CN113253682A - Nonlinear chemical process fault detection method - Google Patents

Abstract

The invention relates to a nonlinear chemical process fault detection method, which comprises the following specific steps: in the off-line modeling stage, firstly, the training data is normalized, then M random slow feature analysis models are constructed, and corresponding dominant subspace statistic and residual space statistic control limit are solved; in the on-line detection stage, test data are collected and normalized, then the test data are mapped to M random slow feature analysis models to obtain M groups of leading subspace statistics and residual error space statistics, and integrated monitoring statistics are obtained through a weighted probability index fusion mechanism

Sum statistic BIC_QAnd respectively compared with 1-alpha for judging whether a fault occurs, wherein alpha is a confidence level. According to the invention, by utilizing the data characteristics of the random Fourier mapping deep excavation nonlinear process, a nonlinear slow characteristic analysis model can be established more efficiently, and the fault detection effect is improved.

Description

Nonlinear chemical process fault detection method

Technical Field

The invention belongs to the technical field of industrial process detection, relates to a nonlinear chemical process fault detection technology, and particularly relates to a nonlinear chemical process fault detection method based on random slow characteristic analysis.

Background

In the modern industrial production process, the real-time fault detection technology becomes an important support for ensuring safe production and improving product quality. Various faults such as instrument failure, valve sticking, material leakage and the like can occur in the production process, so that the faults can cause measurement deviation and product quality reduction, and dangerous safety accidents can be caused, so that equipment damage and casualties are caused, and the normal operation of enterprises is directly influenced. Accordingly, researchers and engineers have been working on developing advanced process monitoring and fault detection techniques. The data driving method is a research hotspot in recent 20 years, does not need to establish an accurate mathematical model, has low requirement on prior knowledge, and is particularly suitable for safety monitoring and fault detection of complex industrial processes.

As an emerging data-driven fault detection method, a random Slow Feature Analysis (SFA) method can extract unchanged or slowly-changing information from an input signal as a monitoring feature, and has been widely applied to the field of industrial process fault detection in recent years. The SFA method mainly aims at fault detection of a linear industrial process, and aims at a nonlinear problem, a nonlinear SFA method based on a kernel function is proposed, which is abbreviated as: nuclear SFA or KSFA. However, although the KSFA method can effectively process nonlinear data, in the calculation process, since an n × n-dimensional kernel matrix related to the training sample dimension n needs to be constructed and subjected to eigenvalue decomposition, the calculation complexity related to the kernel matrix and the kernel vector also increases sharply with the increase of the number of training samples, which not only requires a huge storage space for data storage, but also further increases the calculation time required for modeling. Under the background of industrial big data, how to improve the fault detection sensitivity and reduce the modeling complexity is an urgent problem to be solved in a nonlinear processing method.

Disclosure of Invention

Aiming at the problems of high computational complexity, low fault detection sensitivity and the like in the prior art, the invention provides a nonlinear chemical process fault detection method based on random slow feature analysis (SFA for short), which can solve the problem of time consumption of traditional nuclear matrix computation and improve the fault detection sensitivity.

In order to achieve the aim, the invention provides a nonlinear chemical process fault detection method, which comprises the following specific steps:

s1, collecting normal operation condition data of the non-linear chemical process historical database as training data X₀Carrying out normalization processing to obtain training data X;

s2, applying random Fourier mapping to the training data X to solve random Fourier mapping variables and construct a random Fourier mapping matrix phi (X);

s3, carrying out generalized eigenvalue decomposition on the covariance matrix of the random Fourier mapping matrix phi (X) to establish a random slow characteristic analysis model;

s4, repeating the steps S2 and S3, establishing M off-line models, and respectively calculating the dominant subspace statistic T of the random Fourier mapping variables_0,i ²Sum residual spatial statistic Q_0,iI is 1, …, M; further computing dominant subspace statistic T of random Fourier mapping variables_0,i ²Corresponding control limit

Sum residual spatial statistic Q_0,iCorresponding control limit Q_lim,i；

S5, collecting real-time data under nonlinear chemical process fault working conditions as test data x_newAnd obtaining test data x after normalization processing_t；

S6, test data x_tSolving a random Fourier mapping variable by applying random Fourier mapping;

s7, calculating dominant subspace statistic T corresponding to M groups of random Fourier mapping variables_t,i ²Sum residual spatial statistic Q_t,i；

S8, performing M groups of dominant subspace statistics T by using weighted probability index fusion mechanism_t,i ²Sum residual spatial statistic Q_t,iComputing integrated monitoring statistics

Sum statistic BIC_QAnd respectively comparing the statistical values with 1-alpha, wherein alpha is a confidence level, and if any statistical value is larger than 1-alpha, the occurrence of a fault is indicated.

