CN117556202B - Industrial process micro fault detection method based on probability correlation slow feature analysis - Google Patents
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Abstract
The invention provides an industrial process micro fault detection method based on probability correlation slow feature analysis, and belongs to the technical field of multi-variable industrial process fault detection. The method solves the technical problem that the conventional slow characteristic analysis method algorithm is difficult to effectively detect the micro faults of the complex nonlinear industrial process. The technical proposal is as follows: the method comprises the following steps: s1, designing a variable space division method based on JS divergence; s2, adopting a sliding window local slow feature analysis algorithm based on JS divergence for a latent variable space with unobvious fault information; and S3, fusing the detection results of the two spaces through a Bayesian inference mechanism to obtain a comprehensive total monitoring result. The beneficial effects of the invention are as follows: the method fuses JS divergence and slow feature analysis, so that space division of multivariable data is realized, effective mining of micro-fault information is realized, and the micro-fault detection rate is remarkably improved.
Description
Technical Field
The invention relates to the technical field, in particular to an industrial process micro fault detection method based on probability correlation slow feature analysis.
Background
Due to rapid development of technology and continuous increase of the demand for diversified products, the process industry process as an important foundation and support for national economy development is increasingly automated, large-sized and complicated. In a complex industrial production process, any minor faults may cause great damage to the whole production system, affect the economic benefit of enterprises, and may even cause casualties, so that it is necessary to perform fault detection on the industrial process to reduce risks. On the other hand, with the development of computer technology and sensor technology, a large amount of data generated by industrial processes has been recorded and saved, which makes a data-driven failure detection method gradually mainstream. In such a background, researchers have successively proposed many fault detection algorithms such as Principal Component Analysis (PCA), independent principal component analysis (ICA), slow Feature Analysis (SFA), and the like.
SFA is used as an unsupervised data transformation and dimension reduction method, and can extract slowly-changing components from data. In an industrial process, the SFA can also realize separate description of steady-state distribution and time variation distribution, and has good interpretation capability in terms of time coherence. Chinese patent CN106647718a discloses a method for detecting faults in a nonlinear industrial process based on bayesian core slow feature analysis, and the detection results based on the core slow feature analysis (KSFA) are fused by bayesian reasoning, so that the fault detection capability of nonlinear data is remarkably improved; in addition, in the patent CN110244692A, a researcher introduces probability information into fault detection, and fuses the Kullback-Leibler divergence (English: kullback-Leibler Divergence, abbreviated: KLD) with PCA, so that the method effectively improves the tiny fault detection capability in the chemical process. Aiming at the thought, researchers fuse KLD divergence with SFA, and put forward a fault detection method (PRSFA for short) based on probability-related slow features, so that a small fault detection effect is improved.
However, in the research process, it is found that, as with other mainstream algorithms, the fault detection methods such as KSFA and PRSFA can realize the detection of most fault types and the improvement of some micro fault detection effects, but the detection of micro faults in a multi-variable complex industrial process is still not ideal, and the faults often occur in early stages of the process, have the characteristics of low amplitude, slow change, easy process interference, measurement noise inundation and the like, and if the faults cannot be detected in time, the faults often develop into process faults or production accidents along with the production operation of industrial engineering. Therefore, how to extract effective fault information from complex nonlinear industrial process data and realize timely monitoring of micro faults is a more challenging research problem in the current industrial process.
Disclosure of Invention
Aiming at the technical problem that the traditional SFA algorithm is difficult to effectively detect the micro faults of the complex nonlinear industrial process, the invention provides the industrial process micro fault detection method based on probability correlation slow feature analysis; according to the method, JS divergence is introduced into an SFA algorithm, so that the fine division of multivariate data is realized, a probability-dependent global-local SFA algorithm based on variable space division is designed on the basis, the effective extraction of micro fault probability information is realized, and the micro fault detection rate is greatly improved.
