CN111736567A - Multi-block fault monitoring method based on fault sensitivity slow characteristic - Google Patents
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Abstract
The invention discloses a multi-block fault monitoring method based on fault sensitivity slow characteristics, which comprises the steps of collecting data in an industrial production system, and dividing the obtained data into a training set and a test set; carrying out slow feature analysis on the training set, and calculating a slow feature transformation matrix; defining a fault sensitivity coefficient, and obtaining the sensitivity of each slow characteristic to the fault through the coefficient in the slow characteristic transformation matrix; defining a fault sensitivity degree threshold, selecting a fault sensitivity slow characteristic for each dimensional variable of a training set, and using the fault sensitivity slow characteristic as a training sub-block; according to the invention, through the analysis of a statistic calculation formula, the fault sensitivity coefficient is defined, the slow features are reordered, the slow feature which is most sensitive to the fault in the variable direction is selected, the sensitive slow feature is selected for each dimensional variable, and the parallel monitoring is carried out, so that the dynamic monitoring of multiple dimensions and the effective monitoring on a large-scale process can be effectively realized.
Description
Technical Field
The invention relates to the technical field of fault monitoring and diagnosis in an industrial production process, in particular to a multi-block fault monitoring method based on a fault sensitivity slow characteristic.
Background
Modern industrial processes increasingly require high product quality and safety, and if complex industrial processes break down, huge losses are caused, so that the process is very important to be effectively monitored. With the rapid development of sensing and detecting technologies, the informatization degree of industrial production is continuously improved, and a large amount of production process data is generated, so that a Multivariate Statistical Process Monitoring (MSPM) method is widely applied. The Principal Component Analysis (PCA), Partial Least Squares (PLS) and Independent Component Analysis (ICA) are relatively classical multivariate statistical monitoring methods; however, none of these approaches effectively solves dynamic and large scale problems.
The conventional MSPM method is a static process monitoring method, considering samples independent from each other, in other words, samples at the current time are independent from samples at past times. However, since industrial processes are very complex and have unknown dynamic characteristics, static monitoring methods will ignore important process dynamic information, resulting in poor monitoring performance.
Modern production processes featuring large scale and multiple operating units are increasing and when such production processes fail, only part of the variables may be affected, and if only a global model is built, local information may be overwhelmed, and thus, multi-block or distributed process monitoring becomes an effective solution.
Disclosure of Invention
This section is for the purpose of summarizing some aspects of embodiments of the invention and to briefly introduce some preferred embodiments. In this section, as well as in the abstract and the title of the invention of this application, simplifications or omissions may be made to avoid obscuring the purpose of the section, the abstract and the title, and such simplifications or omissions are not intended to limit the scope of the invention.
The invention is provided in view of the fact that the existing fault monitoring method cannot effectively monitor dynamic and large-scale processes.
Therefore, the invention aims to provide a multi-block fault monitoring method based on a fault sensitivity slow characteristic.
In order to solve the technical problems, the invention provides the following technical scheme: a multi-block fault monitoring method based on fault sensitivity slow characteristics comprises the following steps,
collecting data in an industrial production system, and dividing the obtained data into a training set and a test set;
carrying out slow feature analysis on the training set, and calculating a slow feature transformation matrix;
defining a fault sensitivity coefficient, and obtaining the sensitivity of each slow characteristic to faults according to the coefficient in the slow characteristic transformation matrix;
defining a fault sensitivity degree threshold, selecting a fault sensitivity slow characteristic for each dimension variable of a training set, and taking the fault sensitivity slow characteristic as a training sub-block;
respectively calculating fault statistics for each training sub-block, and calculating the radius of the hypersphere as a fault control limit by adopting a support vector data description model;
and respectively calculating fault statistics for each test sample, substituting the fault statistics into a support vector data description model to calculate the distance from the center of the sphere, and judging whether a fault occurs or not by comparing the distance with the center of the sphere and the radius.
As an optimized scheme of the multi-block fault monitoring method based on the fault sensitivity slow characteristic, the method comprises the following steps: the method for collecting data in an industrial production system and dividing the data into a training set and a test set comprises the following steps:
collecting data in an industrial production system through a sensor;
dividing the data into normal data and fault data according to different working conditions;
taking normal data as a training set and taking fault data as a test set;
and respectively carrying out standardization processing on the training set and the test set.