Preferably, in step S1, training data X is used₀Mean value of

And standard deviation of

Training data X by equation (1)_oNormalization processing is carried out, and the expression of formula (1) is as follows:

training data X₀The normalized training data X can be obtained after normalization processing by the formula (1).

Preferably, in step S2, the specific step of constructing the random fourier mapping matrix Φ (X) is: for training data X ═ X₁,x₂,...,x_n]^T∈R^n×mWherein n represents the number of samples, m represents the number of variables, and the gaussian kernel function is approximated by a standard monte carlo approximation integration method through a formula (2), so as to construct a random fourier mapping variable as follows:

in the formula, x_jJ is 1,2.. and n is a vector of the training data X; omega_kK 1,2, L is a gaussian random vector, obeys a mean of 0 and a variance of 0

C is a parameter of a Gaussian kernel function; b_k1,2, L is a random variable, subject to [ -pi, pi [ -n]The intervals are uniformly distributed; l is the number of random variables; t represents matrix transposition;

for all training data X ═ X₁,x₂,...,x_n]^T∈R^n×mConstructing a random Fourier mapping matrix phi (X) < phi (X)₁),φ(x₂),…,φ(x_n)]^T。

Preferably, in step S3, the specific steps of establishing the random slow feature analysis model are as follows: in that

Under the condition (1), the random slow feature analysis SFA transform is converted into a generalized eigenvalue decomposition problem shown in formula (3), and the expression of formula (3) is:

Av_k＝λ_kSv_k (3)

wherein A represents the first derivative of the random Fourier mapping matrix phi (X)

The covariance matrix of (a); s represents the covariance matrix of the random Fourier mapping matrix phi (X), lambda_kIs a generalized eigenvalue, v_kIs the corresponding generalized eigenvector;

for arbitrary training vectors x_j∈R^mAnd the corresponding random slow characteristic component model is expressed as follows:

t_k＝φ(x_j)^Tv_k (4)

in the formula, t_kAs a training vector x_jCorresponding random slow feature components.

Preferably, in step S4, a dominant subspace statistic T of the random Fourier mapping variables is calculated_0,i ²Sum residual spatial statistic Q_0,iAnd further statistic T_0,i ²To what is providedShould control the limit

And the corresponding statistic Q_0,iControl limit Q_lim,iThe specific method comprises the following steps:

obtaining p dominant subspace variables according to the accumulated contribution rate, dividing the sample space of the random Fourier mapping variable into a dominant subspace and a residual space, and calculating the dominant subspace statistic T of the random Fourier mapping variable by formula (5) for M groups of off-line model data_0,i ²The residual spatial statistic of the random fourier mapping variable is calculated by (6), and formula (5) and formula (6) are expressed as:

T_0,i ²＝[t₁,…,t_p][t₁,…,t_p]^T (5)

Q_0,i＝[t_p+1,…,t_L][t_p+1,…,t_L]^T (6)

for the confidence level alpha, computing dominant subspace statistic T of random Fourier mapping variables for M groups of off-line model data through a nuclear density estimation method_0,i ²Corresponding control limit

Sum residual spatial statistic Q_0,iCorresponding control limit Q_lim,i。

Preferably, in step S5, training data X is used₀Mean value of

And standard deviation of

Test data x by equation (7)_newNormalization processing is performed, and the expression of formula (7) is:

test data x_newThe normalized test data x can be obtained after normalization processing by the formula (7)_t。

Preferably, in step S6, the gaussian random vector ω in step S2 is used_kAnd a random variable b_kConstructing test data x_tj∈R^mThe random fourier mapping variables are:

in the formula, phi (x)_t) For test data x_tThe random fourier mapping variable of (1).

