CN111208793A - State monitoring method of non-stationary industrial process based on slow characteristic analysis - Google Patents

State monitoring method of non-stationary industrial process based on slow characteristic analysis Download PDF

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CN111208793A
CN111208793A CN202010103466.XA CN202010103466A CN111208793A CN 111208793 A CN111208793 A CN 111208793A CN 202010103466 A CN202010103466 A CN 202010103466A CN 111208793 A CN111208793 A CN 111208793A
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邹筱瑜
潘杰
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Zhejiang University ZJU
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    • G05B19/41885—Total factory control, i.e. centrally controlling a plurality of machines, e.g. direct or distributed numerical control [DNC], flexible manufacturing systems [FMS], integrated manufacturing systems [IMS], computer integrated manufacturing [CIM] characterised by modeling, simulation of the manufacturing system
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Abstract

The invention discloses a method for monitoring the state of a non-stationary industrial process based on slow characteristic analysis, which adopts slow characteristic analysis and stationarity test to obtain characteristic quantity capable of indicating the change of process working condition information, decomposes the process non-stationarity into segmental stationarity in a characteristic space, and automatically divides the working condition of the non-stationary process without a stable working point; then, utilizing a stationary modeling technology to respectively carry out statistical modeling and state monitoring on each stable working condition; finally, the monitoring indexes based on Bayesian inference synthesize the information of each working condition, and provide the comprehensive state monitoring result. The method enhances the understanding of the operation characteristics of the specific process, improves the state monitoring efficiency and the accuracy of the abnormal detection result, can be finally applied to the actual industrial production field, and ensures the safe and reliable operation of the non-stable industrial process and the high-quality pursuit of the product.

Description

State monitoring method of non-stationary industrial process based on slow characteristic analysis
Technical Field
The invention belongs to the field of non-stationary process statistical state monitoring, and particularly relates to a method for automatically and orderly dividing a non-stationary industrial process into different stable operation working conditions based on slow characteristic analysis and carrying out statistical modeling and state monitoring according to working condition division results under the condition of no working condition indicating variable.
Background
In recent years, with the urgent market demand of modern society for various products, various specifications and high-quality products, industrial production is more focused on an efficient process capable of producing various products, and safety and reliability of production operation have become the focus of attention of engineers. However, the fluctuation of the process operation condition can cause the industrial production process to show non-stationary characteristics, i.e. the statistical characteristics (such as mean value, mean square value and the like) of the process variables are functions of time and change violently in different sampling periods. The non-stationary operation process has time-varying property and no long-term stable working point, so that the statistical analysis and online application facing the non-stationary industrial process face challenges.
To deal with the non-stationarity, Wilms, Zou, et al use a co-integration analysis method to extract the long-term equilibrium relationship between variables. However, the assumption of variable-dependent co-integration may not hold in practical applications. Kheidri et al propose a non-stationary adaptive tracking strategy based on a moving window, but the modeling cost is high, and it is difficult to judge whether the data is an abnormal value. The multimodal process is a special non-stationary process with limited stable operating points. Thus, the multimodal process is piecewise smooth. Wang et al, Haghani et al, Chang et al, Yu et al respectively establish a submodel for each stable operating mode, but a general non-stationary process may not have a fixed stable operating point, nor have a unique operating condition indicating variable, so it is difficult to divide the non-stationary process into stable operating points.
The method presented in this application is particularly applicable in the context of copper flotation, which is a typical non-stationary industrial process. The flotation method is used as a mineral separation technology, can improve the utilization rate of low-grade mineral resources and obtain high-grade ores, and is widely applied to the field of mineral separation. Mineral flotation is a complex physicochemical process that uses differences in the physicochemical properties of the mineral surface to separate the minerals. The mineral flotation process is carried out in a flotation tank, firstly, crushed minerals are mixed with water to form slurry, a large amount of air bubbles are generated by continuously blowing air and stirring of an impeller into the flotation tank, hydrophobic useful mineral particles are adhered to the air bubbles under the action of a medicament and rise along with the air bubbles to form a foam layer, hydrophilic mineral particles are mostly left in the slurry, the foam layer foam carries the useful mineral particles to overflow from an overflow groove to form a foam product, and the useless mineral left in the slurry is discharged along with underflow. Due to the fact that the property of raw ores changes, the performance of equipment is degraded, the production environment is changed, the production scheme is changed and the like in industrial production, a plurality of operation working conditions exist in the copper flotation process. Among them, the variation of the properties of the raw ore is the most important cause of the multi-working conditions in the production process. Some mining fields have large changes in three-dimensional space, large grade changes and discontinuous ore deposits, which are commonly called as 'chicken nest ore'. Because the ore property changes violently, the flotation process is in a state of frequent working condition change and non-steady operation. However, the properties of the ore cannot be measured in real time, so that offline and online statistical analysis in the actual production process faces huge challenges, and the production is difficult to be guided by summarizing expert rules aiming at different working conditions.