In order to achieve the aim of the invention, the invention adopts the technical scheme that: an industrial process micro fault detection method based on probability-related slow feature analysis comprises the following steps:
Step S1: the method comprises the steps of obtaining normal working condition data in a historical database as training data X 0, and normalizing the data by means of a mean value (X 0) and a standard deviation std (X 0) to obtain normalized training data X;
Step S2: calculating the mean value and variance of the training data X by adopting a sliding window, so as to calculate JS divergence and obtain a JS divergence component X JS of the training data;
Step S3: calculating evaluation indexes of all variables under normal working conditions by JS divergence component X JS in training data, and calculating variable evaluation index control limit Dev lim by a KDE method;
Step S4: real-time data in the industrial process is collected as test data X new, and standardized processing is carried out on the test data by utilizing the mean (X 0) and standard deviation std (X 0) of training data X 0 to obtain standardized test data X T;
Step S5: calculating JS divergence component X JST of the test data by utilizing a sliding window algorithm with the same parameters as the step S2;
Step S6: calculating an evaluation index Dev XT,j of each variable from JS divergence components X JST of the test data;
step S7: dividing the data into a significant variable space and a latent variable space according to whether the variable evaluation index Dev XT,j exceeds the control limit Dev lim obtained in the step S3;
Step S8: in the salient space, a JS-divergence-based global slow feature analysis algorithm is adopted for data, and salient space statistics are calculated And control limit/>
Step S9: in the latent space, a JS-divergence-based local slow feature analysis algorithm is adopted for data, and latent space statistics are calculatedAnd control limit/>
Step S10: calculating the data fault probability of the two spaces through a Bayesian inference mechanism, integrating the probabilities of the two spaces to calculate final monitoring statistics BIC (Bayesian Inference Control), and judging whether faults occur according to whether the control limit alpha is exceeded;
Further, in step S1, the specific expression for normalizing the training data X 0 by its mean (X 0) and standard deviation std (X 0) is:
X＝(X0-mean(X0))/std(X0) (1)
In the formula, x= [ X 1,X2,...,Xn]T∈Rn×m, n represents the number of samples, and m represents the number of variables.
Further, in step S2, the specific step of calculating the JS divergence component X JS of the training data X using the sliding window is;
The sliding window algorithm is specifically described as follows: the window width W is set to be H, the step length is set to be 1, each sampling time is moved backwards once, the number of data samples is N, and the total number of the data samples is N=n-H+1 sampling times;
And introducing another group of normal working condition data which is different from the training data into the historical database as reference data.
Calculating the mean and variance of the normalized reference data X B as a reference mean μ B and a reference variance λ B;
calculating a mean mu X (k) and a variance lambda X (k) of the training data X (k) at a kth sampling time;
The JS divergence component at the kth sampling timing of the training data X is calculated from the formula (2), and the expression of the formula (2) is as follows:
Further, in the step S3, the specific steps of calculating the evaluation indexes of all the variables under the normal working condition from the JS divergence component X JS of the training data are as follows:
Step S2 is performed on the reference data X B, and the JS divergence component X JSB of the reference data is calculated according to the formula X JSB(k)＝JS(λB,μB,λB(k),μB (k));
For JS divergence component X JS∈RN×m of training data, N is the sampling number, m represents the total number of variables, and the mean (X JS,j) and standard deviation std (X JS,j) of the jth variable are calculated;
For JS divergence component X JSB∈RN×m of reference data, N is the sampling number, m represents the total number of variables, and the reference Mean (X JSB,j) and the reference standard deviation Std (X JSB,j) of the jth variable are calculated;
calculating an evaluation index of the j-th variable of the training data X from the formula (3), the expression of the formula (3) being as follows:
Given confidence level The control limit Dev lim is determined according to a kernel density estimation method (abbreviated as KDE method).
Further, in step S4, the test data X new is normalized by using the mean (X 0) and the standard deviation std (X 0) of the training data X 0 by the formula (4), where the expression of the formula (4) is:
XT＝(Xnew-mean(X0))/std(X0) (4)
x T is the data of the standardized X new.
Further, in step S5, the JS divergence component X JST of the test data X T is calculated using the sliding window algorithm with the same parameters as in step S2, and the specific steps are as follows:
Step S2 has calculated a reference mean μ B and a reference variance λ B;
Calculating a mean mu XT (k) and a variance lambda XT (k) of the k-th sampling time test data X T (k);
the JS divergence component at the kth sampling time of the test data X T is calculated by equation (2), as follows:
XJST(k)＝JS(λB,μB,λXT(k),μXT(k))，k＝1,2,…,N
Further, in step S6, an evaluation index Dev XT of each variable is calculated from the JS divergence component X JST of the test data:
For JS divergence component X JST∈RN×m of test data, N is the sampling number, m represents the total number of variables, and the mean (X JST,j) and standard deviation std (X JST,j) of the jth variable are calculated;
calculating an evaluation index of the j-th variable of the test data X from the formula (5), the expression being as follows:
Further, in step S7, according to whether the test data variable evaluation index Dev XT exceeds the control limit Dev lim obtained in step S3, the data is divided into a significant variable space and a latent variable space, see fig. 2, and the specific steps are as follows:
If the evaluation index Dev XT,j of the j-th variable in the test data meets the following conditions: dev XT,j＞Devlim means that the j-th variable has more significant fault information, and the j-th variable is divided into significant variable spaces; otherwise, the hidden variable space is divided. The number of significant spatial variables is a, the number of latent spatial variables is b, a+b=m.