As an optimized scheme of the multi-block fault monitoring method based on the fault sensitivity slow characteristic, the method comprises the following steps: the sensors are temperature sensors, pressure sensors and flow sensors.
As an optimized scheme of the multi-block fault monitoring method based on the fault sensitivity slow characteristic, the method comprises the following steps: the training set standardization processing step comprises:
calculating the average value mu of the training set X;
calculating the standard deviation of the training set X;
standardized training set
As an optimized scheme of the multi-block fault monitoring method based on the fault sensitivity slow characteristic, the method comprises the following steps: the average value and the standard deviation of the standard treatment of the test set Y adopt the average value and the standard deviation of a training set;
wherein, the standardized test set Y:
as an optimized scheme of the multi-block fault monitoring method based on the fault sensitivity slow characteristic, the method comprises the following steps: and slow feature analysis is carried out on the training set, and the step of calculating the slow feature transformation matrix is as follows:
giving an m-dimensional time sequence signal, and arranging according to a sequence from slow to fast;
the problem of slow characteristic is converted into an optimization problem;
transforming the linear slow characteristic analysis;
whitening the data by adopting SVD;
converting the optimization problem into a solution orthogonal matrix;
and acquiring a slow feature transformation matrix according to the whitening matrix and the orthogonal matrix.
As an optimized scheme of the multi-block fault monitoring method based on the fault sensitivity slow characteristic, the method comprises the following steps: the fault sensitivity coefficient is defined as:
ij＝|wij|
wherein the content of the first and second substances,ijis the sensitivity coefficient, w, of the ith slow characteristic to the occurrence of a fault on the jth dimension variableijThe element in the ith row and the jth column of the slow feature transformation matrix is used.
As an optimized scheme of the multi-block fault monitoring method based on the fault sensitivity slow characteristic, the method comprises the following steps: the fault sensitivity threshold is defined as:
wherein the content of the first and second substances,jlima threshold for the fault sensitive slow feature is selected for the jth variable dimension,
the maximum fault sensitivity coefficient on the jth variable dimension is mu, and mu is a coefficient between 0 and 1.
As an optimized scheme of the multi-block fault monitoring method based on the fault sensitivity slow characteristic, the method comprises the following steps: the fault statistics in the slow feature analysis model are calculated as follows:
wherein s iskA slow feature matrix selected by fault sensitivity.
As an optimized scheme of the multi-block fault monitoring method based on the fault sensitivity slow characteristic, the method comprises the following steps: the fault statistics and fault control limits under the support vector data description model are as follows:
s.t.||Φ(yi)-a||2≤R2+ξi
wherein R is the radius of the hyper-sphere, a is the center of the hyper-sphere, a penalty factor C balances the volume of the hyper-sphere and the error rate of the training sample, and xiiIs the relaxation variable.
Wherein the optimization problem of the above formula can be converted into an optimization problem for solving its dual problem:
where K is the kernel function, alphaiIs a lagrange multiplier; x is the number ofiAnd xjfor the ith and jth training samples, the support vector is such that 0 < alphaiSamples of < C;
wherein, by solving this optimization problem, the radius of the hyper-sphere can be obtained:
wherein, the distance between the test sample and the center of the hyper-sphere is as follows:
the invention has the beneficial effects that: according to the invention, through the analysis of a statistic calculation formula, the fault sensitivity coefficient is defined, the slow features are reordered, the slow feature which is most sensitive to the fault in the variable direction is selected, the sensitive slow feature is selected for each dimensional variable, and the parallel monitoring is carried out, so that the effective monitoring on a multi-dimensional dynamic and large-scale process can be effectively realized.
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In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings needed to be used in the description of the embodiments will be briefly introduced below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and it is obvious for those skilled in the art to obtain other drawings based on these drawings without inventive exercise. Wherein:
fig. 1 is a process flow diagram of the TE process of the multi-block fault monitoring method based on the fault sensitivity slow feature of the present invention.
FIG. 2 is a modeling flow chart of a multi-block fault monitoring method based on a fault sensitivity slow characteristic.