Slow Feature Analysis (SFA) was developed to learn invariant or slowly varying features from vector input signals, the slow features obtained being arranged in order from slow to fast. SFAs have also found little application in non-stationary process modeling, but in practice they can split the original signal into slow signals of different frequencies. Wherein the slow, non-stationary characteristic reflects the intrinsic change in the operating conditions, while the fast characteristic reflects the process noise. Therefore, a non-stationary industrial process state monitoring method based on slow feature analysis and orderly division of working modes can be established. Therefore, the application provides a method for monitoring the state of a non-stationary industrial process based on slow feature analysis. And separating signals by adopting the SFA as a filter, and then carrying out stability test on the characteristics of the SFA. Thus, four features of particular significance are available, namely, a slow stationary feature, a slow non-stationary feature, a fast stationary feature, and a fast non-stationary feature. The slow and non-steady characteristics reflect the internal changes of the working conditions, and the sectional stationarity can be shown. Under the inspiration of multi-modal process state monitoring, aiming at the condition without working condition indicating variables, the working condition is divided into a plurality of ordered stable operation stages by using slow non-stable characteristics. And establishing an ordered operation automatic identification technology in the feature space, and orderly dividing the stable working time period. Then, a multivariate statistical method such as Principal Component Analysis (PCA) or Partial Least Squares (PLS) is used to establish a statistical monitoring model for each stable operating period.
Disclosure of Invention
The invention aims to provide a method for monitoring the state of a non-stationary industrial process based on slow characteristic analysis, aiming at the defects of the working condition division and state monitoring technology of the existing non-stationary production process. The method uses SFA to select slow, non-stationary features. And decomposing the process non-stationarity into segment stationarity in a feature space by using the obtained features, and automatically dividing the working condition of the non-stationarity process without a stable working point. Then, each stable working condition is subjected to statistical modeling and state monitoring by using a stationary modeling technology. The method does not need to carry out the assumption of the co-integration relation on the process variables, can still obtain the characteristics of the indicated working conditions and carry out the automatic division of the working conditions by slow characteristic analysis under the condition of no working condition indicated variable, and then establishes a statistical model by utilizing the residual characteristics to monitor the process state, thereby ensuring the safe and reliable operation of the non-stable production process.
The purpose of the invention is realized by the following technical scheme: a method for monitoring the condition of a non-stationary industrial process based on slow signature analysis, the method comprising the steps of:
(1) acquiring data to be analyzed: acquiring J measured variables in a non-stationary process, measuring each measured variable N times, and collecting data of the non-stationary processx njComposing a two-dimensional data matrixX(N×J)，x njTo representXThe (N × J) th row and J column.
(2) Data matrixXNormalization processing of (N × J): to pairx njThe normalization process of subtracting the mean value and dividing by the standard deviation is performed, and the calculation formula is as follows:
Figure BDA0002387653280000041
a matrix X (N × J) with a mean of 0 and a variance of 1 is obtained for each column.
Wherein x isnjThe normalized sample is represented as a sample after normalization,
Figure BDA00023876532800000412
is the mean of the jth variable, sjIs the jth variableStandard deviation.
(3) Slow Feature Analysis (SFA) modeling of matrix X (nxj): the modeling formula is as follows
S＝XW (2)
Wherein S is the X-th slow feature, W is the projection matrix of the slow feature, and the features in S are sorted from slow to fast.
(4) Stability testing of the slow feature: and (3) performing stationarity test on each column of S by using ADF test to obtain a stationarity characteristic type, wherein the stationarity characteristic type comprises the following steps: a stationary feature and a non-stationary feature; the first a features in S can be considered as slowly changing features, the later features are quickly changing features, and a is less than or equal to 3.
(5) The automatic division of the working conditions in the feature space comprises the following sub-steps:
(5.1) by SSNDenote the slow non-stationary features in S, let SSNDivided into equal-sized windows along the sample direction and arranged in time sequence, wherein the characteristics contained in the k-th window are expressed as
Figure BDA0002387653280000042
Defining two windows
Figure BDA0002387653280000043
And
Figure BDA00023876532800000413
similarity of middle features gammak,k'The following were used:
Figure BDA0002387653280000044
wherein | | | purple hair2Represents
Figure BDA0002387653280000045
And
Figure BDA00023876532800000414
the euclidean distance between, theta is a hyperparameter.