Further, in step S8, a global slow feature analysis algorithm based on JS divergence is applied to the data in the significant variable space to calculate significant spatial statisticsAnd control limit/>The flow chart is shown in fig. 3;
in the significant variable space, a JS-divergence-based global slow feature analysis algorithm is adopted for data, and significant space statistics are calculated The method comprises the following specific steps:
offline stage:
the standardized training data X O in the salient space is input data X, X (t) = [ X 1(t),x2(t),...,xa(t)]T, and the slow features of the training data X O are extracted by adopting a traditional global SFA algorithm:
① A whitening step: singular value decomposition is performed on the covariance matrix r= < X (t) T>t of X (t): r=uΛu T,Q＝Λ-1/2UT is a whitening matrix, and the whitening transformation can be described as:
② First order derivative of whitening data z (t) and covariance matrix thereof Singular value decomposition is performed as follows: wherein P is a feature vector matrix; Ω=diag (λ 1,λ2,...,λa) is a eigenvalue matrix, and eigenvalues λ i are arranged from small to large, indicating how fast or slow the slow characteristic changes;
③ The transformation matrix w=pΛ -1/2UT, the extracted slow features are calculated as follows: s (t) =wx (t);
The variation speed of the slow characteristic S (t) is calculated by omega=diag (lambda 1,λ2,...,λa) and the variation speed of the normalized input data X is calculated According to the formula/>The number of dominant slow features is calculated, q=0.1 representing the number of quantiles on 0.1 of the set { delta (X j) }.
The main slow characteristic of the training data is S O(t)＝[s1(t),s2(t),...,sM(t)]T;
The JS divergence component of S O (t) is calculated using a sliding window:
Calculating the overall mean mu SO and the overall variance lambda SO of the slow feature S O of the training data;
Calculating a mean mu SO (k) and a variance lambda SO (k) of the slow training data feature S O in the kth sliding window;
The JS divergence component at the kth sampling timing of the training data X is calculated from formula (2):
SOJS(k)＝JS(λSO,μSO,λSO(k),μSO(k))。
The construction statistics are as follows:
Given confidence level Calculating control limit/>, corresponding to statistic T 2, through KDE method
On-line stage:
The slow features of the salient space online test data X OT are found by the transformation matrix W obtained at ③ as follows:
SOT(t)＝WXOT(t)＝[s1(t),s2(t),...,sM(t)]T
calculating the mean mu SOT (k) and the variance lambda SOT (k) of the data in the kth sliding window;
The JS divergence component is calculated by the formula (2):
SOTJS(k)＝JS(λSO,μSO,λSOT(k),μSOT(k))
Constructing on-line monitoring statistics
According to statisticsWhether or not the control limit is exceeded/>And judging whether a fault occurs.
Further, in step S9, a local slow feature analysis algorithm based on JS divergence is applied to the data in the latent space to calculate a latent space statisticControl limit/>The flow chart is shown in fig. 4;
offline stage:
① Firstly, taking all standardized training data X L in a latent space as input data, and obtaining global slow features S G of the training data after the global SFA step in the step S8;
② Adopting a sliding window algorithm, wherein the step length is 1, the window width is determined through cross verification, each sliding window is one sampling moment, and all training data are divided into k sampling moments;
③ Taking the training data at the kth sampling moment as input data X, and obtaining local slow features X S (k) of the training data at the kth sampling moment after an independent SFA step;
The method calculates the JS divergence component of the local slow feature of the training data by the following steps
Calculating a mean mu G and a variance lambda G of the training data global slow feature S G;
Calculating the mean mu S (k) and the variance lambda S (k) of the local slow feature X S (k) at the kth sampling time of the training data;
the JS divergence component for the kth sampling time of training data X L is calculated from equation (2):
SLJS(k)＝JS(λG,μG,λS(k),μS(k))
The construction statistics are as follows:
Given confidence level Calculating control limit/>, corresponding to statistic T 2, through KDE method
On-line stage:
① Taking standardized test data in the hidden space as input, adopting a sliding window algorithm, wherein the step length is 1, the window width is the same as that of the offline stage, each sliding window is one sampling moment, and all the test data are divided into k sampling moments;
② Taking the kth sampling moment data as input data X, and obtaining local slow features X ST (k) of the kth sampling moment of the test data after an independent SFA step;
The JS divergence component of the local slow feature of the test data is calculated by the following steps:
The mean mu G and the variance lambda G of the global slow feature S G of the training data are calculated;
calculating the mean mu ST (k) and the variance lambda ST (k) of the local slow feature X ST (k) at the kth sampling time of the test data;
The JS divergence component at the kth sampling time of the test data X LT is calculated from equation (2):
SLTJS(k)＝JS(λG,μG,λST(k),μST(k))
The construction statistics are as follows:
According to statistics Whether or not the control limit is exceeded/>And judging whether a fault occurs.
