CN114854920A - Blast furnace abnormity monitoring method of GRU self-encoder embedded with Gaussian mixture model - Google Patents

Blast furnace abnormity monitoring method of GRU self-encoder embedded with Gaussian mixture model Download PDF

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CN114854920A
CN114854920A CN202210486776.3A CN202210486776A CN114854920A CN 114854920 A CN114854920 A CN 114854920A CN 202210486776 A CN202210486776 A CN 202210486776A CN 114854920 A CN114854920 A CN 114854920A
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杨春节
朱雄卓
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Zhejiang University ZJU
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Abstract

The invention discloses a Gaussian mixture model embedded GRU self-encoder blast furnace abnormity monitoring method, which utilizes GRU as an encoder to capture the dynamic characteristic of data; then, clustering data in the hidden variable space by using a Gaussian mixture model, and adapting to different working modes of the blast furnace; reconstructing the hidden variable by a decoder to obtain a reconstruction error, calculating SPE statistic and an upper limit thereof based on probability to realize the monitoring purpose, and calculating the correlation degree of different variables and faults according to reconstruction error increment when the faults occur; the dynamic characteristics of capturing data using the GRU as an encoder are: the self-encoder is divided into an encoder part and a decoder part, and the GRU is used as the encoder part of the self-encoder. The invention effectively reduces the false alarm rate of the algorithm, can early warn the process fault in time and provides fault related variable information.

Description

Gaussian mixture model embedded GRU self-encoder blast furnace abnormity monitoring method
Technical Field
The invention belongs to the field of industrial process monitoring, and particularly relates to a method for monitoring the abnormity of a blast furnace with a GRU self-encoder embedded in a Gaussian mixture model.
Technical Field
The steel industry is an important supporting industry of modern industry and national economy in China and is also an important and inseparable component of national economy. Blast furnace iron making is a core link of the whole iron and steel industry and is a key process of mass flow conversion in the iron and steel manufacturing process, and the energy consumption of the blast furnace iron making accounts for 70 percent of the total energy consumption of iron and steel production. The realization of safe operation in the blast furnace ironmaking process is the key point of deep energy conservation, emission reduction, quality improvement and efficiency improvement in the steel industry, and an accurate abnormity monitoring model can provide early warning for an operator in time, adjust the furnace condition in advance and avoid the occurrence of dangerous conditions.
In the blast furnace iron-making process, due to the reasons of raw material quality fluctuation, misoperation of personnel, equipment abnormity and the like, the abnormal condition of the blast furnace sometimes occurs. Once the condition of the blast furnace is abnormal, the problems of fuel ratio increase, increase of downtime maintenance time, substandard molten iron quality and the like are often caused, so that not only can the major loss of resources and equipment be caused, the furnace life of the blast furnace be reduced, but also the casualties can be caused even by accidents. Therefore, the method has the advantages of improving the safety of the blast furnace ironmaking process, particularly reducing the occurrence frequency of blast furnace accidents and abnormal furnace conditions, and having very important significance for reducing energy consumption, ensuring the safety of equipment and personnel and improving the economic benefit of the steel production process. However, according to the investigation results, the current fault identification mainly depends on the working experience of the operator, which brings about two disadvantages: firstly, the accumulation of failure experience requires years, and secondly, the continuous observation of data curves by operators is a tedious task and easily causes fatigue errors. With the continuous improvement of the industrial informatization level, data-driven process monitoring becomes a key technology for improving the industrial safety, quality and operation efficiency of the process. The data of the large-scale blast furnace has the characteristics of non-Gaussian distribution, time variation and the like, so that the abnormity monitoring and diagnosis of the large-scale blast furnace become a leading hotspot and difficulty of the current world metallurgical technology research.
Disclosure of Invention
The invention provides a method for monitoring the abnormality of a blast furnace by a GRU self-encoder embedded with a Gaussian mixture model aiming at the problems existing in the abnormality monitoring of the blast furnace, which utilizes the dynamic characteristics of the GRU capturing process to adapt to the dynamic property of blast furnace data; and a Gaussian mixture model is added on the basis, so that the method adapts to different working modes of the blast furnace, and the final model can realize quick and accurate early warning of abnormal furnace conditions of the blast furnace and provide related information of fault variables.