(5.2) use of the similarity γk,k'Go on the window withAnd (3) sequential grouping: for the ith operating mode
Figure BDA0002387653280000046
As initial windows, respectively calculating
Figure BDA0002387653280000047
And
Figure BDA0002387653280000048
similarity between them gammak,k+1,γk,k+2,γk,k+3,., until the window k meets the following two conditions, obtaining the data of the i-th stable working condition
Figure BDA0002387653280000049
The stable condition data comprises
Figure BDA00023876532800000410
The first condition is as follows: starting from k, 3 windows and an initial window
Figure BDA00023876532800000411
Are all smaller than the threshold Γ.
And a second condition: the number of samples contained in the current working condition is required to be larger than the threshold valueN。
And (5.3) repeating the step (5.2) to obtain the result of working condition division.
(6) The establishment of the state monitoring model based on the working condition division result comprises the following substeps:
(6.1) for the ith stable condition, use SiRepresenting the characteristics of S corresponding to the working conditions, wherein
Figure BDA0002387653280000051
Is SiThe slow non-steady feature in (1), i.e. the feature for automatic division of operating conditions, is used
Figure BDA0002387653280000052
Denotes SiIn (1) removing
Figure BDA0002387653280000053
Other features remaining thereafter. Next, utilize
Figure BDA0002387653280000054
And establishing a statistical model of the ith stable working condition.
(6.2) to
Figure BDA0002387653280000055
Statistical modeling analysis using PCA:
Figure BDA0002387653280000056
wherein, PiIndicating the direction of projection, TiAnd (3) representing the pivot score, I is 1,2, …, and I is the total number of operating conditions. PiCan be obtained by eigenvalue decomposition.
(6.3) to indicate a change in Process characteristics, T for the ith Stable regime2And SPE statistics are defined as:
T2,i＝TiΛ-1TiT(5)
Figure BDA0002387653280000057
wherein Λ represents
Figure BDA0002387653280000058
A diagonal matrix formed by the eigenvalues of the covariance matrix,
Figure BDA0002387653280000059
is that
Figure BDA00023876532800000510
The calculation method of (2) is as follows:
Figure BDA00023876532800000511
wherein, T2Statistics clothesFrom the F distribution with the weighting factor, the control limit can be determined
Figure BDA00023876532800000512
And the control limit of the SPE statistic is subject to chi with weight coefficient2Is distributed so that the control limit can be determined
Figure BDA00023876532800000513
(7) Acquiring and processing new test data: new collected process data at time tx t(1 XJ) repeating the steps (2) to (6) to obtain T2And control limits of SPE statistics
Figure BDA00023876532800000514
And
Figure BDA00023876532800000515
(8) the calculation of the online state monitoring index comprises the following substeps:
(8.1)T2the conditional probabilities of the statistics under normal and abnormal conditions are respectively:
Figure BDA0002387653280000061
Figure BDA0002387653280000062
wherein the content of the first and second substances,
Figure BDA0002387653280000063
represents T under the ith stable condition2The statistical quantity is calculated by the statistical quantity,
Figure BDA0002387653280000064
is T2The control limit of the statistical quantity is,
Figure BDA0002387653280000065
is T2The statistical quantity is a normal conditional probability,
Figure BDA0002387653280000066
is T2Statistics abnormal condition probabilities.
The conditional probabilities of the SPE statistics under normal and abnormal conditions are respectively:
Figure BDA0002387653280000067
Figure BDA0002387653280000068
wherein the content of the first and second substances,
Figure BDA0002387653280000069
represents the SPE statistic for the ith steady state condition,
Figure BDA00023876532800000610
is the control limit for the SPE statistics,
Figure BDA00023876532800000611
to be the SPE statistic normal conditional probability,
Figure BDA00023876532800000612
abnormal conditional probability is the SPE statistic.
(8.2) calculation by T2Under the ith stable working condition obtained by statistics, the probability of normal operation of the process is as follows:
Figure BDA00023876532800000613
where Pr (N) and Pr (F) represent the prior probabilities of normal and abnormal processes, respectively.
Under the ith stable working condition obtained by calculating SPE statistics, the probability of normal operation of the process is as follows:
Figure BDA00023876532800000614
(8.3) from T2Statistic calculation online state monitoring index
Figure BDA00023876532800000615
Figure BDA0002387653280000071
Calculating online state monitoring index from SPE statistics
Figure BDA0002387653280000072
Figure BDA0002387653280000073
(9) And (3) judging a state monitoring result: binding state monitoring index
Figure BDA0002387653280000074
And
Figure BDA0002387653280000075
judging whether the process is running normally, if so
Figure BDA0002387653280000076
And
Figure BDA0002387653280000077
are respectively greater than a predetermined threshold value
Figure BDA0002387653280000078
And deltaSPE
Figure BDA0002387653280000079
The process is judged to run normally, otherwise, an exception occurs.