Further, in step S10, the probability of data failure in two spaces is calculated by bayesian inference mechanism, the probability of two spaces is integrated to calculate the final monitoring statistic BIC, and the specific steps of judging whether failure occurs according to whether the control limit is exceeded are as follows:
And (3) converting the statistics obtained in the steps S8 and S9 into a conditional probability obtaining form by adopting a Bayesian inference mechanism to obtain the fault probabilities of the two spaces:
Significant space:
Hidden space:
Wherein: p (X) =p (x|n) P (N) +p (x|f) P (F)
Given a confidence level α, the P (F) value is α and the P (N) value is 1- α;
p (F|X) represents the probability that the test data is considered as fault data, P (N) represents the prior probability that the process working condition is normal, and P (F) represents the prior probability that the process is faulty;
The detection results of the two spaces are fused by a sampling Bayesian probability fusion algorithm, and the whole process statistic is obtained:
when BIC is less than or equal to alpha, the process is considered to be in a normal working condition; when BIC > alpha, the process is considered to be in a fault state;
in the above method, steps S1 to S7 are variable space division stages, and steps S8 to S10 are SFA detection stages.
Compared with the prior art, the invention has the beneficial effects that:
1. the method for detecting the industrial process micro faults introduces JS divergence, provides a variable dividing method based on JS divergence, and realizes effective variable space division of multi-variable complex data.
2. The JS divergence is combined with the sliding window, and the micro fault information is deeply mined through researching the probability information of the process data.
3. On the basis of variable division, a probability-dependent global-local SFA algorithm based on variable space division is provided, so that the operation complexity is effectively reduced, the effective detection of micro faults is realized, and the problem that the traditional data-driven machine learning method is poor in micro fault detection performance of a complex industrial process is effectively solved.
Drawings
The accompanying drawings are included to provide a further understanding of the invention and are incorporated in and constitute a part of this specification, illustrate the invention and together with the embodiments of the invention, serve to explain the invention.
FIG. 1 is a general flow chart of the method of detecting micro-faults.
Fig. 2 is a flowchart of variable space division based on JS divergence in the method of the present invention.
Fig. 3 is a flowchart of a global SFA method based on JS divergence in the method of the present invention.
Fig. 4 is a flowchart of a local SFA method based on JS divergence in the method of the present invention.
FIG. 5 is a schematic diagram of a TE chemical process used in the examples of the present invention.
FIG. 6 (a) is a diagram showing the detection result of TE process fault 3 by using the conventional SFA method according to the embodiment of the present invention.
Fig. 6 (b) is a diagram showing a TE process fault 3 detection result according to the embodiment of the present invention using the conventional PRSFA method.
FIG. 6 (c) is a diagram showing the result of detecting TE process fault 3 by PR-GLSFA according to the present invention.
FIG. 7 (a) is a diagram showing the detection result of TE process fault 15 by using the conventional SFA method according to the embodiment of the present invention.
FIG. 7 (b) is a diagram showing the detection result of TE process fault 15 by using the conventional PRSFA method according to the embodiment of the present invention.
FIG. 7 (c) is a diagram showing the result of detecting the TE process fault 15 by the PR-GLSFA method according to the present invention.
Detailed Description
The present invention will be described in further detail with reference to the drawings and examples, in order to make the objects, technical solutions and advantages of the present invention more apparent. Of course, the specific embodiments described herein are for purposes of illustration only and are not intended to limit the invention.
Example 1
Referring to fig. 1 to 7, the present embodiment is based on tennessee-isman Process (TEENESSE EASTMAN Process), abbreviated as TE Process, which is a typical nonlinear industrial Process, which is a simulation based on actual industrial Process by Eastman chemical company in united states. The first proposal was made by the Eastman chemical company of America, down J.J. and Vogel E.F. in AICHE, 1990, and the FORTRAN source code was given. After that, a Ricker process control research laboratory of Washington university rewrites the TE chemical model by utilizing a Simulink simulation environment of Matlab, so that the TE chemical process can simulate on the Matlab, and the simulated data has the characteristics of nonlinearity, time variability, strong coupling and the like, and the TE process is widely applied to the research of processes such as process monitoring, optimal control, fault detection, fault diagnosis and the like.