A Gaussian mixture model embedded GRU self-encoder blast furnace abnormity monitoring method utilizes GRU as an encoder to capture dynamic characteristics of data; then, clustering data in the hidden variable space by using a Gaussian mixture model, and adapting to different working modes of the blast furnace; reconstructing the hidden variable by a decoder to obtain a reconstruction error, calculating SPE statistic and an upper limit thereof based on probability to realize the monitoring purpose, and calculating the correlation degree of different variables and faults according to reconstruction error increment when the faults occur;
the dynamic characteristics of capturing data using the GRU as an encoder are:
the self-encoder is divided into an encoder part and a decoder part, and the GRU is used as the encoder part of the self-encoder.
The model utilizes a Gaussian mixture model to cluster data in an implicit variable space as follows:
inputting a process variable X (n multiplied by m) into an encoder, namely a GRU model, encoding to obtain an implicit variable Z (n multiplied by a) with a dimension a (a is less than m), performing soft clustering in an implicit variable space by using a Gaussian mixture model, setting a clustering number k according to the number of working modes of the process, and solving by an EM (effective energy-efficient) algorithm to obtain the weight, the mean value and the variance of different Gaussian components: omega { (pi) { ( 1 ,μ 1 ,Σ 1 ),...,(π k ,μ k ,Σ k ) In which (pi) i ,μ i ,Σ i ) The weight, mean and variance of the ith gaussian component are represented in turn.
The decoder is a single-layer full-connection layer.
The probability-based SPE statistics are: after the process variable X (n × m) is reconstructed by the self-encoder, the output is reconstructed according to the input variable X and the reconstructed output
Figure BDA0003630295830000021
Calculating reconstruction error e and SPE statistics:
Figure BDA0003630295830000022
SPE＝e T e
in the off-line training phase, highThe method comprises the steps that different samples are clustered into k Gaussian components through a Gaussian mixture model, and then the SPE statistic of the samples in each Gaussian component is calculated through a kernel density estimation method to obtain the upper limit SPE of the monitoring statistic UCL (ii) a In the on-line monitoring stage, the new sample x is new After arrival, the probabilities ascribed to different Gaussian components are calculated
Figure BDA0003630295830000023
Then monitoring statistics upper limit SPE by utilizing probability dynamic calculation UCLnew ：
Figure BDA0003630295830000024
Wherein
Figure BDA0003630295830000025
The probability of attributing a new sample to the jth gaussian component.
When a fault occurs, the correlation degree of different variables and the fault is calculated according to the reconstruction error increment: assuming that the time of the fault occurrence is time t, the reconstruction error of the sample at this time is recorded as e t And then the reconstruction error increment is | e t -e t-1 And judging the correlation between the variable quantity and the fault according to the reconstruction error increment of each variable quantity at the fault occurrence time.
The method comprises the following specific processes:
step 1: modeling off line;
step 1.1: the process variable X (n × m) of the blast furnace sensor was collected, and the normalized data was recorded as X train (n × m), the number of samples is n, the number of variables is m, and the samples and the variables are input into a GRU encoder to carry out feature extraction to obtain an implicit variable Z (n × a);
step 1.2: determining the number of Gaussian components of a Gaussian mixture model as k according to the working mode number of the process, solving the hidden variable Z by using the Gaussian mixture model to obtain the weight, the mean value and the covariance omega { (pi) of each Gaussian component 1 ,μ 1 ,Σ 1 ),...,(π k ,μ k ,Σ k )}；
Step 1.3: decoding the hidden variable Z by a decoder consisting of a single-layer full-connection layer to obtain a decoding result
Figure BDA0003630295830000031
Calculating a reconstruction error e and SPE statistic of the sample, and then sequentially obtaining monitoring statistic upper limit SPE of different Gaussian components by using a kernel density estimation method according to a clustering result of the sample UCL ；
Step 2: monitoring on line;
step 2.1: when there is a new sample x of the blast furnace new When the arrival comes, the data are normalized in the same way, and the normalized data are recorded as x test Then inputting the data into a self-encoder for training parameters during off-line modeling to obtain a reconstruction result
Figure BDA0003630295830000032
Calculating a reconstruction error e according to the clustering result of the Gaussian mixture model test And calculating the upper limit SPE of the monitoring statistic according to the probability of the clustering result UCLtest ：
SPE test ＝e test T e test
Figure BDA0003630295830000033
Wherein
Figure BDA0003630295830000034
For the probability that a new sample belongs to the jth Gaussian component, and SPE UCLj The upper limit of the monitoring statistic for the jth gaussian component.