Further, in step 1, the measured variables are: inlet ore pulp flow, ore granularity, ore concentration, ore pulp pH value, aeration quantity, collecting agent addition quantity, foaming agent addition quantity, regulator addition quantity, lime addition quantity, underflow flow, ore pulp oxygen content, foam flow rate, foam stability, RGB channel red, RGB channel green and RGB channel blue.
Compared with the prior art, the invention has the beneficial effects that: the invention automatically and orderly divides a non-steady operation industrial process into different steady operation working conditions under the condition that the process has no working condition indicating variable, and carries out statistical modeling and state monitoring according to the working condition division result. And (3) acquiring characteristic quantity capable of indicating process working condition information change by adopting slow characteristic analysis and stability test, decomposing process non-stability into piecewise stability in a characteristic space, and automatically dividing the working condition of the non-stable process without a stable working point. Then, each stable working condition is subjected to statistical modeling and state monitoring by using a stationary modeling technology. The method does not need to carry out the assumption of the co-integration relation on the process variables, can still obtain the characteristics of the indicated working conditions and carry out the automatic division of the working conditions by slow characteristic analysis under the condition of no working condition indicated variable, and then establishes a statistical model by utilizing the residual characteristics to monitor the process state, thereby ensuring the safe and reliable operation of the non-stable production process. The method automatically divides working conditions, enhances the understanding of the operation characteristics of a specific process, improves the monitoring efficiency and the accuracy of an abnormal detection result, can be finally applied to an actual industrial production field, and ensures the safe and reliable operation of a non-stable industrial process and the high-quality pursuit of products.
Drawings
FIG. 1 is a schematic diagram of a flotation process in an embodiment of the invention;
FIG. 2 is a flow chart of a method for monitoring the operating condition status of a non-stationary industrial process according to the present invention;
FIG. 3 is a schematic diagram of the method for automatically dividing the working conditions in the feature space according to the present invention;
FIG. 4 is a trend graph after variable normalization in an embodiment of the present invention;
FIG. 5 is a diagram illustrating the result of dividing the operating condition of the feature space according to an embodiment of the present invention;
FIG. 6 is a trend graph of the intermediate statistics under condition 2 in case 1 according to the present invention;
FIG. 7 is a trend graph of the intermediate statistics under condition 3 in case 1 according to the present invention;
FIG. 8 is a graph of the trend of the monitoring index of example 1 according to the present invention;
FIG. 9 is a trend graph of PCA monitoring statistics in example 1 of the present invention;
FIG. 10 is a graph of the trend of the monitoring index of example 2 according to the present invention;
FIG. 11 is a trend graph of PCA monitoring statistics in example 2 of the present invention.
Detailed Description
The invention is further described with reference to the following drawings and specific embodiments.
The copper flotation process is typically a non-stationary process due to variations in the properties of the raw ore and fluctuations in the production environment. The China is a large country for producing and consuming metal copper, the demand for the metal copper is increased year by year, and the copper is the first copper consuming country in the world. The flotation method is used as a mineral separation technology, can improve the utilization rate of low-grade mineral resources and obtain high-grade ores, and is widely applied to the field of mineral separation. Mineral flotation is a complex physicochemical process that utilizes differences in the physicochemical properties of the mineral surfaces to separate the minerals, and is affected by a number of factors that make it difficult to control the flotation process. The mineral flotation process is carried out in a flotation tank, firstly, crushed minerals are mixed with water to form slurry, a large amount of air bubbles are generated through continuous stirring of air and an impeller blown into the flotation tank, hydrophobic useful mineral particles are adhered to the air bubbles under the action of a medicament and rise along with the air bubbles to form a foam layer, hydrophilic mineral particles are mostly left in the slurry, the foam layer foam carries the useful mineral particles to overflow from an overflow groove to form a foam product, and the useless mineral left in the slurry is discharged along with underflow, as shown in a schematic diagram of the flotation principle in figure 1.
FIG. 2 is a flow chart of the method for monitoring the working condition state of the non-stationary industrial process, which specifically comprises the following steps:
(1) acquiring data to be analyzed: obtaining J measurement variables in a non-stationary process, each measurementMeasuring the quantity of the non-stationary process N timesx njComposing a two-dimensional data matrixX(N×J)，x njTo representXThe (N × J) th row and J column.
(2) Data matrixXNormalization processing of (N × J): to pairx njThe normalization process of subtracting the mean value and dividing by the standard deviation is performed, and the calculation formula is as follows:
Figure BDA0002387653280000091
a matrix X (N × J) with a mean of 0 and a variance of 1 is obtained for each column.
Wherein x isnjThe normalized sample is represented as a sample after normalization,
Figure BDA0002387653280000092
is the mean of the jth variable, sjIs the standard deviation of the jth variable.
