CN110794797A - PCA fault monitoring method based on mutual information and multi-block information extraction - Google Patents

PCA fault monitoring method based on mutual information and multi-block information extraction Download PDF

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CN110794797A
CN110794797A CN201911185101.XA CN201911185101A CN110794797A CN 110794797 A CN110794797 A CN 110794797A CN 201911185101 A CN201911185101 A CN 201911185101A CN 110794797 A CN110794797 A CN 110794797A
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熊伟丽
翟超
马君霞
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Jiangnan University
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Abstract

The invention discloses a PCA fault monitoring method based on mutual information and multi-block information extraction, which comprises the steps of collecting data in an industrial production system, and dividing the data into a training set and a test set; calculating mutual information values among variables in a training set, partitioning the variables according to the mutual information values, and partitioning the variables in a testing set according to the variable partitioning results of the training set; respectively extracting characteristic information from each subblock after being partitioned, wherein the characteristic information of the training set and the training set jointly form a new training information block, and the characteristic information of the test set and the test set jointly form a new test information block; the method provided by the invention has the advantages that the correlation among variables is considered, meanwhile, the implicit information of data is mined, the process variables are partitioned by calculating mutual information values among the process variables, then, the accumulated error information and the second-order difference information are extracted from each variable block, and each variable block is expanded into three characteristic information subblocks together with the observed value information.

Description

PCA fault monitoring method based on mutual information and multi-block information extraction
Technical Field
The invention relates to the technical field of fault monitoring and diagnosis in an industrial production process, in particular to a PCA fault monitoring method based on mutual information and multi-block information extraction.
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, these methods are all to establish a global model, do not consider local information in the production process, and easily ignore locally generated faults.
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. Scholars both at home and abroad have proposed a variety of multi-block monitoring methods to obtain the relationships between complex process variables and to reflect the local characteristics of the process.
The multi-block monitoring method based on variable blocking obtains a monitoring effect superior to a single model by blocking the variables through constructing some rules on the basis of analyzing the relation among the process variables, but only uses the observed values of the process variables and does not mine other effective information implicit in the process data.
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 provides a PCA fault monitoring method based on mutual information and multi-block information extraction, which solves the problem that the monitoring effect is poor because the hidden information of a data center cannot be mined while the correlation of variables is considered.
Therefore, the invention aims to provide a PCA fault monitoring method based on mutual information and multi-block information extraction.
In order to solve the technical problems, the invention provides the following technical scheme: a PCA fault monitoring method based on mutual information and multi-block information extraction comprises,
collecting data in an industrial production system, and dividing the obtained data into a training set and a test set;
calculating mutual information values among variables in a training set, partitioning the variables according to the mutual information values, and partitioning the variables in a testing set according to the variable partitioning results of the training set;
respectively extracting characteristic information from each subblock after being partitioned, wherein the characteristic information of the training set and the training set jointly form a new training information block, and the characteristic information of the test set and the test set jointly form a new test information block;
establishing PCA models for the generated training information blocks respectively, calculating fault control limits by using a training set, and calculating monitoring statistics by using a test set;
and calculating the BIC statistic and the BIC control limit through Bayesian inference, and judging whether the control limit is exceeded or not to obtain a final monitoring result.
As a preferred scheme of the PCA fault monitoring method based on mutual information and multi-block information extraction of the present invention, wherein: the steps of collecting data in an industrial production system and dividing the obtained data into a training set and a test set include:
collecting data in an industrial production system through a sensor;
dividing the obtained 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 normal data and the fault data.
As a preferred scheme of the PCA fault monitoring method based on mutual information and multi-block information extraction of the present invention, wherein: the training set standardization processing step comprises:
calculating the average value mu of the training set X;
calculating the standard deviation delta of the training set X;
standardized training set
Figure BDA0002292207860000021
Wherein, the mean value and standard deviation of the test set Y adopt the mean value and standard deviation of the training set.