Preferably, in step S7, dominant subspace statistics T corresponding to M sets of random fourier mapping variables are calculated_t,i ²Sum residual spatial statistic Q_t,iThe specific method comprises the following steps: using the generalized eigenvector v obtained in step S3_kWill phi (x)_t) Projecting to a low dimensional space to obtain phi (x)_t) The corresponding random slow feature components are expressed as:

t_t,k＝φ(x_t)^Tv_k (9)

in the formula, t_t,kFor test data x_tCorresponding random slow feature components;

constructing a monitoring statistic T for a dominant subspace of M sets of random Fourier mapping variables for process monitoring from equation (10)_t,i ²Constructing residual spatial statistics Q of M sets of random Fourier mapping variables for process monitoring from (11)_t,iThe formula (10) and the formula (11) are expressed as follows:

T_t,i ²＝[t_t,1,…,t_t,p][t_t,1,…,t_t,p]^T (10)

Q_t,i＝[t_t,p+1,…,t_t,L][t_t,p+1,…,t_t,L]^T (11)

。

preferably, in step S8, an integrated monitoring statistic is calculated

Sum statistic BIC_QThe specific method comprises the following steps:

performing data integration on the M groups of statistics by using a weighted probability index fusion mechanism to serve as monitoring statistics, and calculating the occurrence probability of the samples under normal and fault conditions by using probability formulas (12) to (14), wherein the formulas (12) to (14) are expressed as follows:

P_T,i(x_t|N)＝exp(-T_t,i ²/T_lim,i) (12)

P_Q,i(x_t|N)＝exp(-Q_t,i/Q_lim,i) (13)

P_T,i(x_t|F)＝exp(-T_lim,i/T_t,i ²) (14)

P_Q,i(x_t|F)＝exp(-Q_lim,i/Q_t,i) (15)

in the formula, P_T,i(x_tN) is test data x under normal conditions_tSample occurrence probabilities of the dominant subspace statistics; p_Q,i(x_tN) is test data x under normal conditions_tSample occurrence probability of residual spatial statistics; p_T,i(x_tI F) is test data x under fault condition_tSample occurrence probabilities of the dominant subspace statistics; p_Q,i(x_tI F) is test data x under fault condition_tSample occurrence probability of residual spatial statistics;

after all the M group statistics are converted into posterior probabilities, the integrated monitoring statistics are calculated through formula (16) and formula (17)

Sum statistic BIC_QThe equations (16), (17) are expressed as:

compared with the prior art, the invention has the advantages and positive effects that:

according to the nonlinear chemical process fault detection method provided by the invention, on one hand, random Fourier mapping is introduced to approximate kernel function transformation, so that the computational complexity of a monitoring model is effectively reduced, and the problem of time consumption of traditional kernel matrix computation is solved; on the other hand, by utilizing an integrated learning theory of the weighted probability index, the integrated monitoring statistic based on the multiple statistic models is constructed, the statistic of the multiple statistic models is converted into the fault probability, and then an integral monitoring index is formed by fusion, so that the problem of poor performance of a single monitoring model is solved, and the detection performance of the fault is effectively improved. The nonlinear chemical process fault detection method provided by the invention overcomes the defects that the traditional KSFA method has complex calculated amount due to complex eigenvalue decomposition of a kernel matrix, solves the problem of single modeling and effectively improves the fault detection performance.

Drawings

FIG. 1 is a flow chart of a method for fault detection in a nonlinear chemical process according to an embodiment of the present invention;

FIG. 2 is a schematic diagram of a Continuous Stirred Tank Reactor (CSTR) system according to an embodiment of the present invention;

FIG. 3a is a schematic diagram of the monitoring results of CSTR system failure 1 using the conventional SFA method;

FIG. 3b is a schematic diagram showing the monitoring results of CSTR system failure 1 using the conventional KSFA method;

FIG. 3c is a schematic diagram showing the monitoring result of the CSTR system fault 1 by using the nonlinear chemical process fault detection method of the present invention.

Detailed Description

The invention is described in detail below by way of exemplary embodiments. It should be understood, however, that elements, structures and features of one embodiment may be beneficially incorporated in other embodiments without further recitation.

Referring to fig. 1, the invention provides a nonlinear chemical process fault detection method, which comprises the following specific steps:

s1, collecting normal operation condition data of the non-linear chemical process historical database as training data X₀Using training data X₀Mean value of

And standard deviation of

Training data X by equation (1)_oNormalization processing is carried out, and the expression of formula (1) is as follows:

training data X₀The normalized training data X can be obtained after normalization processing by the formula (1).

S2, random Fourier mapping variables are solved by applying random Fourier mapping to the training data X, and a random Fourier mapping matrix phi (X) is constructed.