(3) Slow Feature Analysis (SFA) modeling of matrix X (nxj): the modeling formula is as follows
S＝XW (2)
Wherein S is the X-th slow feature, W is the projection matrix of the slow feature, and the features in S are sorted from slow to fast.
(4) Stability testing of the slow feature: and (3) performing stationarity test on each column of S by using ADF test to obtain a stationarity characteristic type, wherein the stationarity characteristic type comprises the following steps: a stationary feature and a non-stationary feature; the first a features in S can be considered as the features which change slowly, the later features are the features which change quickly, and a is less than or equal to 3. The features can then be divided into four categories, namely: the physical meanings of the slow stationary characteristic, the slow non-stationary characteristic, the fast stationary characteristic and the fast non-stationary characteristic are shown in table 1.
Table 1: physical significance of the four characteristics
Type of feature Explanation of the invention
Slow steady characteristic Internal information independent of process variations
Slow non-stationary characteristic Internal information relating to process variations
Fast steady characteristic External information independent of process variations
Fast non-stationary characteristic External information relating to process variations
The process internal information typically reflects the operating state of the process and the external information typically reflects the noise of the process. Therefore, in the four types of characteristics, the slow non-stationary characteristics mainly reflect the internal changes of the working conditions, and the working conditions can be automatically divided in the characteristic space by using the slow non-stationary characteristics to the non-stationary processes of the assumption of the non-variable co-integration relation, the non-working condition indication variable and the non-stable working point.
(5) The automatic division of the operating conditions in the feature space, as shown in fig. 3, comprises the following substeps:
(5.1) by SSNDenote the slow non-stationary features in S, let SSNDivided into equal-sized windows along the sample direction and arranged in time sequence, wherein the characteristics contained in the k-th window are expressed as
Figure BDA0002387653280000101
Defining two windows
Figure BDA0002387653280000102
And
Figure BDA0002387653280000103
similarity of middle features gammak,k'The following were used:
Figure BDA0002387653280000104
wherein | | | purple hair2Represents
Figure BDA0002387653280000105
And
Figure BDA0002387653280000106
the euclidean distance between, theta is a hyperparameter.
(5.2) use of the similarity γk,k'Orderly grouping the windows: for the ith operating mode
Figure BDA0002387653280000107
As initial windows, respectively calculating
Figure BDA0002387653280000108
And
Figure BDA0002387653280000109
similarity between them gammak,k+1,γk,k+2,γk,k+3,., until the window k meets the following two conditions, obtaining the data of the i-th stable working condition
Figure BDA00023876532800001010
The stable condition data comprises
Figure BDA00023876532800001011
The first condition is as follows: to avoid misclassification, 3 windows starting from k x and the initial window
Figure BDA00023876532800001012
Are all smaller than the threshold Γ.
And a second condition: to ensure the modeling data volume, the workerThe number of samples contained in the condition is greater than the threshold valueN。
And (5.3) repeating the step (5.2) to obtain the result of working condition division.
(6) The establishment of the state monitoring model based on the working condition division result comprises the following substeps:
(6.1) for the ith stable condition, use SiRepresenting the characteristics of S corresponding to the working conditions, wherein
Figure BDA0002387653280000111
Is SiThe slow non-steady feature in (1), i.e. the feature for automatic division of operating conditions, is used
Figure BDA0002387653280000112
Denotes SiIn (1) removing
Figure BDA0002387653280000113
Other features remaining thereafter. Next, utilize
Figure BDA0002387653280000114
And establishing a statistical model of the ith stable working condition.
(6.2) to
Figure BDA0002387653280000115
Statistical modeling analysis using PCA:
Figure BDA0002387653280000116
wherein, PiIndicating the direction of projection, TiAnd (3) representing the pivot score, I is 1,2, …, and I is the total number of operating conditions. PiCan be obtained by eigenvalue decomposition.
(6.3) to indicate a change in Process characteristics, T for the ith Stable regime2And SPE statistics are defined as:
T2,i＝TiΛ-1TiT(5)
Figure BDA0002387653280000117
wherein Λ represents
Figure BDA0002387653280000118
A diagonal matrix formed by the eigenvalues of the covariance matrix,
Figure BDA0002387653280000119
is that
Figure BDA00023876532800001110
The calculation method of (2) is as follows:
Figure BDA00023876532800001111
wherein, T2The statistics are subjected to an F distribution with a weighting factor, whereby the control limits can be determined
Figure BDA00023876532800001112
And the control limit of the SPE statistic is subject to chi with weight coefficient2Is distributed so that the control limit can be determined
Figure BDA00023876532800001113
(7) Acquiring and processing new test data: new collected process data at time tx t(1 XJ) repeating the steps (2) to (6) to obtain T2And control limits of SPE statistics
Figure BDA00023876532800001114
And
Figure BDA00023876532800001115
(8) the calculation of the online state monitoring index comprises the following substeps:
(8.1)T2the conditional probabilities of the statistics under normal and abnormal conditions are respectively:
Figure BDA0002387653280000121
Figure BDA0002387653280000122
wherein the content of the first and second substances,
Figure BDA0002387653280000123
represents T under the ith stable condition2The statistical quantity is calculated by the statistical quantity,
Figure BDA0002387653280000124
is T2The control limit of the statistical quantity is,
Figure BDA0002387653280000125
is T2The statistical quantity is a normal conditional probability,
Figure BDA0002387653280000126
is T2Statistics abnormal condition probabilities.