Comparison statistics SPE test And statistic upper bound SPE UCLtest If it is SPE test ≥SPE UCLtest It represents a fault, otherwise it is in normal operation.
If the fault is judged to occur at the moment t, the reconstruction error increment | e of the moment t is calculated t -e t-1 According to which the magnitude of the correlation between each variable and the fault is judged。
The invention has the beneficial effects that:
1. the structure of the self-encoder is modified, and the GRU is utilized to effectively extract the dynamic information of the process.
2. The embedding of the gaussian mixture model effectively adapts to the different working modes of the process.
3. The model considers the dynamic property and non-Gaussian property (different working modes) of the process, effectively reduces the false alarm rate of the algorithm, can timely carry out early warning on process faults and provides fault related variable information.
Drawings
Fig. 1-1, 1-2, 1-3, 1-4 are respectively a variation trend chart of 4 key variables (hot air pressure, total pressure difference, theoretical combustion temperature, and blowing kinetic energy).
Fig. 2 is an autocorrelation analysis plot of 4 key variables.
3-1, 3-2 are two-dimensional distribution diagrams of 4 key variables.
Fig. 4 is an architecture diagram of a monitoring system.
FIG. 5 is a SPE statistics monitoring graph.
Fig. 6 is a diagram of the delta of the reconstructed error of the variables when a fault occurs.
Detailed Description
The invention is further illustrated below with reference to the figures and examples.
A Gaussian mixture model embedded GRU self-encoder blast furnace abnormity monitoring method utilizes GRU as an encoder to capture dynamic characteristics of data; secondly, soft clustering data in the hidden variable space by using a Gaussian mixture model to adapt to different working modes of the blast furnace; and reconstructing the hidden variable by a decoder to obtain a reconstruction error, calculating SPE statistic and an upper limit thereof based on probability to realize the monitoring purpose, and calculating the correlation degree of different variables and faults according to reconstruction error increment when the faults occur.
The dynamic characteristics of capturing data using the GRU as an encoder are: the self-encoder is divided into an encoder part and a decoder part, the GRU is used as the encoder part of the self-encoder, the time step of the GRU determines that the input comprises a variable of a plurality of moments, and the selection of the parameter can be determined by a cross-validation method.
The model utilizes a Gaussian mixture model to cluster data in an implicit variable space as follows:
inputting a process variable X (n × m) into an encoder, namely a GRU model, encoding to obtain an implicit variable Z (n × a) with a dimension a (a is less than m), clustering by using a Gaussian mixture model in an implicit variable space, setting a clustering number k according to the number of working modes of the process, and solving by using an EM (effective electromagnetic) algorithm to obtain weights, mean values and variances of different Gaussian components: omega { (pi) { ( 1 ,μ 1 ,Σ 1 ),...,(π k ,μ k ,Σ k ) In which (pi) i ,μ i ,Σ i ) The weight, mean and variance of the ith gaussian component are represented in turn.
The decoder is a single-layer full-connection layer.
The probability-based SPE statistics are:
after the process variable X (n × m) is reconstructed by the self-encoder, the output is reconstructed according to the input variable X and the reconstructed output
Figure BDA0003630295830000041
Calculating reconstruction error e and SPE statistics:
Figure BDA0003630295830000051
SPE＝e T e
in an off-line training stage, different samples are clustered into k Gaussian components by the Gaussian mixture model, and then the SPE statistic of the sample in each Gaussian component is calculated by using a kernel density estimation method to calculate the upper limit of the monitoring statistic SPE UCL (ii) a In the on-line monitoring stage, the new sample x is new After arrival, calculating the probability of belonging to different Gaussian components
Figure BDA0003630295830000052
Then monitoring statistics upper limit SPE by utilizing probability dynamic calculation UCLnew ：
Figure BDA0003630295830000053
Wherein
Figure BDA0003630295830000054
The probability of attributing a new sample to the jth gaussian component.
When a fault occurs, the correlation degree of different variables and the fault is calculated according to the reconstruction error increment:
assuming that the time of the fault occurrence is time t, the reconstruction error of the sample at this time is recorded as e t And then the reconstruction error increment is | e t -e t-1 And judging the correlation between the variable quantity and the fault according to the reconstruction error increment of each variable quantity at the fault occurrence time.