Specifically, the specific steps of constructing the random fourier mapping matrix phi (X) are as follows: for training data X ═ X₁,x₂,...,x_n]^T∈R^n×mWherein n represents the number of samples, m represents the number of variables, and the gaussian kernel function is approximated by a standard monte carlo approximation integration method through a formula (2), so as to construct a random fourier mapping variable as follows:

in the formula, x_jJ is 1,2.. and n is a vector of the training data X; omega_kK 1,2, L is a gaussian random vector, obeys a mean of 0 and a variance of 0

C is a parameter of a Gaussian kernel function; b_k1,2, L is a random variable, subject to [ -pi, pi [ -n]The intervals are uniformly distributed; l is the number of random variables; t represents matrix transposition;

for all training data X ═ X₁,x₂,...,x_n]^T∈R^n×mConstructing a random Fourier mapping matrix phi (X) < phi (X)₁),φ(x₂),…,φ(x_n)]^T。

S3, utilizing the random Fourier mapping matrix phi (X) to carry out generalized eigenvalue decomposition on the covariance matrix, and establishing a random slow characteristic analysis model.

Specifically, the specific steps of establishing the random slow characteristic analysis model are as follows: in that

Under the condition (1), the random slow feature analysis SFA transform is converted into a generalized eigenvalue decomposition problem shown in formula (3), and the expression of formula (3) is:

Av_k＝λ_kSv_k (3)

wherein A represents the first derivative of the random Fourier mapping matrix phi (X)

The covariance matrix of (a); s represents the covariance matrix of the random Fourier mapping matrix phi (X), lambda_kIs a generalized eigenvalue, v_kIs the corresponding generalized eigenvector;

for arbitrary training vectors x_j∈R^mAnd the corresponding random slow characteristic component model is expressed as follows:

t_k＝φ(x_j)^Tv_k (4)

in the formula, t_kAs a training vector x_jCorresponding random slow feature components.

S4, repeating the steps S2 and S3, establishing M off-line models, and respectively calculating a dominant subspace system of the random Fourier mapping variablesMeasurement T_0,i ²Sum residual spatial statistic Q_0,iI is 1, …, M; further computing dominant subspace statistic T of random Fourier mapping variables_0,i ²Corresponding control limit

Sum residual spatial statistic Q_0,iCorresponding control limit Q_lim,i(ii) a The method comprises the following specific steps:

obtaining p dominant subspace variables according to the accumulated contribution rate, dividing the sample space of the random Fourier mapping variable into a dominant subspace and a residual space, and calculating the dominant subspace statistic T of the random Fourier mapping variable by formula (5) for M groups of off-line model data_0,i ²The residual spatial statistic of the random fourier mapping variable is calculated by (6), and formula (5) and formula (6) are expressed as:

T_0,i ²＝[t₁,…,t_p][t₁,…,t_p]^T (5)

Q_0,i＝[t_p+1,…,t_L][t_p+1,…,t_L]^T (6)

for the confidence level alpha, computing dominant subspace statistic T of random Fourier mapping variables for M groups of off-line model data through a nuclear density estimation method_0,i ²Corresponding control limit

Sum residual spatial statistic Q_0,iCorresponding control limit Q_lim,i。

S5, collecting real-time data under nonlinear chemical process fault working conditions as test data x_newUsing training data X₀Mean value of

And standard deviation of

Test data x by equation (7)_newNormalization processing is performed, and the expression of formula (7) is:

test data x_newThe normalized test data x can be obtained after normalization processing by the formula (7)_t。

S6, test data x_tSolving a random Fourier mapping variable by applying random Fourier mapping; the specific method comprises the following steps:

using the Gaussian random vector ω in step S2_kAnd a random variable b_kConstructing test data x_t∈R^mThe random fourier mapping variables are:

in the formula, phi (x)_t) For test data x_tRandom fourier mapping variables of

S7, calculating dominant subspace statistic T corresponding to M groups of random Fourier mapping variables_t,i ²Sum residual spatial statistic Q_t,i(ii) a The specific method comprises the following steps:

using the generalized eigenvector v obtained in step S3_kWill phi (x)_t) Projecting to a low dimensional space to obtain phi (x)_t) The corresponding random slow feature components are expressed as:

t_t,k＝φ(x_t)^Tv_k (9)

in the formula, t_t,kFor test data x_tCorresponding random slow feature components;

constructing a monitoring statistic T for a dominant subspace of M sets of random Fourier mapping variables for process monitoring from equation (10)_t,i ²Constructing residual spatial statistics Q of M sets of random Fourier mapping variables for process monitoring from (11)_t,iEquation (10)) Formula (11) is expressed as:

T_t,i ²＝[t_t,1,…,t_t,p][t_t,1,…,t_t,p]^T (10)

Q_t,i＝[t_t,p+1,…,t_t,L][t_t,p+1,…,t_t,L]^T (11)

。

s8, performing M groups of dominant subspace statistics T by using weighted probability index fusion mechanism_t,i ²Sum residual spatial statistic Q_t,iComputing integrated monitoring statistics

Sum statistic BIC_QAnd respectively comparing the statistical values with 1-alpha, wherein alpha is a confidence level, and if any statistical value is larger than 1-alpha, the occurrence of a fault is indicated.

In particular, integrated monitoring statistics are computed

Sum statistic BIC_QThe specific method comprises the following steps:

performing data integration on the M groups of statistics by using a weighted probability index fusion mechanism to serve as monitoring statistics, and calculating the occurrence probability of the samples under normal and fault conditions by using probability formulas (12) to (14), wherein the formulas (12) to (14) are expressed as follows:

P_T,i(x_t|N)＝exp(-T_t,i ²/T_lim,i) (12)

P_Q,i(x_t|N)＝exp(-Q_t,i/Q_lim,i) (13)

P_T,i(x_t|F)＝exp(-T_lim,i/T_t,i ²) (14)

P_Q,i(x_t|F)＝exp(-Q_lim,i/Q_t,i) (15)

in the formula, P_T,i(x_tN) is test data x under normal conditions_tSample occurrence probabilities of the dominant subspace statistics; p_Q,i(x_tN) is test data x under normal conditions_tSample occurrence probability of residual spatial statistics; p_T,i(x_tI F) is test data x under fault condition_tSample occurrence probabilities of the dominant subspace statistics; p_Q,i(x_tI F) is test data x under fault condition_tSample occurrence probability of residual spatial statistics;

after all the M group statistics are converted into posterior probabilities, the integrated monitoring statistics are calculated through formula (16) and formula (17)

Sum statistic BIC_QThe equations (16), (17) are expressed as:

in the above method, steps S1 to S4 are off-line modeling stages, and steps S5 to S8 are on-line testing stages.

After the training data are normalized, mapping the data to a nonlinear space through random Fourier mapping and expanding a user-defined dimension, and performing calculation analysis on the mapped data by using a random slow characteristic analysis method to obtain dominant subspace statistics and residual space statistics of M groups of random Fourier mapping variables and determine corresponding control limits; collecting test data, carrying out normalization processing on the test data by using the variance and the mean value of the training data, carrying out nonlinear mapping on the test data through random Fourier mapping, further carrying out calculation analysis on the mapped data by using a slow feature analysis method to obtain a leading subspace statistic and a residual space statistic, repeatedly carrying out M times of random slow feature analysis modeling and analysis, and respectively processing the leading subspace statistic and the residual space statistic for many times through a weighted probability index fusion mechanism to obtain an integrated monitoring statistic which can integrate the multi-party modeling characteristics.

The fault detection method of the invention introduces random Fourier mapping, approximates kernel function transformation, effectively reduces the computational complexity of the monitoring model, and improves the problem of time consumption of traditional kernel matrix computation; on the other hand, by utilizing an integrated learning theory of the weighted probability index, the integrated monitoring statistic based on the multiple statistic models is constructed, the statistic of the multiple statistic models is converted into the fault probability, and then an integral monitoring index is formed by fusion, so that the problem of poor performance of a single monitoring model is solved, and the detection performance of the fault is effectively improved. The fault detection method provided by the invention can be used for more accurately detecting the fault information in the nonlinear chemical process by utilizing the data characteristic of the random Fourier mapping deep excavation nonlinear process and omnibearing modeling, so that the fault detection capability is improved, and the fault detection effect is improved.

In order to illustrate the effect of the method for detecting the fault in the nonlinear chemical process, the invention is further described with reference to specific embodiments.

Example (b): referring to FIG. 2, a continuous stirred tank reactor (hereinafter referred to as CSTR) will be described as an example.