Fig. 3 is a diagram illustrating a monitoring result of a conventional method PCA on a TE process fault 16 of the multi-block fault monitoring method based on the fault sensitivity slow characteristic of the present invention.
Fig. 4 is a diagram illustrating the monitoring result of the multi-block fault monitoring method based on the fault sensitivity slow characteristic to the fault 16 in the TE process.
FIG. 5 is a statistical contribution percentage of each slow feature based on the conventional slow feature ranking for the multi-block fault monitoring method based on fault-sensitive slow features of the present invention.
FIG. 6 is a statistical contribution percentage of slow features after reordering based on fault sensitivity of the multi-block fault monitoring method based on fault sensitivity slow features of the present invention.
Detailed Description
In order to make the aforementioned objects, features and advantages of the present invention comprehensible, embodiments accompanied with figures are described in detail below.
In the following description, numerous specific details are set forth in order to provide a thorough understanding of the present invention, but the present invention may be practiced in other ways than those specifically described and will be readily apparent to those of ordinary skill in the art without departing from the spirit of the present invention, and therefore the present invention is not limited to the specific embodiments disclosed below.
Furthermore, reference herein to "one embodiment" or "an embodiment" means that a particular feature, structure, or characteristic described in connection with the embodiment is included in at least one implementation of the invention. The appearances of the phrase "in one embodiment" in various places in the specification are not necessarily all referring to the same embodiment, nor are separate or alternative embodiments mutually exclusive of other embodiments.
Furthermore, the present invention is described in detail with reference to the schematic drawings, and in the detailed description of the embodiments of the present invention, the cross-sectional views illustrating the device structure are not enlarged partially according to the general scale for the convenience of illustration, and the schematic drawings are only examples, which should not limit the scope of the present invention. In addition, the three-dimensional dimensions of length, width and depth should be included in the actual fabrication.
Example 1
Referring to fig. 1, there is provided an overall structural diagram of a multi-block fault monitoring method based on a fault sensitivity slow characteristic, as shown in fig. 1, the multi-block fault monitoring method based on the fault sensitivity slow characteristic comprises the steps of,
s1: collecting data in an industrial production system, and dividing the obtained data into a training set and a test set;
s2: carrying out slow feature analysis on the training set, and calculating a slow feature transformation matrix;
s3: defining a fault sensitivity coefficient, and obtaining the sensitivity of each slow characteristic to the fault through the coefficient in the slow characteristic transformation matrix;
s4: defining a fault sensitivity degree threshold, selecting a fault sensitivity slow characteristic for each dimensional variable of a training set, and using the fault sensitivity slow characteristic as a training sub-block;
s5: respectively calculating fault statistics for each training sub-block, and calculating the radius of a hypersphere as a fault control limit by adopting a Support Vector Data Description (SVDD) model;
s6: and respectively calculating fault statistics for each test sample, substituting the fault statistics into a Support Vector Data Description (SVDD) model to calculate the distance from the center of the sphere, and judging whether a fault occurs or not by comparing the distance with the center of the sphere and the radius.
Aiming at a dynamic large-scale industrial process, the invention provides a concept of fault sensitivity slow characteristics, defines a fault sensitivity degree coefficient through the analysis of a statistical calculation formula, reorders the slow characteristics, and selects the slow characteristics which are most sensitive to faults in a variable direction; then based on the thought of multi-block monitoring, each dimension variable is selected for sensitive slow characteristics and is monitored in parallel, so that the fault can be effectively monitored in any dimension no matter where the fault occurs; and finally, sub-block monitoring results are fused into a visual monitoring result through SVDD, so that a multi-block monitoring method is provided for dynamic fault monitoring.
Specifically, the method comprises the following steps of,
s1: collecting data in an industrial production system, and dividing the data into a training set and a test set;
wherein, the step of collecting data in the industrial production system and dividing the data into a training set and a test set comprises:
s11: data in an industrial production system (Tennessee-Ismann process, blast furnace ironmaking production equipment) is collected through a sensor; it should be noted that the sensors are temperature sensors, pressure sensors, flow sensors, etc., and the industrial production system is equipment related to the Tennessee-Ishman process or the blast furnace iron-making industrial production line, such as a reactor, a condenser, a compressor, a separator, a stripping tower, etc.;
s12: dividing the obtained data into normal data and fault data according to different working conditions; the acquisition working condition comprises a normal working condition and a fault working condition;
s13: taking normal data as a training set and taking fault data as a test set;
s14: and respectively carrying out standardization processing on the normal data and the fault data.