The conditional probabilities of the SPE statistics under normal and abnormal conditions are respectively:
Figure BDA0002387653280000127
Figure BDA0002387653280000128
wherein the content of the first and second substances,
Figure BDA0002387653280000129
represents the SPE statistic for the ith steady state condition,
Figure BDA00023876532800001210
is the control limit for the SPE statistics,
Figure BDA00023876532800001211
to be the SPE statistic normal conditional probability,
Figure BDA00023876532800001212
abnormal conditional probability is the SPE statistic.
(8.2) calculation by T2Under the ith stable working condition obtained by statistics, the probability of normal operation of the process is as follows:
Figure BDA00023876532800001213
where Pr (N) and Pr (F) represent the prior probabilities of normal and abnormal processes, respectively.
Under the ith stable working condition obtained by calculating SPE statistics, the probability of normal operation of the process is as follows:
Figure BDA00023876532800001214
(8.3) from T2Statistic calculation online state monitoring index
Figure BDA00023876532800001215
Figure BDA0002387653280000131
Calculating online state monitoring index from SPE statistics
Figure BDA0002387653280000132
Figure BDA0002387653280000133
(9) And (3) judging a state monitoring result: binding state monitoring index
Figure BDA0002387653280000134
And
Figure BDA0002387653280000135
judging whether the process is running normally, if so
Figure BDA0002387653280000136
And
Figure BDA0002387653280000137
are respectively greater than a predetermined threshold value
Figure BDA0002387653280000138
And
Figure BDA0002387653280000139
the process is judged to run normally, otherwise, an exception occurs.
In step 1, the measured variables are: the method comprises the following steps of 1 inlet ore pulp flow, 2 ore granularity, 3 ore concentration, 4 ore pulp pH value, 5 aeration amount, 6 collecting agent adding amount, 7 foaming agent adding amount, 8 adjusting agent adding amount, 9 lime adding amount, 10 underflow flow rate, 11 ore pulp oxygen content, 12 foam flow rate, 13 foam stability, 14 RGB channel red, 15 RGB channel green and 16 RGB channel blue. The measurement data to be analyzed are first normalized, and the normalized trend graph is shown in fig. 4. Obviously, the variation trend of each variable has no obvious rule, and no obvious co-integration relation exists, so that direct modeling analysis is difficult. The partitioning method of the invention is utilized to carry out slow characteristic analysis on copper flotation process data, and 1 slow non-stationary characteristic is obtained by analyzing the characteristic stationarity. The slow non-stationary characteristic is used for automatic ordered working condition division, and the division result is shown in figure 5. Wherein, the solid line represents the characteristic value, and the dashed-solid line represents the working condition division result. Therefore, 5 operating conditions are obtained through orderly and automatic division of the working conditions, and PCA monitoring models are respectively established. The condition monitoring method of the present invention was tested by two examples below.
Example 1
Data for normal operation under condition 2 shown in FIG. 5: the results of the intermediate statistics under condition 2 are shown in fig. 6, with the solid line being the intermediate statistics and the dashed line being the control limit. It can be seen that the sample points are substantially below the control limit. The result of the intermediate statistics under the working condition 3 is shown in fig. 7, and the SPE statistics is in an intermittent and overrun state because the current test working condition does not accord with the working condition 3, so that the phenomenon that the model does not match occurs. IntoIn one step, the process state monitoring index is obtained according to the step (8.3), as shown in fig. 8, the solid line is the index trend, and the dotted line is the threshold. It can be seen that based on T2And the state monitoring index of the SPE statistic is larger than the threshold value, namely the process running state is normal. The monitoring results were consistent with the experimental setup. The results of the monitoring using PCA are shown in fig. 9, and it can be seen that under normal operating conditions, the PCA can also be used to obtain correct results.
Example 2
The process regime switches from 2 to 3, with anomalies occurring at sample points 20 to 120: the trend of the monitoring index obtained by the method provided by the invention is shown in fig. 10, wherein the 20 th to 200 th sampling points are indicated in the dotted line box, and it can be seen that the process abnormality is found in the SPE-based monitoring index preparation. The condition monitoring was carried out by the PCA method, and the results are shown in FIG. 11. Can find that T2And SPE statistics are below the control limit, and the PCA cannot detect process abnormity. The alignment results of example 2 demonstrate the effectiveness and sensitivity of the proposed method.
