1, 2, …, γ, and the symbol | | | | | | represents the length of the calculation vector;
⑥ calculate the input Y according to the formula shown belowkRow vector of the middle τ th row
Figure FSB00001858913000000213
Output s converted by p-th neuron node of hidden layerτ，p：
Figure FSB0000185891300000031
In the above formula, τ is 1, 2, …, N, and the corresponding hidden layer output vector is
Figure FSB0000185891300000032
⑦ repeat step ⑥ until input Y is obtainedkHidden layer output corresponding to all N line vectors
Figure FSB0000185891300000033
⑧ according to formula bk＝(Sk TSk)-1Sk TzkComputing hidden layer output SkTo the output layer output zkRegression coefficient vector b betweenk；
⑨ calculating an estimate of the output using the trained RBF neural network
Figure FSB0000185891300000034
3. The fault detection method based on the distributed nonlinear dynamical relation model according to claim 1, wherein the specific implementation process of establishing the fault detection model by using the principal component analysis algorithm in the step (8) is as follows:
① calculation
Figure FSB0000185891300000035
Covariance matrix of
Figure FSB0000185891300000036
② solving all the eigenvalues λ of C1≥λ2≥…≥λmCorresponding feature vector α1，α2…，αm；
③ setting the reserved main component number η as the minimum value satisfying the following formula conditions, and combining the corresponding η eigenvectors into a load matrix P [ α ]1，α2…，αη]；
Figure FSB0000185891300000037
④ dividing the characteristic value lambda1，λ2，…，ληInto a diagonal matrix Λ ∈ Rη×ηThe Λ is a covariance matrix of the principal component;
⑤ calculating the upper control limit D of the monitoring statistical indexes D and Q according to the formulalimAnd Qlim：
Figure FSB0000185891300000038
In the above formula, F (β, N- η) represents a value of F distribution with a degree of freedom of η and N- η with a confidence of β -99%,
Figure FSB0000185891300000039
Represents a degree of freedom of h-2 a2The value of the chi-square distribution of/v under the confidence β, the weighting coefficient g ═ v/(2a), a, and v respectively represent the estimated mean and the estimated variance of the monitoring statistic indicator Q.
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