The specific process is as follows:
step 1: modeling off line;
step 1.1: the process variable X (n × m) of the blast furnace sensor was collected, and the normalized data was recorded as X train (n × m), the number of samples is n, the number of variables is m, and the samples and the variables are input into a GRU encoder to carry out feature extraction to obtain an implicit variable Z (n × a);
step 1.2: determining the number of Gaussian components of a Gaussian mixture model as k according to the working mode number of the process, solving the hidden variable Z by using the Gaussian mixture model to obtain the weight, the mean value and the covariance omega { (pi) of each Gaussian component 1 ,μ 1 ,Σ 1 ),...,(π k ,μ k ,Σ k )}；
Step 1.3: decoding the hidden variable Z by a decoder consisting of a single-layer full-connection layer to obtain a decoding result
Figure BDA0003630295830000055
Calculating a reconstruction error e and SPE statistic of the sample, and then sequentially obtaining monitoring statistic upper limit SPE of different Gaussian components by using a kernel density estimation method according to a clustering result of the sample UCL 。
Step 2: monitoring on line;
step 2.1: when there is a new sample x of the blast furnace new When the arrival comes, the data are normalized in the same way, and the normalized data are recorded as x test Then inputting the data into a self-encoder for training parameters during off-line modeling to obtain a reconstruction result
Figure BDA0003630295830000061
Calculating a reconstruction error e according to the clustering result of the Gaussian mixture model test And calculating the upper limit SPE of the monitoring statistic according to the probability of the clustering result UCLtest ：
SPE test ＝e test T e test
Figure BDA0003630295830000062
Wherein
Figure BDA0003630295830000063
For the probability that a new sample belongs to the jth Gaussian component, and SPE UCLj The upper limit of the monitoring statistic for the jth gaussian component.
Comparison statistics SPE test And statistic upper bound SPE UCLtest If it is SPE test ≥SPE UCLtest It represents a fault, otherwise it is in normal operation.
If the fault is judged to occur at the moment t, the reconstruction error increment | e of the moment t is calculated t -e t-1 And determining the size of the correlation between each variable and the fault according to the correlation.
Examples
1. Introduction of process variables to blast furnace
The experiment was carried out on a 2650 cubic meter blast furnace of the Guangxi Liuzhou iron and steel group. The data of the furnace was sampled once for an average of 10s and contained 27 variables as shown in table 1.
Table 1 variable list of data set
Figure BDA0003630295830000064
There are some repetitive variables in the table, such as multiple top pressures, top temperatures, etc., due to sensors being placed in different locations or being redundant, which will be averaged in subsequent processes to avoid repetitive variables.
According to the experience of operators, hot blast pressure, total pressure drop, theoretical combustion temperature and blast kinetic energy are key indexes reflecting the operation state of the blast furnace. The variation of these four key indicators in a day is selected as shown in fig. 1-1, 1-2, 1-3, 1-4.
It can be seen from fig. 1-1, 1-2, 1-3, and 1-4 that there is a peak-like disturbance in some variables at intervals, which is caused by the switching of blast furnace bodies and hot blast furnaces, and a blast furnace often has more than one hot blast furnace, and when one hot blast furnace is supplying air to the blast furnace, the other hot blast furnaces need to store heat, and then the switching is performed after a period of time to ensure the uninterrupted operation of the blast furnace, so that the blast furnace has two significant working modes, namely, a normal operation mode and a hot blast furnace switching mode.
2. Blast furnace process variable analysis
The dynamic property:
the autocorrelation analysis of the 4 representative variables is shown in fig. 2. The dynamics of the data refer to the correlation between variables at different times. As can be seen from the figure, the autocorrelation coefficients of the 4 typical variables are high, and the dynamics of the variables are obvious. Dynamic considerations are therefore necessary for process monitoring.
Non-gaussian distribution:
as the blast furnace has different working modes and transition states, the data can present non-Gaussian distribution characteristics. The distribution characteristics of 4 key variables are shown in figures 3-1 and 3-2, and the data show a remarkable non-Gaussian distribution situation.
3. Algorithm framework
The framework of the whole algorithm is shown in fig. 4.