It should be noted that the training set standardization processing steps include:
calculating the average value mu of the training set X;
calculating the standard deviation of the training set X;
standardized training set
It is emphasized that the mean and standard deviation of the test set Y were the mean and standard deviation of the training set.
S2: carrying out slow feature analysis on the training set, and calculating a slow feature transformation matrix;
the method comprises the following steps of carrying out slow feature analysis on a training set, and calculating a slow feature transformation matrix:
giving an m-dimensional time sequence signal, and arranging according to a sequence from slow to fast;
the problem of slow characteristic is converted into an optimization problem;
transforming the linear slow characteristic analysis;
whitening the data by adopting SVD;
converting the optimization problem into a solution orthogonal matrix;
and acquiring a slow feature transformation matrix according to the whitening matrix and the orthogonal matrix.
Specifically, the slow feature analysis and the calculation of the slow feature transformation matrix are as follows: given an m-dimensional timing signal x (t) ═ x1(t),x2(t),...,xm(t)]The objective of slow feature analysis is to find a transformation function g (t) ═ g1(t),g2(t),...,gm(t)]To ensure that the extracted target feature s (t) ═ g [ x (t) ]]＝[s1(t),s2(t),...,sm(t)]The arrangement is performed in the order from slow to fast. The problem of extracting slow features can be transferred to the following optimization problem:
<si>teither 0 (zero mean constraint)
<si,sj>t0, i ≠ j (uncorrelated constraints)
Wherein s isiIs the ith slow feature; Δ s is the first difference of the slow features;<·>is expected for the sequence.
The linear slow signature analysis can be transformed into the form:
s(t)＝Wx(t)
where W is the transformation matrix.
To calculate W, the SVD decomposition is first employed and the data is whitened to satisfy the above constraints. R ═<x(t)x(t)T>tAnd (3) carrying out SVD (singular value decomposition) on the covariance matrix of x (t):
R＝UΛUT
wherein, U is an eigenvector matrix, Λ is a diagonal matrix containing eigenvalues, and the whitening matrix is Q ═ Λ-1/2UT。
The whitened data (i.e., training set) can be written as:
z＝Λ-1/2UTx＝Qx
wherein "z" represents data after whitening processing is performed on original data;
thus, the slow feature can be obtained by:
s＝Wx＝WQ-1z＝Pz
wherein "P" is a slow feature extracted from the training set, where P ═ WQ-1。
Because of this, it is possible to reduce the number of the,<z>t0, the first constraint is satisfied.
Constraints two and three are equivalent to the following equations:
<ssT>＝P<zzT>tPT＝PPT＝I
thus, the above optimization problem can be further translated into solving the orthogonal matrix P, such that
And minimum. By pairs<(Δz)(Δz)T>By performing SVD (representing singular value decomposition) decomposition, the following can be obtained:
<(Δz)(Δz)T>t＝PTΩP
where Δ z represents the difference in z;
the slow signature transformation matrix W can then be derived from the following equation:
W＝PQ＝PΛ-1/2UT
s3: defining a fault sensitivity coefficient, and obtaining the sensitivity of each slow characteristic to the fault through the coefficient in the slow characteristic transformation matrix;
wherein the fault sensitivity coefficient is defined as follows:
ij＝|wij|
whereinijIs the sensitivity coefficient, w, of the ith slow characteristic to the occurrence of a fault on the jth dimension variableijThe element in the ith row and the jth column of the slow feature transformation matrix is used.
S4: defining a fault sensitivity degree threshold, selecting a fault sensitivity slow characteristic for each dimensional variable of a training set, and using the fault sensitivity slow characteristic as a training sub-block;
wherein, the fault sensitivity threshold is defined as follows:
wherein isjlimA threshold for the fault sensitive slow feature is selected in the jth variable dimension,
the maximum fault sensitivity coefficient on the jth variable dimension is mu, and mu is a coefficient between 0 and 1.