As a preferred scheme of the PCA fault monitoring method based on mutual information and multi-block information extraction of the present invention, wherein: the formula for calculating mutual information is as follows:
I(x,y)＝H(x)+H(y)-H(x,y)
in the formula, I (x, y) represents mutual information values of variables x and y, H (x) and H (y) are respectively edge entropies of the two variables, and H (x, y) is a joint entropy of the two variables;
wherein, the calculation formula of the edge entropy H (x) of the variable x is as follows:
H(x)＝-∫xp(x)logp(x)dx
the calculation formula of the edge entropy H (y) of the variable y is as follows:
H(y)＝-∫yp(y)logp(y)dy
wherein, the calculation formula of the joint entropy H (x, y) of the variable x and the variable y is as follows:
H(x,y)＝-∫∫x,yp(x,y)logp(x,y)dxdy。
as a preferred scheme of the PCA fault monitoring method based on mutual information and multi-block information extraction of the present invention, wherein: the characteristic information comprises accumulated error information and second-order difference information;
the accumulated error information is obtained by calculating the difference between the accumulated training set in a certain time period and the average value of the training set;
and the second-order difference information is used for carrying out primary difference on the data and then carrying out primary difference on the data after difference.
As a preferred scheme of the PCA fault monitoring method based on mutual information and multi-block information extraction of the present invention, wherein: under the normal working condition after normalization, the training set is X ∈ Rn×m(n is the number of samples, m is the number of sample dimensions), the value of which is 0;
setting the standard value as the mean value of the variable, and directly adding the sample values to obtain the accumulated error information;
constructing a new data set X by using the accumulated error information of the previous T moments as new characteristic informationl∈R(n-T)×m；
Wherein, the accumulated error information x at the time tl(t) is:
Figure BDA0002292207860000031
where x (t) is the sample at time t in the raw process variable data, xl(t) represents the accumulated error information at time t, and x (t-l) represents the sample value at time one before time t.
As a preferred scheme of the PCA fault monitoring method based on mutual information and multi-block information extraction of the present invention, wherein: the training set after the standardization is X epsilon Rn×mConstructing a new feature data set X by calculating a second order difference for each time variabled∈R(n-2)×mThe second order difference information at time t is:
xd(t)＝(x(t)-x(t-1))-(x(t-1)-x(t-2))
in the formula, xd(t) is second order difference information at time t, and x (t) is raw data normalized at time t.
As a preferred scheme of the PCA fault monitoring method based on mutual information and multi-block information extraction of the present invention, wherein: the process of establishing the PCA model is as follows:
the process training set subjected to standardized preprocessing is X epsilon Rn×mPerforming principal component analysis can obtain:
X＝TPT+E
in the formula, T is belonged to Rn×kScoring the matrix for the pivot, P ∈ Rm×kFor the load matrix, E ∈ Rn×mIs a residual matrix.
As a preferred scheme of the PCA fault monitoring method based on mutual information and multi-block information extraction of the present invention, wherein: respectively building the generated training information blocksEstablishing PCA model, calculating fault control limit with training set, calculating monitoring statistic with testing set, and constructing T in principal component space and residual space2And SPE statistics.
As a preferred scheme of the PCA fault monitoring method based on mutual information and multi-block information extraction of the present invention, wherein: the process of calculating BIC statistic by Bayesian inference is as follows:
in Bayesian inference, test set xtestIn the ith sub-block T2The conditional probability of a statistical fault can be expressed as:
wherein the conditional probability
Figure BDA0002292207860000043
And
Figure BDA0002292207860000044
the definition is as follows:
Figure BDA0002292207860000045
Figure BDA0002292207860000046
wherein N and F represent normal and fault conditions, respectively;
Figure BDA0002292207860000047
and
Figure BDA0002292207860000048
respectively as the prior probabilities of a normal sample and a fault sample;
Figure BDA0002292207860000049
t in ith sub-block for new sample2Statistics;
Figure BDA00022922078600000410
is T of the corresponding i-th sub-block2A control limit for the statistic;
the statistics after BIC fusion are as follows:
Figure BDA00022922078600000411
similarly, the SPE statistic after BIC fusion is:
the invention has the beneficial effects that: the method provided by the invention has the advantages that the correlation among variables is considered, meanwhile, the implicit information of data is mined, the process variables are partitioned by calculating mutual information values among the process variables, then, the accumulated error information and the second-order difference information are extracted from each variable block, each variable block is expanded into three characteristic information subblocks together with the observed value information, the monitoring results of each subblock are fused by adopting a Bayesian method to obtain the final monitoring result, and a multi-block modeling method is provided for fault monitoring.