4. Complete process of GRU self-encoder blast furnace abnormity monitoring method embedded in Gaussian mixture model
Step 1: modeling off line;
step 1.1: the process variable X (n × m) of the blast furnace sensor was collected, and the normalized data was recorded as X train (n × m), the number of samples is n, the number of variables is m, and the hidden variables Z (n × a) are obtained by inputting the hidden variables into a GRU encoder for feature extraction;
step 1.2: determining the number of Gaussian components of a Gaussian mixture model as k according to the working mode number of the process, solving the hidden variable Z by using the Gaussian mixture model to obtain the weight, the mean value and the covariance omega { (pi) of each Gaussian component 1 ,μ 1 ,Σ 1 ),...,(π k ,μ k ,Σ k )}；
Step 1.3: decoding the hidden variable Z by a decoder consisting of a single-layer full-connection layer to obtain a decoding result
Figure BDA0003630295830000071
Calculating a reconstruction error e and SPE statistic of the sample, and then sequentially obtaining monitoring statistic upper limit SPE of different Gaussian components by using a kernel density estimation method according to a clustering result of the sample UCL ；
Step 2: monitoring on line;
step 2.1: when there is a new sample x of the blast furnace new When the arrival comes, the data are normalized in the same way, and the normalized data are recorded as x test Then inputting the data into a self-encoder for training parameters during off-line modeling to obtain a reconstruction result
Figure BDA0003630295830000072
Calculating a reconstruction error e according to the clustering result of the Gaussian mixture model test And calculating the upper limit SPE of the monitoring statistic according to the probability of the clustering result UCLtest ：
SPE test ＝e test T e test
Figure BDA0003630295830000081
Wherein
Figure BDA0003630295830000082
For the probability that a new sample belongs to the jth Gaussian component, and SPE UCLj The upper limit of the monitoring statistic for the jth gaussian component.
Comparison statistics SPE test And statistic upper bound SPE UCLtest If it is SPE test ≥SPE UCLtest It represents a fault, otherwise it is in normal operation.
If the fault is judged to occur at the moment t, the reconstruction error increment | e of the moment t is calculated t -e t-1 And determining the size of the correlation between each variable and the fault according to the correlation.
5. The system finally outputs a result:
100000 pieces of blast furnace sensor historical data are taken as a training set, 30000 pieces are taken as a cross validation set, and 20500 pieces are finally taken as a test set to validate the system, wherein the test set of 20500 samples comprises a fault of blast furnace temperature abnormity, and the fault time marked by a worker is 20435.
The effect of the test set after model training was complete is shown in fig. 5 (the last 5000 samples were taken for ease of presentation). The small circles in the figure represent false alarm sample points, while the upward arrows represent true failures. The time when the monitoring system finds the fault is 20380, which is 55 sampling points earlier than the time marked by workers, i.e. the fault is early-warned 550 seconds in advance, and the effectiveness of the system is fully reflected. And finally, the system provides error increment for reconstructing the variable at the fault moment, and as shown in fig. 6, the variable related to the fault can be judged according to the size of the reconstruction error. Wherein the sequence of the 20 variables is as follows: the method comprises the following steps of oxygen enrichment rate, air permeability index, standard wind speed, oxygen enrichment flow, cold wind flow, blowing kinetic energy, furnace bosh gas quantity, furnace bosh gas index, theoretical combustion temperature, total pressure difference, actual wind speed, cold wind temperature, hot wind temperature, resistance coefficient, set coal injection quantity, actual coal injection quantity in the hour, top temperature, top pressure, cold wind pressure and hot wind pressure.
The embodiments in the above description can be further combined or replaced, and the embodiments are only described as preferred examples of the present invention, and do not limit the concept and scope of the present invention, and various changes and modifications made to the technical solution of the present invention by those skilled in the art without departing from the design concept of the present invention belong to the protection scope of the present invention. The scope of the invention is given by the appended claims and any equivalents thereof.

Claims (6)

1. A Gaussian mixture model embedded GRU self-encoder blast furnace abnormity monitoring method is characterized in that GRU is used as an encoder to capture dynamic characteristics of data; then, clustering data in the hidden variable space by using a Gaussian mixture model to adapt to different working modes of the blast furnace; reconstructing the hidden variable by a decoder to obtain a reconstruction error, calculating SPE statistic and an upper limit thereof based on probability to realize the monitoring purpose, and calculating the correlation degree of different variables and faults according to reconstruction error increment when the faults occur;
the dynamic characteristics of capturing data using the GRU as an encoder are:
the self-encoder is divided into an encoder part and a decoder part, and the GRU is used as the encoder part of the self-encoder.