Generally speaking, the state monitoring method provided by the invention can effectively divide the process working condition and distinguish the normal state and the abnormal state of the process. This is difficult to achieve with conventional non-stationary process state monitoring methods under unknown operating condition indicating variables. The method has high precision and sensitivity, is beneficial to industrial engineers to accurately judge the process running state, and ensures the high-efficiency running of the actual production process.
The invention relates to a method for monitoring the state of a non-stationary process based on slow characteristic analysis, which automatically and orderly divides a non-stationary industrial process into different stable operation working conditions according to the condition without working condition index variable, and carries out statistical modeling and state monitoring according to the working condition division result. And (3) acquiring characteristic quantity capable of indicating process working condition information change by adopting slow characteristic analysis and stability test, decomposing process non-stability into piecewise stability in a characteristic space, and automatically dividing the working condition of the non-stable process without a stable working point. Then, each stable working condition is subjected to statistical modeling and state monitoring by using a stationary modeling technology. Finally, the monitoring indexes based on Bayesian inference synthesize the information of each working condition, and provide the comprehensive state monitoring result. The method does not need to carry out the assumption of the co-integration relation on the process variables, can still obtain the characteristics of the indicated working conditions through slow characteristic analysis under the condition of no working condition indicating variables, carries out the automatic division of the working conditions, and then establishes a statistical model by utilizing the residual characteristics to monitor the process state, thereby ensuring the safe and reliable operation of the non-stable production process. The invention enhances the understanding of the operation characteristics of the specific process, improves the state monitoring efficiency and the accuracy of the abnormal detection result, and can be finally applied to the actual industrial production field to ensure the safe and reliable operation of the non-stable industrial process and the high-quality pursuit of the product.
It is to be understood that the invention is not limited to the copper flotation process described in the above embodiments, and that equivalent modifications or substitutions may be made by those skilled in the art without departing from the spirit of the invention, and are intended to be included within the scope of the appended claims.

Claims (2)

1. A method for monitoring the state of a non-stationary industrial process based on slow signature analysis, characterized in that it comprises the following steps:
(1) acquiring data to be analyzed: acquiring J measured variables in a non-stationary process, measuring each measured variable N times, and collecting data of the non-stationary processx njComposing a two-dimensional data matrixX(N×J)，x njTo representXThe (N × J) th row and J column.
(2) Data matrixXNormalization processing of (N × J): to pairx njThe normalization process of subtracting the mean value and dividing by the standard deviation is performed, and the calculation formula is as follows:
Figure FDA0002387653270000011
a matrix X (N × J) with a mean of 0 and a variance of 1 is obtained for each column.
Wherein x isnjThe normalized sample is represented as a sample after normalization,
Figure FDA0002387653270000012
is the mean of the jth variable, sjIs the standard deviation of the jth variable.
(3) Slow Feature Analysis (SFA) modeling of matrix X (nxj): the modeling formula is as follows
S＝XW (2)
Wherein S is the X-th slow feature, W is the projection matrix of the slow feature, and the features in S are sorted from slow to fast.
(4) Stability testing of the slow feature: and (3) performing stationarity test on each column of S by using ADF test to obtain a stationarity characteristic type, wherein the stationarity characteristic type comprises the following steps: a stationary feature and a non-stationary feature; the first a features in S can be considered as slowly changing features, the later features are quickly changing features, and a is less than or equal to 3.
(5) The automatic division of the working conditions in the feature space comprises the following sub-steps:
(5.1) by SSNDenote the slow non-stationary features in S, let SSNDivided into equal-sized windows along the sample direction and arranged in time sequence, wherein the characteristics contained in the k-th window are expressed as
Figure FDA0002387653270000013
Defining two windows
Figure FDA0002387653270000014
And
Figure FDA0002387653270000015
similarity of middle features gammak,k'The following were used:
Figure FDA0002387653270000021
wherein | | | purple hair2Represents
Figure FDA0002387653270000022
And
Figure FDA0002387653270000023
the euclidean distance between, theta is a hyperparameter.
(5.2) use of the similarity γk,k'Orderly grouping the windows: for the ith operating mode
Figure FDA0002387653270000024
As initial windows, respectively calculating
Figure FDA0002387653270000025
And
Figure FDA0002387653270000026
similarity between them gammak,k+1,γk,k+2,γk,k+3,., until the window k meets the following two conditions, obtaining the data of the i-th stable working condition
Figure FDA0002387653270000027
The stable condition data comprises
Figure FDA0002387653270000028
The first condition is as follows: starting from k, 3 windows and an initial window
Figure FDA0002387653270000029
Are all smaller than the threshold Γ.