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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 an industrial process of the PCA fault monitoring method based on mutual information and multi-block information extraction of the present invention.
FIG. 2 is a modeling flow chart of the PCA fault monitoring method based on mutual information and multi-block information extraction.
FIG. 3 is a diagram of mutual information values between variables of the PCA fault monitoring method based on mutual information and multi-block information extraction.
Fig. 4 is a monitoring result diagram of a conventional method of the PCA fault monitoring method based on mutual information and multi-block information extraction according to the present invention.
Fig. 5 is a diagram of the monitoring result of the PCA fault monitoring method based on mutual information and multi-block information extraction for TE process faults.
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 drawings, and in the detailed description of the embodiments of the present invention, the cross-sectional view illustrating the structure of the device is not enlarged partially according to the general scale for convenience of illustration, and the drawings are only exemplary and should not be construed as limiting 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 structure diagram of a PCA fault monitoring method based on mutual information and multi-block information extraction, as shown in fig. 1, a PCA fault monitoring method based on mutual information and multi-block information extraction includes the steps of,
s1: collecting data in an industrial production system, and dividing the data into a training set and a test set;
s2: calculating mutual information values among variables in a training set, partitioning the variables according to the mutual information values, and partitioning the variables in a testing set according to the variable partitioning results of the training set;
s3: respectively extracting characteristic information from each subblock after being partitioned, wherein the characteristic information of the training set and the training set jointly form a new training information block, and the characteristic information of the test set and the test set jointly form a new test information block;
s4: establishing PCA models for the generated training information blocks respectively, calculating fault control limits by using a training set, and calculating monitoring statistics by using a test set;
s5: and calculating the BIC statistic and the BIC control limit through Bayesian inference, and judging whether the control limit is exceeded or not to obtain a final monitoring result.
The method provided by the invention has the advantages that the correlation among variables is considered, meanwhile, the implicit information of data is mined, the process variables are partitioned by calculating mutual information values among the process variables, then, the accumulated error information and the second-order difference information are extracted from each variable block, each variable block is expanded into three characteristic information subblocks together with the observed value information, the monitoring results of each subblock are fused by adopting a Bayesian method to obtain the final monitoring result, and a multi-block modeling method is provided for 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;
the method comprises the following steps of collecting data in an industrial production system, and dividing the data into a training set and a test set:
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 sensor is a temperature sensor, a pressure sensor, a flow sensor and the like, and the industrial production system is equipment related to a Tennessee-Ismann process or a blast furnace iron-making industrial production line, such as a reactor, a condenser, a compressor, a separator, a stripping tower and the like;
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 delta of the training set X;
standardized training set
Figure BDA0002292207860000071
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: calculating mutual information values among variables in a training set, partitioning the variables according to the mutual information values, and partitioning the variables in a testing set according to the variable partitioning results of the training set;
the mutual information calculation formula is as follows:
I(x,y)＝H(x)+H(y)-H(x,y)
in the formula, I (x, y) represents mutual information values of variables x and y, H (x) and H (y) are respectively edge entropies of the two variables, H (x, y) is joint entropy of the two variables, the dimension of the collected sample is the number of the variables, and the variables x and y only represent any two variables in the variables;
wherein, the calculation formula of the edge entropy H (x) of the variable x is as follows:
H(x)＝-∫xp(x)logp(x)dx
the calculation formula of the edge entropy H (y) of the variable y is as follows:
H(y)＝-∫yp(y)logp(y)dy
wherein, the calculation formula of the joint entropy H (x, y) of the variable x and the variable y is as follows:
H(x,y)＝-∫∫x,yp(x,y)logp(x,y)dxdy。
s3: respectively extracting characteristic information from each subblock after being partitioned, wherein the characteristic information of the training set and the training set jointly form a new training information block, and the characteristic information of the test set and the test set jointly form a new test information block;
the characteristic information comprises accumulated error information and second-order difference information;
the accumulated error information is obtained by calculating the difference between the accumulated training set in a certain time period and the average value of the training set;
and the second-order difference information is used for carrying out primary difference on the data and then carrying out primary difference on the data after the difference.