2. The method of claim 1, wherein the model uses a gaussian mixture model to cluster data in hidden variable space as:
inputting a process variable X (n multiplied by m) into an encoder, namely a GRU model, encoding to obtain an implicit variable Z (n multiplied by a) with a dimension a (a is less than m), performing soft clustering in an implicit variable space by using a Gaussian mixture model, setting a clustering number k according to the number of working modes of the process, and solving by an EM (effective energy-efficient) algorithm to obtain the weight, the mean value and the variance of different Gaussian components: omega { (pi) { ( 1 ,μ 1 ,Σ 1 ),...,(π k ,μ k ,Σ k ) In which (pi) i ,μ i ,Σ i ) The weight, mean and variance of the ith gaussian component are represented in turn.
3. The method of claim 1, wherein the decoder is a single fully-connected layer.
4. The method in accordance with claim 1, wherein the probability-based SPE statistic is:
after the process variable X (n × m) is reconstructed by the self-encoder, the output is reconstructed according to the input variable X and the reconstructed output
Figure FDA0003630295820000011
Calculating reconstruction error e and SPE statistics:
Figure FDA0003630295820000012
SPE＝e T e
in an off-line training stage, different samples are clustered into k Gaussian components by the Gaussian mixture model, and then the SPE statistic of the sample in each Gaussian component is calculated by using a kernel density estimation method to calculate the upper limit of the monitoring statistic SPE UCL (ii) a In the on-line monitoring stage, the new sample x is new After arrival, the probabilities attributed to different Gaussian components are calculated
Figure FDA0003630295820000013
Then monitoring statistics upper limit SPE by utilizing probability dynamic calculation UCLnew ：
Figure FDA0003630295820000014
Wherein
Figure FDA0003630295820000021
The probability of attributing a new sample to the jth gaussian component.
5. The method of claim 1, wherein the calculating the correlation degree of the different variables with the fault according to the reconstruction error increment when the fault occurs is as follows: suppose thatThe time when the fault occurs is t time, and the reconstruction error of the sample at the time is recorded as e t And then the reconstruction error increment is | e t -e t-1 And judging the correlation between the variable quantity and the fault according to the reconstruction error increment of each variable quantity at the fault occurrence time.
6. The method according to claim 1, wherein the specific process is as follows:
step 1: modeling off line;
step 1.1: the process variable X (n × m) of the blast furnace sensor was collected, and the normalized data was recorded as X train (n × m), the number of samples is n, the number of variables is m, and the samples and the variables are input into a GRU encoder to carry out feature extraction to obtain an implicit variable Z (n × a);
step 1.2: determining the number of Gaussian components of a Gaussian mixture model as k according to the working mode number of the process, solving the hidden variable Z by using the Gaussian mixture model to obtain the weight, the mean value and the covariance omega { (pi) of each Gaussian component 1 ,μ 1 ,Σ 1 ),...,(π k ,μ k ,Σ k )}；
Step 1.3: decoding the hidden variable Z by a decoder consisting of a single-layer full-connection layer to obtain a decoding result
Figure FDA0003630295820000022
Calculating a reconstruction error e and SPE statistic of the sample, and then sequentially obtaining monitoring statistic upper limit SPE of different Gaussian components by using a kernel density estimation method according to a clustering result of the sample UCL ；
Step 2: monitoring on line;
step 2.1: when there is a new sample x of the blast furnace new When the arrival comes, the data are normalized in the same way, and the normalized data are recorded as x test Then inputting the data into a self-encoder for training parameters during off-line modeling to obtain a reconstruction result
Figure FDA0003630295820000023
Calculating a reconstruction error e according to the clustering result of the Gaussian mixture model test And calculating the upper limit SPE of the monitoring statistic according to the probability of the clustering result UCLtest ：
SPE test ＝e test T e test
Figure FDA0003630295820000024
Wherein
Figure FDA0003630295820000025
For the probability that a new sample belongs to the jth Gaussian component, and SPE UCLj The upper limit of the monitoring statistic for the jth Gaussian component.
Comparison statistics SPE test And statistic upper bound SPE UCLtest If it is SPE test ≥SPE UCLtest It represents a fault, otherwise it is in normal operation.
If the fault is judged to occur at the moment t, the reconstruction error increment | e of the moment t is calculated t -e t-1 And judging the size of the correlation between each variable and the fault according to the correlation.
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