The TE chemical process comprises five main units: a reactor, a condenser, a compressor, a separator and a stripper. After the primary gaseous feed enters the process, two liquid products are produced from the four reactants by the operation of the several sections and the chemical reactions therein. In addition, an inert product and a by-product are produced, comprising a total of eight components: A. b, C, D, E, F, G, H. The various reactions in the reactor are:
A(g)+C(g)+D(g)---＞G(1iq)
A(g)+C(g)+E(g)---＞H(1iq)
A(g)+E(g)---＞F(liq)
3D(g)--->2F(liq)
the flow is shown in fig. 5:
The whole TE chemical process comprises 12 operation variables and 41 measurement variables, and the common 11 operation variables and 22 measurement variables are selected for testing in the example. All process measurements had gaussian noise interference and all variables are shown in table 1.
21 Faults are preset in the TE chemical process, and the faults are classified into fault types such as steps and unknowns. The faults IDV (1) to IDV (15) and IDV (21) are 16 known faults, the faults IDV (16) to IDV (20) are 5 unknown faults, and in the actual experimental and simulation process, the faults IDV (3), IDV (9) and IDV (15) belong to micro faults and are difficult to detect. The present embodiment selects 6 of the faults, covers all fault types, and includes all minor faults in the TE process, as shown in table 2 below.
Table 1 list of variables
TABLE 2 Process failure types
| Failure number | Cause of failure | Fault type |
| IDV(3) | D feed temperature variation | Minor faults |
| IDV(5) | Condenser cooling water injection temperature variation | Step failure |
| IDV(9) | D feed temperature variation | Minor faults |
| IDV(11) | Reactor cooling water injection temperature variation | Random failure |
| IDV(15) | Condenser cooling water valve lock | Minor faults |
| IDV(20) | Unknown | Unknown faults |
In this embodiment, normal samples are used as training data and reference data, sampling data under fault conditions are used as test data, the number of samples under each fault condition is 960, and faults of all data are added after 160 th sample points.
After the occurrence of faults is detected, in order to evaluate the fault detection effects of different monitoring methods, the fault detection effects of different methods are compared through two performance indexes of fault False Alarm Rate (FAR) and Fault Detection Rate (FDR). The lower the FAR, the higher the FDR, and the better the detection effect of the method is considered.
Where N Tf and N Ff are the number of fault samples detected before and after a fault occurs, and N T and N F are the number of normal samples and fault samples, respectively.
In the TE process simulation of the present embodiment, the conventional SFA method, the conventional PRSFA method and the PR-GLSFA method of the present invention are adopted as comparison. In this example, the width of all sliding windows is 130, and the KDE method calculates the confidence level of the control limitAll set to 99% and the confidence level α of the bayesian inference mechanism in the PR-GLSFA method is set to 0.1.
Fault 3 is a minor fault caused by D feed temperature change. The graphs of the detection effect of the three methods of the conventional SFA method, the conventional PRSFA method and the PR-GLSFA method of the present invention on the fault 3 are shown in FIGS. 6 (a) -6 (c). In the following fig. 6 (a), the conventional SFA method has poor monitoring effect on the fault 3 due to small fault amplitude and slow change, and the detection rate of the monitoring statistic T 2 is only 16.75%, and the false detection rate is 16.87%. The traditional PRSFA method is also not ideal for detecting the fault 3, the fault detection rate is 8.37%, the fault false alarm rate is 4.37%, the effect is shown in fig. 6 (b), and although KL divergence is introduced to extract fault probability information compared with the traditional SFA, for a complex multivariable industrial process, tiny faults tend to occur on smaller data scale and have great difference in expression of different variables. Compared with the two traditional algorithms, the PR-GLSFA algorithm of the invention firstly separates key significant reflected variables from a plurality of variables by utilizing the data probability information, then adopts innovative probability-related local slow feature analysis to extract fault information on a small data scale for the latent variables containing the latent fault information, has obvious effect, and has the fault detection rate of 99.75% and the fault false alarm rate of 3.75% as shown in fig. 6 (c), so that the PR-GLSFA algorithm provided by the invention can greatly improve the detection effect on the micro fault 3 in the TE process.