CSTR is a widely used equipment in the chemical industry where irreversible exothermic reactions take place in the reactor and new substances are formed. The reaction process involves 4 state variables [ C_a,T,T_c,h]And 6 input variables [ Q, Q_f,C_af,T_f,Q_c,T_cf]See table 1 for details. The simulation totally collects 1000 fault-free data as training data, and additionally generates 6 faults, specifically as shown in table 1, each fault comprises 1000 samples, and the fault is introduced into the system at 161 th sample.

TABLE 1

Fault of	Description of the invention	Amplitude value
			F1	The flow rate of the feed A is changed in steps	+3L/min
F2	The concentration of the feed A of the reaction kettle is changed in a slope way	+3×0(-4)(mol/L)/min
			F3	Catalyst activity deactivation with ramping	+3K/min
F4	The heat transfer quantity is changed in a slope manner	-100(J/min(K))/min
			F5	Temperature sensor in the reactor is deviated	+2K
F6	Deviation of jacket temperature sensor	+3K

The CSTR system of the embodiment is subjected to fault detection by adopting the fault detection method (hereinafter referred to as BRSFA method). And after the fault is detected, comparing fault detection results of different methods through a fault detection rate FDR index in order to evaluate the fault detection performance of different fault detection methods. The fault detection rate FDR is defined as the ratio of the detected fault data to the actual total fault data. Obviously, the larger the value of the FDR is, the better the fault detection effect of the fault detection method of the industrial process is; on the contrary, the worse the fault detection effect of the industrial process fault detection method.

In the CSTR system simulation of this embodiment, three methods, i.e., the conventional SFA method, the conventional KSFA method, and the BRSFA method of the present invention, are used as simulation comparisons. In this embodiment, the three methods each determine the number of main guide subspace components according to a cumulative contribution rate of 70%. In the conventional KSFA method and the BRSFA method, the value of a Gaussian kernel parameter c is 35000, in the BRSFA simulation process, the number of random Fourier mapping characteristics is 60, and the number of models participating in Bayesian fusion is 20. The 99% confidence limits are used to calculate the control limits for each method.

The three algorithms are all operated on a computer with a CPU of i54200U and a memory of 4GB, and the test results of the off-line modeling time of the three methods are listed in Table 2. The off-line modeling time is the time required to model 960 training data, all statistics being the average of 10 runs. By comparison, it can be seen that the conventional SFA method requires the least amount of time, only 3.23594 s. The conventional KSFA method is obviously inferior in processing speed because of involving a calculation process of a kernel vector, and the online calculation time of a single sample is 41.31982 s. The BRSFA method of the invention needs 19.01012s time which is higher than that of the traditional SFA method due to the calculation of a plurality of groups of RSFA models, but is obviously lower than the online monitoring time of the traditional KSFA method. Therefore, the BRSFA method of the invention approximates the kernel matrix, reduces the running time of on-line monitoring, and has the advantages of nonlinear processing and reduced operation amount.

TABLE 2

	SFA	KSFA	BRSFA
				Average	3.23594s	41.31982s	19.01012s

Failure 1 was a step change in the flow rate of feed a, the monitoring results of which are shown in fig. 3a-3 c. For the fault, the traditional SFA method cannot perform nonlinear processing on the fault well, and the monitoring result of the fault 1 is shown in fig. 3a, and the statistic T is measured²The detection rate of (a) was 78.10%, and the detection rate of the statistic Q was only 45.48%. The traditional KSFA method can well process the nonlinearity of data through Gaussian mapping, the monitoring result of the traditional KSFA method on the fault 1 is shown in figure 3b, and the statistic T²The detection rate is improved to 89.52%, the detection rate of the Q statistic is improved to 68.69%, but the traditional KSFA method can only carry out modeling, does not consider the difference of different models, and the selection of nuclear parameters is difficult to fully consider all fault situations. The monitoring result of the BRSFA method of the invention on the fault 1 is shown in figure 3c, and the statistic quantity thereof is

Sum statistic BIC_QThe detection rates are respectively improved to 95.00% and 95.36%, which shows that the BRSFA method can well avoid the defect of a single model, does not have too high dependency on the selection of the nuclear parameters while carrying out nonlinear processing, and can effectively detect the occurrence of faults.

Table 3 shows the failure detection rates for 6 failures in the CSTR system for the conventional SFA method, the conventional KSFA method and the BRSFA method of the present invention.