Specifically, the process of accumulating the error information is as follows: under the normal working condition after standardization (normal production process under the condition of no fault), the training set is X belonging to Rn×m(n is the number of samples, m is the number of sample dimensions), the value of which is 0;
setting the standard value as the mean value of the variable, and obtaining the accumulated error information by directly adding the sample values;
constructing a new data set X by using the accumulated error information of the previous T moments as new characteristic informationl∈R(n-T)×m；
Wherein, the accumulated error information x at the time tl(t) is:
where x (t) is the sample at time t in the raw process variable data, xl(t) represents the accumulated error information at time t, and x (t-l) represents the sample value at time one before time t
The second-order difference information process is as follows: the training set after the standardization is X epsilon Rn×mConstructing a new feature data set X by calculating a second order difference for each time variabled∈R(n-2)×mSecond order difference information at time tComprises the following steps:
xd(t)＝(x(t)-x(t-1))-(x(t-1)-x(t-2))
in the formula, xd(t) second order difference information at time t, and x (t) raw data normalized at time t
S4: establishing PCA models for the generated training information blocks respectively, calculating fault control limits by using a training set, and calculating monitoring statistics by using a test set;
the process of establishing the PCA model is as follows:
the process training set subjected to standardized preprocessing is X epsilon Rn×mPerforming principal component analysis can obtain:
X＝TPT+E
in the formula, T is belonged to Rn×kScoring the matrix for the pivot, P ∈ Rm×kFor the load matrix, E ∈ Rn×mIs a residual error matrix;
respectively establishing PCA models for the generated training information blocks, calculating fault control limits by using a training set, and calculating monitoring statistics by using a test set, wherein T is respectively constructed in a principal component space and a residual error space2And SPE statistics.
In the specific process, one test sample in the test set is set as x belonging to Rm×1Of which T2And SPE statistics are:
Figure BDA0002292207860000091
SPE＝xT(I-PPT)x≤SPElim
in the formula, Λ is a diagonal matrix formed by eigenvalues corresponding to the first k principal elements, I is an identity matrix,
Figure BDA0002292207860000092
and SPElimFor the control limit of the statistic, the calculation method is as follows:
Figure BDA0002292207860000093
wherein b is the number of principal elements, m is the number of variables, Fb,n-b,αIs the F distribution threshold with b, n-b degrees of freedom and α confidence,cαthe threshold values for the standard plus-minus distribution under a confidence level of α.
S5: and calculating the BIC statistic and the BIC control limit through Bayesian inference, and judging whether the control limit is exceeded or not to obtain a final monitoring result.
The process of calculating BIC statistic by Bayesian inference is as follows:
in Bayesian inference, test set xtestIn the ith sub-block T2The conditional probability of a statistical fault can be expressed as:
Figure BDA0002292207860000096
Figure BDA0002292207860000097
wherein the conditional probability
Figure BDA0002292207860000098
And
Figure BDA0002292207860000099
the definition is as follows:
Figure BDA00022922078600000910
Figure BDA0002292207860000101
wherein N and F represent normal and fault conditions, respectively;and
Figure BDA0002292207860000103
respectively as the prior probabilities of a normal sample and a fault sample;
Figure BDA0002292207860000104
t in ith sub-block for new sample2Statistics;
Figure BDA0002292207860000105
is T of the corresponding i-th sub-block2A control limit for the statistic;
the statistics after BIC fusion are as follows:
Figure BDA0002292207860000106
similarly, the SPE statistic after BIC fusion is:
Figure BDA0002292207860000107
wherein, the BIC statistic and the BIC control limit are calculated by Bayesian inference, and a fault control limit is respectively defined in the principal component space and the residual error space according to the PCA fault monitoring methodAnd SPElimIf T is2Statistics exceed or statistics exceed SPElimIf the fault is over-limit, the over-limit indicates that the fault occurs, fault isolation is carried out on the fault, 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 composition measurement variables and 12 manipulated variable simulation models, it is noted that TE process models are created by eastman chemical company and used to evaluate a realistic industrial process for process control and monitoring; 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 1 TE Process Fault description
Figure BDA0002292207860000109
Figure BDA0002292207860000111
By adopting the PCA fault monitoring method based on mutual information and multi-block information extraction provided by the invention, 33 variables in total of 22 process measurement variables and 11 operation variables except stirring speed in a TE process are selected for modeling and monitoring, as shown in Table 2; calculating mutual information values among the selected variables as shown in figure 3, wherein the mutual information values among most variables corresponding to the sizes (the range is 0-1) of the variables in different colors do not exceed 0.2, so that a mutual information threshold value is set to be 0.2, and if the mutual information values between two variables exceed the threshold value, when a fault occurs, the fault is affected similarly, and the fault is divided into sub-blocks to be easier to detect; for example, if the mutual information value of the variables 12 and 29 reaches 0.9966, and the mutual information value of the variables 15 and 30 is 0.9963, the variables 12 and 29 are divided into one block, similarly, the variables 15 and 30 are divided into one block, and the variables with mutual information values smaller than the threshold value 0.2 with all other variables are divided into one sub-block for monitoring. The specific variable blocking results are shown in table 3.