Fault 15 is a minor fault caused by the condenser cooling water valve seizing. Referring to fig. 7 (a), the failure detection rate of the conventional SFA method is only 27.12%, and the monitoring of the system is hardly realized; referring to fig. 7 (b), the fault detection rate of the conventional PRSFA method is provided in comparison with SFA, and the fault detection rate reaches 63.62%, but still fails to meet the monitoring requirements of the actual industrial process; compared with the two algorithms, the PR-GLSFA algorithm provided by the invention can realize effective detection of the fault 15, as shown in fig. 7 (c), the fault detection rate reaches 99.80%, meanwhile, the lower false detection rate is maintained, the fault false alarm rate is only 4.15%, and the effectiveness of the method is verified.
Table 3 shows the fault detection effect of the conventional SFA method, the conventional PRSFA method and the PR-GLSFA method of the present invention on the 6 faults of the TE process.
TABLE 3 Table 3
As can be seen from the above table, the conventional SFA method and the conventional PRSFA method have an unsatisfactory detection effect on the TE process, and particularly, the occurrence of the three micro faults of the IDV (3), the IDV (9) and the IDV (15) is hardly detected. The PR-GLSFA method provided by the invention realizes effective mining of variable space division and micro fault information by utilizing the data probability information, greatly improves the fault detection rate, maintains a lower fault false alarm rate and achieves a good monitoring effect. In conclusion, the PR-GLSFA method of the invention has a significantly better micro fault detection effect than the other two methods.
The foregoing description of the preferred embodiments of the invention is not intended to limit the invention to the precise form disclosed, and any such modifications, equivalents, and alternatives falling within the spirit and scope of the invention are intended to be included within the scope of the invention.
Claims (8)
1. The industrial process micro fault detection method based on probability correlation slow feature analysis is characterized by comprising the following steps of:
Step S1: the method comprises the steps of obtaining normal working condition data in a historical database as training data X 0, and normalizing the data by means of a mean value (X 0) and a standard deviation std (X 0) to obtain normalized training data X;
Step S2: calculating the mean value and variance of the training data X by adopting a sliding window, so as to calculate JS divergence and obtain a JS divergence component X JS of the training data;
step S3: calculating evaluation indexes of all variables under normal working conditions by JS divergence component X JS in training data, and calculating variable evaluation index control limit Dev lim by a nuclear density estimation method;
Step S4: real-time data in the industrial process is collected as test data X new, and standardized processing is carried out on the test data by utilizing the mean (X 0) and standard deviation std (X 0) of training data X 0 to obtain standardized test data X T;
Step S5: calculating JS divergence component X JST of the test data by utilizing a sliding window algorithm with the same parameters as the step S2;
Step S6: calculating an evaluation index Dev XT,j of each variable from JS divergence components X JST of the test data;
step S7: dividing the data into a significant variable space and a latent variable space according to whether the variable evaluation index Dev XT,j exceeds the control limit Dev lim obtained in the step S3;
Step S8: in the salient space, a JS-divergence-based global slow feature analysis algorithm is adopted for data, and salient space statistics are calculated And control limit/>
Step S9: in the latent space, a JS-divergence-based local slow feature analysis algorithm is adopted for data, and latent space statistics are calculatedAnd control limit/>
In step S8, a JS-divergence-based global slow feature analysis algorithm is adopted for data in a significant variable space to calculate a significant spatial statisticAnd control limit/>
In the significant variable space, a JS-divergence-based global slow feature analysis algorithm is adopted for data, and significant space statistics are calculatedThe method comprises the following specific steps:
offline stage:
the standardized training data X O in the salient space is input data X, X (t) = [ X 1(t),x2(t),...,xa(t)]T, and the slow features of the training data X O are extracted by adopting a traditional global SFA algorithm:
① A whitening step: singular value decomposition is performed on the covariance matrix r= < X (t) T>t of X (t): r=uΛu T,Q＝Λ-1/2UT is a whitening matrix, and the whitening transformation can be described as:
② First order derivative of whitening data z (t) and covariance matrix thereof Singular value decomposition is performed as follows: wherein P is a feature vector matrix; Ω=diag (λ 1,λ2,...,λa) is a eigenvalue matrix, and eigenvalues λ i are arranged from small to large, indicating how fast or slow the slow characteristic changes;
③ The transformation matrix w=pΛ -1/2UT, the extracted slow features are calculated as follows: s (t) =wx (t);
The variation speed of the slow characteristic S (t) is calculated by omega=diag (lambda 1,λ2,...,λa) and the variation speed of the normalized input data X is calculated According to the formula/>Calculating the number of main slow features, q=0.1 representing the number of digits on 0.1 of the set { delta (X j) };