TABLE 3

The 6 failure monitoring effects of the CSTR are listed in Table 3, and the comparison shows that the traditional KSFA method can solve the problem of process data nonlinearity which cannot be solved by the traditional SFA to a certain extent, but the defect is that the method is easily restricted by nuclear parameters and cannot achieve a good detection effect on all failures. The BRSFA method can well detect the nonlinear data, effectively integrates various models by introducing a weighted exponential probability fusion mechanism, overcomes the defect of a single model, can more comprehensively mine the nonlinear characteristic of the data compared with the traditional KSFA method, and improves the detection rate of faults.

By combining the analysis, the fault detection effect of the BRSFA method provided by the invention is obviously superior to that of the traditional SFA method and the traditional KSFA method.

The above-described embodiments are intended to illustrate rather than to limit the invention, and any modifications and variations of the present invention are possible within the spirit and scope of the claims.

Claims (9)

1. A nonlinear chemical process fault detection method is characterized by comprising the following specific steps:

s1, collecting normal operation condition data of the non-linear chemical process historical database as training data X₀Carrying out normalization processing to obtain training data X;

s2, applying random Fourier mapping to the training data X to solve random Fourier mapping variables and construct a random Fourier mapping matrix phi (X);

s3, carrying out generalized eigenvalue decomposition on the covariance matrix of the random Fourier mapping matrix phi (X) to establish a random slow characteristic analysis model;

s4, repeating the steps S2 and S3, establishing M off-line models, and respectively calculating the random FourierDominant subspace statistic T of mapping variables_0,i ²Sum residual spatial statistic Q_0,iI is 1, …, M; further computing dominant subspace statistic T of random Fourier mapping variables_0,i ²Corresponding control limit

Sum residual spatial statistic Q_0,iCorresponding control limit Q_lim,i；

S5, collecting real-time data under nonlinear chemical process fault working conditions as test data x_newAnd obtaining test data x after normalization processing_t；

S6, test data x_tSolving a random Fourier mapping variable by applying random Fourier mapping;

s7, calculating dominant subspace statistic T corresponding to M groups of random Fourier mapping variables_t,i ²Sum residual spatial statistic Q_t,i；

S8, performing M groups of dominant subspace statistics T by using weighted probability index fusion mechanism_t,i ²Sum residual spatial statistic Q_t,iComputing integrated monitoring statistics

Sum statistic BIC_QAnd respectively comparing the statistical values with 1-alpha, wherein alpha is a confidence level, and if any statistical value is larger than 1-alpha, the occurrence of a fault is indicated.

2. The method of claim 1, wherein in step S1, training data X is used₀Mean value of

And standard deviation of

Training data X by equation (1)_oNormalized, the table of formula (1)The expression is as follows:

training data X₀The normalized training data X can be obtained after normalization processing by the formula (1).

3. The method for fault detection in a nonlinear chemical process as recited in claim 2, wherein in step S2, the specific step of constructing the random fourier mapping matrix Φ (X) is: for training data X ═ X₁,x₂,...,x_n]^T∈R^n×mWherein n represents the number of samples, m represents the number of variables, and the gaussian kernel function is approximated by a standard monte carlo approximation integration method through a formula (2), so as to construct a random fourier mapping variable as follows:

in the formula, x_jJ is 1,2.. and n is a vector of the training data X; omega_kK 1,2, L is a gaussian random vector, obeys a mean of 0 and a variance of 0

C is a parameter of a Gaussian kernel function; b_k1,2, L is a random variable, subject to [ -pi, pi [ -n]The intervals are uniformly distributed; l is the number of random variables; t represents matrix transposition;

for all training data X ═ X₁,x₂,...,x_n]^T∈R^n×mConstructing a random Fourier mapping matrix phi (X) < phi (X)₁),φ(x₂),…,φ(x_n)]^T。

4. The method according to claim 3, wherein in step S3,the specific steps for establishing the random slow characteristic analysis model are as follows: in that

Under the condition (1), the random slow feature analysis SFA transform is converted into a generalized eigenvalue decomposition problem shown in formula (3), and the expression of formula (3) is:

Av_k＝λ_kSv_k (3)

wherein A represents the first derivative of the random Fourier mapping matrix phi (X)

The covariance matrix of (a); s represents the covariance matrix of the random Fourier mapping matrix phi (X), lambda_kIs a generalized eigenvalue, v_kIs the corresponding generalized eigenvector;

for arbitrary training vectors x_j∈R^mAnd the corresponding random slow characteristic component model is expressed as follows:

t_k＝φ(x_j)^Tv_k (4)

in the formula, t_kAs a training vector x_jCorresponding random slow feature components.