S5: respectively calculating fault statistics for each training sub-block, and calculating the radius of a hypersphere as a fault control limit by adopting a Support Vector Data Description (SVDD) model;
wherein: the fault statistics in the slow feature analysis model are calculated as follows:
wherein s iskSlow feature matrix selected by fault sensitivity
The fault statistics and fault control limits under the Support Vector Data Description (SVDD) model are as follows:
s.t.||Φ(yi)-a||2≤R2+ξi
wherein R is the radius of the hyper-sphere, a is the center of the hyper-sphere, a penalty factor C balances the volume of the hyper-sphere and the error rate of the training sample, and xiiIs the relaxation variable. The optimization problem of the above formula can be converted into an optimization problem for solving the dual problem:
where K is the kernel function, alphaiIs a lagrange multiplier; x is the number ofiAnd xjfor the ith and jth training samples, and the support vector is such that 0 < alphai< sample of C.
By solving this optimization problem, the radius of the hyper-sphere can be obtained:
as a new fault control limit.
S6: and respectively calculating fault statistics for each test sample, substituting the fault statistics into a Support Vector Data Description (SVDD) model to calculate the distance from the center of the sphere, and judging whether a fault occurs or not by comparing the distance with the center of the sphere and the radius.
The distance between the test sample and the center of the hyper-sphere is as follows:
as new fault statistics.
If the distance between the test sample and the center of the hyper-sphere is larger than the radius of the hyper-sphere, the over-limit is determined as the over-limit, the over-limit indicates that a fault occurs, the fault is isolated, and an alarm prompt is sent; not overrun, indicating normal.
Example 2
In order to verify the effectiveness and feasibility of the method, five main units are established on a Tennessee Eastman (TE) software platform: the reactor, condenser, compressor, separator and stripper, as shown in fig. 1, contain 22 process measurement variables, 19 constituent measurement variables and 12 operating variable simulation models, it is noted that TE process models are created by eastman chemical company and used to evaluate a realistic industrial process of process control and monitoring methods; in the TE process, 21 different types of faults are preset, wherein the fault types comprise step change, random change, slow drift and valve viscosity, 16 faults are known faults, and 5 faults are unknown faults; in the experiment, 960 samples under normal working conditions are used as a training data set, 960 samples under fault working conditions are used as a fault test set, faults are introduced from the 161 st sample point, and table 1 shows 21 fault descriptions of the TE process.
TABLE 1TE Process Fault description
By adopting the fault sensitivity slow characteristic-based multi-block fault monitoring method provided by the invention, 33 variables in total of 22 process measurement variables and 11 operation variables except the stirring speed in the TE process are selected for modeling and monitoring, as shown in Table 2. Carrying out slow characteristic analysis on the training data set to obtain a slow characteristic transformation matrix W; by defined fault sensitivity factorijAnd a threshold valuejlim(the value of mu in the method is selected to be 0.6) 33 dimensional variables are respectively selected for fault sensitivity slow characteristics, so that 33 subblocks can be obtained, and the specific blocking result is shown in table 3.
TABLE 2TE Process monitoring variables
Table 3 subblock division results
| Number of sub-blocks | Slow feature number | Number of sub-blocks | |
| 1 | 16,25,27 | 18 | 5 |
| 2 | 16,21,32 | 19 | 13,30 |
| 3 | 6,7,8,9,20,28 | 20 | 4,16,23 |
| 4 | 11 | 21 | 32 |
| 5 | 14,15,19,30 | 22 | 5,31 |
| 6 | 18 | 23 | 7,9,12,14,26,32 |
| 7 | 12,21,26,27 | 24 | 7,8,9,20,28 |
| 8 | 14,17,23,25,31 | 25 | 16,25,27 |
| 9 | 11,15,21,26,33 | 26 | 12,17,27 |
| 10 | 18,21,28,29,30 | 27 | 17,21,22,29,31 |
| 11 | 4,8,10,11,22,23,31,32 | 28 | 18,21,27,28,29,30 |
| 12 | 22,28,30 | 29 | 22,28,30 |
| 13 | 12,14,23,26,27 | 30 | 24 |
| 14 | 16,19,23,25,30,31 | 31 | 5,13 |
| 15 | 24 | 32 | 11,15,33 |
| 16 | 14,21,22,23 | 33 | 3,4,5 |
| 17 | 3,4,5 |
Table 4 shows the results of monitoring 18 kinds of faults in the TE process by the conventional PCA fault monitoring method and the method of the present invention, and faults 3, 9, and 15 are difficult to be monitored in many ways, so no comparison is made here. It can be seen that the monitoring results of the method of the invention under all fault conditions are superior to the traditional PCA fault monitoring method (the numerical meaning in the table is fault detection rate, and the larger the numerical value is, the better the monitoring effect is).