the main slow characteristic of the training data is S O(t)＝[s1(t),s2(t),...,sM(t)]T;
The JS divergence component of S O (t) is calculated using a sliding window:
Calculating the overall mean mu SO and the overall variance lambda SO of the slow feature S O of the training data;
Calculating a mean mu SO (k) and a variance lambda SO (k) of the slow training data feature S O in the kth sliding window;
The JS divergence component of the kth sampling time of the training data X is calculated:
SOJS(k)＝JS(λSO,μSO,λSO(k),μSO(k))；
The construction statistics are as follows:
Given confidence level Calculating control limit/>, corresponding to statistic T 2, through nuclear density estimation method
On-line stage:
The slow features of the salient space online test data X OT are found by the transformation matrix W obtained at ③ as follows:
SOT(t)＝WXOT(t)＝[s1(t),s2(t),...,sM(t)]T
calculating the mean mu SOT (k) and the variance lambda SOT (k) of the data in the kth sliding window;
The JS divergence component is calculated:
SOTJS(k)＝JS(λSO,μSO,λSOT(k),μSOT(k))
Constructing on-line monitoring statistics
According to statisticsWhether or not the control limit is exceeded/>Judging whether a fault occurs or not;
in step S9, a JS-divergence-based local slow feature analysis algorithm is adopted for data in the latent space to calculate a latent space statistic Control limit/>
Offline stage:
① Firstly, taking all standardized training data X L in a latent space as input data, and obtaining global slow features S G of the training data after the global SFA step in the step S8;
② Adopting a sliding window algorithm, wherein the step length is 1, the window width is determined through cross verification, each sliding window is one sampling moment, and all training data are divided into k sampling moments;
③ Taking the training data at the kth sampling moment as input data X, and obtaining local slow features X S (k) of the training data at the kth sampling moment after an independent SFA step;
the local slow feature JS divergence component of the training data is calculated by the following steps:
Calculating a mean mu G and a variance lambda G of the training data global slow feature S G;
Calculating the mean mu S (k) and the variance lambda S (k) of the local slow feature X S (k) at the kth sampling time of the training data;
The JS spread component of the kth sampling time of training data X L is calculated:
SLJS(k)＝JS(λG,μG,λS(k),μS(k))
The construction statistics are as follows:
Given confidence level Calculating control limit/>, corresponding to statistic T 2, through nuclear density estimation method
On-line stage:
① Taking standardized test data in the hidden space as input, adopting a sliding window algorithm, wherein the step length is 1, the window width is the same as that of the offline stage, each sliding window is one sampling moment, and all the test data are divided into k sampling moments;
② Taking the kth sampling moment data as input data X, and obtaining local slow features X ST (k) of the kth sampling moment of the test data after an independent SFA step;
The JS divergence component of the local slow feature of the test data is calculated by the following steps:
The mean mu G and the variance lambda G of the global slow feature S G of the training data are calculated;
calculating the mean mu ST (k) and the variance lambda ST (k) of the local slow feature X ST (k) at the kth sampling time of the test data;
the JS divergence component of the kth sampling time of the test data X LT is calculated:
SLTJS(k)＝JS(λG,μG,λST(k),μST(k))
The construction statistics are as follows:
According to statistics Whether or not the control limit is exceeded/>Judging whether a fault occurs or not;
Step S10: calculating the data fault probability of two spaces through a Bayesian inference mechanism, integrating the probabilities of the two spaces to calculate a final monitoring statistic BIC, and judging whether faults occur according to whether the control limit alpha is exceeded;
In step S10, the probability of data failure in two spaces is calculated by bayesian inference, the probability of two spaces is integrated to calculate the final monitoring statistic BIC, and the specific steps of judging whether failure occurs according to whether the control limit is exceeded are as follows:
And (3) converting the statistics obtained in the steps S8 and S9 into a conditional probability obtaining form by adopting a Bayesian inference mechanism to obtain the fault probabilities of the two spaces:
Significant space:
Hidden space:
Wherein: p (X) =p (x|n) P (N) +p (x|f) P (F)
Given a confidence level α, the P (F) value is α and the P (N) value is 1- α;
p (F|X) represents the probability that the test data is considered as fault data, P (N) represents the prior probability that the process working condition is normal, and P (F) represents the prior probability that the process is faulty;
The detection results of the two spaces are fused by a sampling Bayesian probability fusion algorithm, and the whole process statistic is obtained:
when BIC is less than or equal to alpha, the process is considered to be in a normal working condition; when BIC > alpha, the process is considered to be in a fault state;
in the above method, steps S1 to S7 are variable space division stages, and steps S8 to S10 are SFA detection stages.