TABLE 2 TE Process monitoring variables
Figure BDA0002292207860000121
TABLE 3 variable blocking results
Sub-block numbering Variable number
1 12,29
2 15,30
3 17,33
4 1,25
5 18,19,31
6 7,13,16,20,27
7 10,28
8 2,3,4,5,6,8,9,11,14,21,22,23,24,26,32
Dividing 33 process variables into 8 blocks based on a mutual information method, further expanding each variable block into 3 information sub-blocks by extracting accumulated error, second-order difference and observation value information, and finally generating 24 sub-blocks, wherein 1-3 blocks are 3 characteristic information blocks corresponding to the variable block 1, and so on, and 22-24 blocks are 3 information sub-blocks corresponding to the variable block 8; table 4 shows the monitoring results of the conventional PCA fault monitoring method and the method of the present invention for 21 faults in the TE process, and it can be seen that the monitoring results of the method of the present invention are superior to those of the conventional PCA fault monitoring method under all fault conditions (the numerical meaning in the table is fault failure rate, and the smaller the numerical value is, the better the monitoring effect is).
TABLE 4 monitoring results of 21 kinds of failures in TE process under two methods
To further illustrate the performance of the process herein, failure 10, i.e., the random variation in C feed temperature, was chosen for detailed analysis.
FIGS. 4 and 5 show the results of the two methods, wherein the abscissa indicates the number of faulty samples, the first 160 samples are normal samples, and the samples are faulty samples from 161 sample points; the ordinate represents the statistic; in the figure, the horizontal line represents the fault control limit, and the sample is regarded as a fault sample when the statistic exceeds the fault control limit. As can be seen from FIG. 4, in the conventional PCA fault monitoring method, T2And SPE statistics only have a small amount of alarms between 280 th sample and 350 th sample and between 650 th sample and 800 th sample, and the fault is not detected in most cases, and as can be seen from Table 2, the fault report-missing rate is as high as 70%; in FIG. 5, BIC is shown in the present inventionSPEThe statistical quantity is almost lower than the fault control limit at the 161 th sample point, namely after the fault starts, the final fault report missing rate is only 15%, and the monitoring effect is far better than that of the PCA method.
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 has been described in detail with reference to the preferred embodiments, it should be understood by those skilled in the art that modifications or equivalent substitutions may 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 PCA fault monitoring method based on mutual information and multi-block information extraction 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;
calculating mutual information values among variables in a training set, partitioning the variables according to the mutual information values, and partitioning the variables in a testing set according to the variable partitioning results of the training set;
respectively extracting characteristic information from each subblock after being partitioned, wherein the characteristic information of the training set subblock and the training set subblock jointly form a new training information block, and the characteristic information of the test set subblock and the test set subblock jointly form a new test information block;
establishing PCA models for the generated training information blocks respectively, calculating fault control limits by using a training set, and calculating monitoring statistics by using a test set;
and calculating the BIC statistic and the BIC control limit through Bayesian inference, and judging whether the control limit is exceeded or not to obtain a final monitoring result.