To further illustrate the performance of the method of the present invention, a fault 16 is selected for detailed analysis. FIGS. 5 and 6 show the PCA method and the monitoring results under the method of the present invention. It can be seen from the figure that the fault monitoring effect under the method of the invention is obviously better than that under the PCA method, and the fault detection rate reaches 0.95. FIG. 5 is a graph of the percentage contribution of statistics corresponding to each slow feature when sorted by conventional slow feature, indicating the sensitivity to the fault. As can be seen from the graph, when the slowest feature is selected to monitor the fault, the largest statistic contribution may not be obtained because the slowest feature is not necessarily the most sensitive to the fault. Fig. 6 shows the percentage contribution of statistics corresponding to slow features in sub-block 31 after reordering the fault sensitivity. Since the variable 31 is the main cause of the fault 16, the sensitivity of the slow features sorted by the sensitivity coefficient in the sub-block 31 to the fault is sequentially reduced, so that it is ensured that the slow features selected according to the threshold are always most sensitive to the fault, and the monitoring performance of the model is further improved.
It is important to note that the construction and arrangement of the present application as shown in the various exemplary embodiments is illustrative only. Although only a few embodiments have been described in detail in this disclosure, those skilled in the art who review this disclosure will readily appreciate that many modifications are possible (e.g., variations in sizes, dimensions, structures, shapes and proportions of the various elements, values of parameters (e.g., temperatures, pressures, etc.), mounting arrangements, use of materials, colors, orientations, etc.) without materially departing from the novel teachings and advantages of the subject matter recited in this application. For example, elements shown as integrally formed may be constructed of multiple parts or elements, the position of elements may be reversed or otherwise varied, and the nature or number of discrete elements or positions may be altered or varied. Accordingly, all such modifications are intended to be included within the scope of this invention. The order or sequence of any process or method steps may be varied or re-sequenced according to alternative embodiments. In the claims, any means-plus-function clause is intended to cover the structures described herein as performing the recited function and not only structural equivalents but also equivalent structures. Other substitutions, modifications, changes and omissions may be made in the design, operating conditions and arrangement of the exemplary embodiments without departing from the scope of the present inventions. Therefore, the present invention is not limited to a particular embodiment, but extends to various modifications that nevertheless fall within the scope of the appended claims.
Moreover, in an effort to provide a concise description of the exemplary embodiments, all features of an actual implementation may not be described (i.e., those unrelated to the presently contemplated best mode of carrying out the invention, or those unrelated to enabling the invention).
It should be appreciated that in the development of any such actual implementation, as in any engineering or design project, numerous implementation-specific decisions may be made. Such a development effort might be complex and time consuming, but would nevertheless be a routine undertaking of design, fabrication, and manufacture for those of ordinary skill having the benefit of this disclosure, without undue experimentation.
It should be noted that the above-mentioned embodiments are only for illustrating the technical solutions of the present invention and not for limiting, and although the present invention is described in detail with reference to the preferred embodiments, it should be understood by those skilled in the art that modifications or equivalent substitutions can be made on the technical solutions of the present invention without departing from the spirit and scope of the technical solutions of the present invention, which should be covered by the claims of the present invention.