5. The nonlinear chemical process fault detection method of claim 4, wherein in step S4, the dominant subspace statistic T of the random Fourier mapping variables is calculated_0,i ²Sum residual spatial statistic Q_0,iAnd further statistic T_0,i ²Corresponding control limit

And the corresponding statistic Q_0,iControl limit Q_lim,iThe specific method comprises the following steps:

obtaining p dominant subspace variables according to the accumulated contribution rate, dividing the sample space of the random Fourier mapping variables into a dominant subspace and a residual space, and carrying out formula processing on M groups of off-line model data(5) Computing dominant subspace statistic T of random Fourier mapping variables_0,i ²The residual spatial statistic of the random fourier mapping variable is calculated by (6), and formula (5) and formula (6) are expressed as:

T_0,i ²＝[t₁,…,t_p][t₁,…,t_p]^T (5)

Q_0,i＝[t_p+1,…,t_L][t_p+1,…,t_L]^T (6)

for the confidence level alpha, computing dominant subspace statistic T of random Fourier mapping variables for M groups of off-line model data through a nuclear density estimation method_0,i ²Corresponding control limit

Sum residual spatial statistic Q_0,iCorresponding control limit Q_lim,i。

6. The method of claim 5, wherein in step S5, the training data X is used₀Mean value of

And standard deviation of

Test data x by equation (7)_newNormalization processing is performed, and the expression of formula (7) is:

test data x_newThe normalized test data x can be obtained after normalization processing by the formula (7)_t。

7. A non-aqueous emulsion as defined in claim 6The linear chemical process fault detection method is characterized in that in step S6, the Gaussian random vector omega in step S2 is used_kAnd a random variable b_kConstructing test data x_t∈R^mThe random fourier mapping variables are:

in the formula, phi (x)_t) For test data x_tThe random fourier mapping variable of (1).

8. The nonlinear chemical process fault detection method of claim 7, wherein in step S7, dominant subspace statistics T corresponding to M groups of random fourier mapping variables are calculated_t,i ²Sum residual spatial statistic Q_t,iThe specific method comprises the following steps: using the generalized eigenvector v obtained in step S3_kWill phi (x)_t) Projecting to a low dimensional space to obtain phi (x)_t) The corresponding random slow feature components are expressed as:

t_t,k＝φ(x_t)^Tv_k (9)

in the formula, t_t,kFor test data x_tCorresponding random slow feature components;

constructing a monitoring statistic T for a dominant subspace of M sets of random Fourier mapping variables for process monitoring from equation (10)_t,i ²Constructing residual spatial statistics Q of M sets of random Fourier mapping variables for process monitoring from (11)_t,iThe formula (10) and the formula (11) are expressed as follows:

T_t,i ²＝[t_t,1,…,t_t,p][t_t,1,…,t_t,p]^T (10)

Q_t,i＝[t_t,p+1,…,t_t,L][t_t,p+1,…,t_t,L]^T (11)。

9. the nonlinear chemical process fault detection method of claim 8, wherein in step S8, an integrated monitoring statistic is calculated

Sum statistic BIC_QThe specific method comprises the following steps: performing data integration on the M groups of statistics by using a weighted probability index fusion mechanism to serve as monitoring statistics, and calculating the occurrence probability of the samples under normal and fault conditions by using probability formulas (12) to (14), wherein the formulas (12) to (14) are expressed as follows:

P_T,i(x_t|N)＝exp(-T_t,i ²/T_lim,i) (12)

P_Q,i(x_t|N)＝exp(-Q_t,i/Q_lim,i) (13)

P_T,i(x_t|F)＝exp(-T_lim,i/T_t,i ²) (14)

P_Q,i(x_t|F)＝exp(-Q_lim,i/Q_t,i) (15)

in the formula, P_T,i(x_tN) is test data x under normal conditions_tSample occurrence probabilities of the dominant subspace statistics; p_Q,i(x_tN) is test data x under normal conditions_tSample occurrence probability of residual spatial statistics; p_T,i(x_tI F) is test data x under fault condition_tSample occurrence probabilities of the dominant subspace statistics; p_Q,i(x_tI F) is test data x under fault condition_tSample occurrence probability of residual spatial statistics;

after all the M group statistics are converted into posterior probabilities, the integrated monitoring statistics are calculated through formula (16) and formula (17)

Sum statistic BIC_QThe equations (16), (17) are expressed as:

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