2. The PCA fault monitoring method based on mutual information and multi-block information extraction as claimed in claim 1, wherein: 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 normal data and the fault data.
3. The PCA fault monitoring method based on mutual information and multi-block information extraction as claimed in claim 2, wherein: the training set standardization processing step comprises:
calculating the average value mu of the training set X;
calculating the standard deviation delta of the training set X;
standardized training set
And the mean value and the standard deviation in the standardized calculation of the test set Y adopt the mean value and the standard deviation of a training set.
4. The PCA fault monitoring method based on mutual information and multi-block information extraction as claimed in any one of claims 1 to 3, wherein: the formula for calculating the mutual information is as follows:
I(x,y)＝H(x)+H(y)-H(x,y)
in the formula, I (x, y) represents mutual information values of variables x and y, H (x) and H (y) are respectively edge entropies of the two variables, and H (x, y) is a joint entropy of the two variables;
wherein, the calculation formula of the edge entropy H (x) of the variable x is as follows:
H(x)＝-∫xp(x)log p(x)dx
the calculation formula of the edge entropy H (y) of the variable y is as follows:
H(y)＝-∫yp(y)log p(y)dy
wherein, the calculation formula of the joint entropy H (x, y) of the variable x and the variable y is as follows:
H(x,y)＝-∫∫x,yp(x,y)log p(x,y)dxdy
。
5. the PCA fault monitoring method based on mutual information and multi-block information extraction as claimed in claim 4, characterized in that: the characteristic information comprises accumulated error information and second-order difference information;
the accumulated error information is obtained by calculating the difference between the accumulated training set in a certain time period and the average value of the training set;
and the second-order difference information is used for carrying out primary difference on the data and then carrying out primary difference on the data after difference.
6. The PCA fault monitoring method based on mutual information and multi-block information extraction of claim 5, wherein: under the normal working condition after standardization, the training set is X epsilon Rn×m(n is the number of samples, m is the number of sample dimensions), the value of which is 0;
setting the standard value as the mean value of the variable, and directly adding the sample values to obtain the accumulated error information;
constructing a new data set X by using the accumulated error information of the previous T moments as new characteristic informationl∈R(n-T)×m；
Wherein, the accumulated error information x at the time tl(t) is:
where x (t) is the sample at time t in the raw process variable data, xl(t) represents the accumulated error information at time t, and x (t-l) represents the sample value at time one before time t.
7. The PCA fault monitoring method based on mutual information and multi-block information extraction as claimed in claim 5 or 6, wherein: the training set after the standardization is X epsilon Rn×mConstructing a new feature data set X by calculating a second order difference for each time variabled∈R(n-2)×mThe second order difference information at time t is:
xd(t)＝(x(t)-x(t-1))-(x(t-1)-x(t-2))
in the formula, xd(t) is second order difference information at time t, and x (t) is raw data normalized at time t.
8. The PCA fault monitoring method based on mutual information and multi-block information extraction of claim 7, wherein: the process of establishing the PCA model is as follows:
the process training set subjected to standardized preprocessing is X epsilon Rn×mPerforming principal component analysis can obtain:
X＝TPT+E
in the formula, T is belonged to Rn×kScoring the matrix for the pivot, P ∈ Rm×kFor the load matrix, E ∈ Rn×mIs a residual matrix.
9. The PCA fault monitoring method based on mutual information and multi-block information extraction of claim 8, wherein: respectively establishing PCA models for the generated training information blocks, calculating fault control limits by using a training set, and calculating monitoring statistics by using a test set, wherein T is respectively constructed in a principal component space and a residual error space2And SPE statistics.