Claims (10)
1. A multi-block fault monitoring method based on fault sensitivity slow characteristics is characterized in that: comprises the steps of (a) preparing a mixture of a plurality of raw materials,
collecting data in an industrial production system, and dividing the obtained data into a training set and a test set;
carrying out slow feature analysis on the training set, and calculating a slow feature transformation matrix;
defining a fault sensitivity coefficient, and obtaining the sensitivity of each slow characteristic to the fault through the coefficient in the slow characteristic transformation matrix;
defining a fault sensitivity degree threshold, selecting a fault sensitivity slow characteristic for each dimensional variable of a training set, and using the fault sensitivity slow characteristic as a training sub-block;
respectively calculating fault statistics for each training sub-block, and calculating the radius of the hypersphere as a fault control limit by adopting a support vector data description model;
and respectively calculating fault statistics for each test sample, substituting the fault statistics into a support vector data description model to calculate the distance from the center of the sphere, and judging whether a fault occurs or not by comparing the distance with the center of the sphere and the radius.
2. The multi-block fault monitoring method based on fault-sensitive slow features of claim 1, characterized in that: the step of collecting data in the industrial production system and dividing the data into a training set and a test set comprises the following steps:
collecting data in an industrial production system through a sensor;
dividing the data into normal data and fault data according to different working conditions;
taking normal data as a training set and taking fault data as a test set;
and respectively carrying out standardization processing on the training set and the test set.
3. The multi-block fault monitoring method based on fault-sensitive slow features as claimed in claim 2, characterized in that: the sensors are temperature sensors, pressure sensors and flow sensors.
4. A multi-block fault monitoring method based on fault-sensitive slow characteristics as claimed in claim 2 or 3, characterized in that: the training set standardization processing step comprises:
calculating the average value mu of the training set X;
calculating the standard deviation of the training set X;
standardized training set
5. The multi-block fault monitoring method based on fault-sensitive slow features of claim 4, wherein: the average value and the standard deviation of the standard treatment of the test set Y adopt the average value and the standard deviation of a training set;
wherein, the standardized test set Y:
6. the multi-block fault monitoring method based on fault-sensitive slow features of claim 5, wherein: and slow feature analysis is carried out on the training set, and the step of calculating the slow feature transformation matrix is as follows:
giving an m-dimensional time sequence signal, and arranging according to a sequence from slow to fast;
the problem of slow characteristic is converted into an optimization problem;
transforming the linear slow characteristic analysis;
whitening the data by adopting SVD;
converting the optimization problem into a solution orthogonal matrix;
and acquiring a slow feature transformation matrix according to the whitening matrix and the orthogonal matrix.
7. The multi-block fault monitoring method based on fault-sensitive slow features as claimed in claim 5 or 6, characterized in that: the fault sensitivity coefficient is defined as:
ij＝|wij|
wherein the content of the first and second substances,ijis the sensitivity coefficient, w, of the ith slow characteristic to the occurrence of a fault on the jth dimension variableijThe element in the ith row and the jth column of the slow feature transformation matrix is used.
8. The multi-block fault monitoring method based on fault-sensitive slow features of claim 7, wherein: the fault sensitivity threshold is defined as:
wherein the content of the first and second substances,jlima threshold for the fault sensitive slow feature is selected for the jth variable dimension,
the maximum fault sensitivity coefficient on the jth variable dimension is mu, and mu is a coefficient between 0 and 1.
9. The multi-block fault monitoring method based on fault-sensitive slow features of claim 8, wherein: the fault statistics in the slow feature analysis model are calculated as follows:
wherein s iskA slow feature matrix selected by fault sensitivity.
10. The multi-block fault monitoring method based on fault-sensitive slow features as claimed in claim 8 or 9, characterized in that: the fault statistics and fault control limits under the support vector data description model are as follows:
s.t.||Φ(yi)-a||2≤R2+ξi
wherein R is the radius of the hyper-sphere, a is the center of the hyper-sphere, a penalty factor C balances the volume of the hyper-sphere and the error rate of the training sample, and xiiIs the relaxation variable.
Wherein the optimization problem of the above formula can be converted into an optimization problem for solving its dual problem:
where K is the kernel function, alphaiIs a lagrange multiplier; x is the number ofiAnd xjfor the ith and jth training samples, the support vector is such that 0 < alphaiSamples of < C;
wherein, by solving this optimization problem, the radius of the hyper-sphere can be obtained:
wherein, the distance between the test sample and the center of the hyper-sphere is as follows:
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