2. The industrial process micro-fault detection method based on probability-dependent slow feature analysis according to claim 1, wherein in step S1, the specific expression for normalizing training data X 0 with its mean (X 0) and standard deviation std (X 0) is:
X＝(X0-mean(X0))/std(X0) (1)
In the formula, x= [ X 1,X2,...,Xn]T∈Rn×m, n represents the number of samples, and m represents the number of variables.
3. The method for detecting industrial process micro-faults based on probability-dependent slow feature analysis of claim 2 in which in step S2 the specific step of calculating the JS divergence component X JS of the training data X using a sliding window is;
The sliding window algorithm is: the window width W is set to be H, the step length is set to be 1, each sampling time is moved backwards once, the number of data samples is N, and the total number of the data samples is N=n-H+1 sampling times;
Introducing another group of normal working condition data which is different from the training data into the historical database as reference data;
calculating the mean and variance of the normalized reference data X B as a reference mean μ B and a reference variance λ B;
calculating a mean mu X (k) and a variance lambda X (k) of the training data X (k) at a kth sampling time;
The JS divergence component at the kth sampling timing of the training data X is calculated from the formula (2), and the expression of the formula (2) is as follows:
4. The method for detecting industrial process micro-faults based on probability-related slow feature analysis of claim 3 in which in the step S3, the specific step of calculating the evaluation index of all variables under normal working conditions from JS divergence component X JS of the training data is as follows:
Step S2 is performed on the reference data X B, and the JS divergence component X JSB of the reference data is calculated according to the formula X JSB(k)＝JS(λB,μB,λB(k),μB (k));
For JS divergence component X JS∈RN×m of training data, N is the sampling number, m represents the total number of variables, and the mean (X JS,j) and standard deviation std (X JS,j) of the jth variable are calculated;
For JS divergence component X JSB∈RN×m of reference data, N is the sampling number, m represents the total number of variables, and the reference Mean (X JSB,j) and the reference standard deviation Std (X JSB,j) of the jth variable are calculated;
calculating an evaluation index of the j-th variable of the training data X from the formula (3), the expression of the formula (3) being as follows:
Given confidence level The control limit Dev lim is determined according to the kernel density estimation method.
5. The method for detecting micro-faults in an industrial process based on probability-dependent slow feature analysis of claim 4 in which in step S4 test data X new is normalised by equation (4) using the mean (X 0) and standard deviation std (X 0) of training data X 0, expression of equation (4) being:
XT＝(Xnew-mean(X0))/std(X0) (4)
x T is the data of the standardized X new.
6. The method for detecting an industrial process micro-fault based on probability-dependent slow feature analysis according to claim 5, wherein in step S5, the JS divergence component X JST of the test data X T is calculated using a sliding window algorithm with the same parameters as in step S2, specifically as follows:
Step S2 has calculated a reference mean μ B and a reference variance λ B;
Calculating a mean mu XT (k) and a variance lambda XT (k) of the k-th sampling time test data X T (k);
the JS divergence component at the kth sampling time of the test data X T is calculated by equation (2), as follows:
XJST(k)＝JS(λB,μB,λXT(k),μXT(k))，k＝1,2,…,N。
7. the method for detecting an industrial process micro-fault based on the probability-dependent slow feature analysis as claimed in claim 6, wherein in step S6, an evaluation index Dev XT of each variable is calculated from JS divergence component X JST of the test data:
For JS divergence component X JST∈RN×m of test data, N is the sampling number, m represents the total number of variables, and the mean (X JST,j) and standard deviation std (X JST,j) of the jth variable are calculated;
calculating an evaluation index of the j-th variable of the test data X from the formula (5), the expression being as follows:
8. The method for detecting industrial process micro-faults based on probability-related slow feature analysis of claim 7, wherein in step S7, according to whether the test data variable evaluation index Dev XT exceeds the control limit Dev lim obtained in step S3, the data is divided into a significant variable space and a latent variable space, and the specific steps are as follows:
If the evaluation index Dev XT,j of the j-th variable in the test data meets the following conditions: dev XT,j＞Devlim means that the j-th variable has more significant fault information, and the j-th variable is divided into significant variable spaces; otherwise, dividing the space into a latent variable space, wherein the number of the obvious space variables is a, and the number of the latent space variables is b, and a+b=m.
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