10. The PCA fault monitoring method based on mutual information and multi-block information extraction of claim 9, wherein: the process of calculating BIC statistic by Bayesian inference is as follows:
in Bayesian inference, test set xtestIn the ith sub-block T2The conditional probability of a statistical fault can be expressed as:
Figure FDA0002292207850000031
wherein the conditional probability
Figure FDA0002292207850000033
And
Figure FDA0002292207850000034
the definition is as follows:
Figure FDA0002292207850000035
wherein N and F represent normal and fault conditions, respectively;
Figure FDA0002292207850000037
and
Figure FDA0002292207850000038
respectively as the prior probabilities of a normal sample and a fault sample;t in ith sub-block for new sample2Statistics;
Figure FDA00022922078500000310
is T of the corresponding i-th sub-block2A control limit for the statistic;
the statistics after BIC fusion are as follows:
Figure FDA0002292207850000041
similarly, the SPE statistic after BIC fusion is:
Figure FDA0002292207850000042
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Cited By (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN111324110A (en) * 2020-03-20 2020-06-23 北京工业大学 Fermentation process fault monitoring method based on multiple shrinkage automatic encoders
CN112000081A (en) * 2020-08-31 2020-11-27 江南大学 Fault monitoring method and system based on multi-block information extraction and Mahalanobis distance
CN112184034A (en) * 2020-09-30 2021-01-05 江南大学 Multi-k neighbor fault monitoring method and system based on mutual information
CN112947649A (en) * 2021-03-19 2021-06-11 安阳师范学院 Multivariate process monitoring method based on mutual information matrix projection
CN115291582A (en) * 2022-02-22 2022-11-04 江南大学 Method, device and equipment for monitoring faults in iron-making process

Citations (6)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US20110191076A1 (en) * 2008-10-09 2011-08-04 Shunji Maeda Error detection method and system
CN103853152A (en) * 2014-03-21 2014-06-11 北京工业大学 Batch process failure monitoring method based on AR-PCA (Autoregressive Principal Component Analysis)
CN105955219A (en) * 2016-05-30 2016-09-21 宁波大学 Distributed dynamic process fault detection method based on mutual information
CN106529079A (en) * 2016-11-29 2017-03-22 上海电机学院 Chemical process failure detection method based on failure-dependent principal component space
CN108762228A (en) * 2018-05-25 2018-11-06 江南大学 A kind of multi-state fault monitoring method based on distributed PCA
CN109189028A (en) * 2018-10-15 2019-01-11 江南大学 PCA method for diagnosing faults based on muti-piece information extraction

Patent Citations (6)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US20110191076A1 (en) * 2008-10-09 2011-08-04 Shunji Maeda Error detection method and system
CN103853152A (en) * 2014-03-21 2014-06-11 北京工业大学 Batch process failure monitoring method based on AR-PCA (Autoregressive Principal Component Analysis)
CN105955219A (en) * 2016-05-30 2016-09-21 宁波大学 Distributed dynamic process fault detection method based on mutual information
CN106529079A (en) * 2016-11-29 2017-03-22 上海电机学院 Chemical process failure detection method based on failure-dependent principal component space
CN108762228A (en) * 2018-05-25 2018-11-06 江南大学 A kind of multi-state fault monitoring method based on distributed PCA
CN109189028A (en) * 2018-10-15 2019-01-11 江南大学 PCA method for diagnosing faults based on muti-piece information extraction

Non-Patent Citations (2)

* Cited by examiner, † Cited by third party
Title
郭金玉 等: ""基于加权差分主元分析的化工过程故障检测"", 《高校化学工程学报》 *
陈兴同: "《信息论与编码简明教程》", 31 July 2016, 中国矿业大学出版社 *

Cited By (6)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN111324110A (en) * 2020-03-20 2020-06-23 北京工业大学 Fermentation process fault monitoring method based on multiple shrinkage automatic encoders
CN112000081A (en) * 2020-08-31 2020-11-27 江南大学 Fault monitoring method and system based on multi-block information extraction and Mahalanobis distance
CN112184034A (en) * 2020-09-30 2021-01-05 江南大学 Multi-k neighbor fault monitoring method and system based on mutual information
CN112184034B (en) * 2020-09-30 2024-04-09 江南大学 Multi-block k-nearest neighbor fault monitoring method and system based on mutual information
CN112947649A (en) * 2021-03-19 2021-06-11 安阳师范学院 Multivariate process monitoring method based on mutual information matrix projection
CN115291582A (en) * 2022-02-22 2022-11-04 江南大学 Method, device and equipment for monitoring faults in iron-making process

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