And a second condition: the number of samples contained in the current working condition is required to be larger than the threshold valueN。
And (5.3) repeating the step (5.2) to obtain the result of working condition division.
(6) The establishment of the state monitoring model based on the working condition division result comprises the following substeps:
(6.1) for the ith stable condition, use SiRepresenting the characteristics of S corresponding to the working conditions, wherein
Figure FDA00023876532700000210
Is SiThe slow non-steady feature in (1), i.e. the feature for automatic division of operating conditions, is used
Figure FDA00023876532700000211
Denotes SiIn (1) removing
Figure FDA00023876532700000212
Other features remaining thereafter. Next, utilize
Figure FDA00023876532700000213
And establishing a statistical model of the ith stable working condition.
(6.2) to
Figure FDA00023876532700000214
Statistical modeling analysis using PCA:
Figure FDA00023876532700000215
wherein, PiIndicating the direction of projection, TiAnd (3) representing the pivot score, I is 1,2, …, and I is the total number of operating conditions. PiCan be obtained by eigenvalue decomposition.
(6.3) to indicate a change in Process characteristics, T for the ith Stable regime2And SPE statistics are defined as:
T2,i＝TiΛ-1TiT(5)
Figure FDA00023876532700000216
wherein Λ represents
Figure FDA00023876532700000217
A diagonal matrix formed by the eigenvalues of the covariance matrix,
Figure FDA00023876532700000218
is that
Figure FDA00023876532700000219
The calculation method of (2) is as follows:
Figure FDA0002387653270000031
wherein, T2The statistics are subjected to an F distribution with a weighting factor, whereby the control limits can be determined
Figure FDA0002387653270000032
And the control limit of the SPE statistic is subject to chi with weight coefficient2Is distributed so that the control limit can be determined
Figure FDA0002387653270000033
(7) Acquiring and processing new test data: new collected process data at time tx t(1 XJ) repeating the steps (2) to (6) to obtain T2And control limits of SPE statistics
Figure FDA0002387653270000034
And
Figure FDA0002387653270000035
(8) the calculation of the online state monitoring index comprises the following substeps:
(8.1)T2the conditional probabilities of the statistics under normal and abnormal conditions are respectively:
Figure FDA0002387653270000036
Figure FDA0002387653270000037
wherein the content of the first and second substances,
Figure FDA0002387653270000038
represents T under the ith stable condition2The statistical quantity is calculated by the statistical quantity,
Figure FDA0002387653270000039
is T2Control limit of statistic, Pr [ T ]t 2,i|N]Is T2The statistical quantity is a normal conditional probability,
Figure FDA00023876532700000310
is T2Statistics abnormal condition probabilities.
The conditional probabilities of the SPE statistics under normal and abnormal conditions are respectively:
Figure FDA00023876532700000311
Figure FDA00023876532700000312
wherein the content of the first and second substances,
Figure FDA00023876532700000313
represents the SPE statistic for the ith steady state condition,
Figure FDA00023876532700000314
is the control limit for the SPE statistics,
Figure FDA00023876532700000315
to be the SPE statistic normal conditional probability,
Figure FDA00023876532700000316
abnormal conditional probability is the SPE statistic.
(8.2) calculation by T2Under the ith stable working condition obtained by statistics, the probability of normal operation of the process is as follows:
Figure FDA0002387653270000041
where Pr (N) and Pr (F) represent the prior probabilities of normal and abnormal processes, respectively.
Under the ith stable working condition obtained by calculating SPE statistics, the probability of normal operation of the process is as follows:
Figure FDA0002387653270000042
(8.3) from T2Statistic calculation online state monitoring index
Figure FDA0002387653270000043
Figure FDA0002387653270000044
Calculating online state monitoring index from SPE statistics
Figure FDA0002387653270000045
Figure FDA0002387653270000046
(9) And (3) judging a state monitoring result: binding state monitoring index
Figure FDA0002387653270000047
And
Figure FDA0002387653270000048
judging whether the process is running normally, if so
Figure FDA0002387653270000049
And
Figure FDA00023876532700000410
are respectively greater than a predetermined threshold value
Figure FDA00023876532700000411
And
Figure FDA00023876532700000412
the process is judged to run normally, otherwise, an exception occurs.
2. The condition monitoring method according to claim 1, wherein in step 1, the measured variables are: inlet ore pulp flow, ore granularity, ore concentration, ore pulp pH value, aeration quantity, collecting agent addition quantity, foaming agent addition quantity, regulator addition quantity, lime addition quantity, underflow flow, ore pulp oxygen content, foam flow rate, foam stability, RGB channel red, RGB channel green and RGB channel blue.
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