CN111208793B - 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 PDFInfo
- Publication number
- CN111208793B CN111208793B CN202010103466.XA CN202010103466A CN111208793B CN 111208793 B CN111208793 B CN 111208793B CN 202010103466 A CN202010103466 A CN 202010103466A CN 111208793 B CN111208793 B CN 111208793B
- Authority
- CN
- China
- Prior art keywords
- stationary
- condition
- slow
- working condition
- spe
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Active
Links
Images
Classifications
-
- G—PHYSICS
- G05—CONTROLLING; REGULATING
- G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
- G05B19/00—Programme-control systems
- G05B19/02—Programme-control systems electric
- G05B19/418—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]
- 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
-
- G—PHYSICS
- G05—CONTROLLING; REGULATING
- G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
- G05B2219/00—Program-control systems
- G05B2219/30—Nc systems
- G05B2219/32—Operator till task planning
- G05B2219/32339—Object oriented modeling, design, analysis, implementation, simulation language
-
- Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
- Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
- Y02P—CLIMATE CHANGE MITIGATION TECHNOLOGIES IN THE PRODUCTION OR PROCESSING OF GOODS
- Y02P90/00—Enabling technologies with a potential contribution to greenhouse gas [GHG] emissions mitigation
- Y02P90/02—Total factory control, e.g. smart factories, flexible manufacturing systems [FMS] or integrated manufacturing systems [IMS]
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
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: at one endAcquiring J measurement variables in each non-stationary process, measuring each measurement 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:
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,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 asDefining two windowsAndsimilarity of middle features gammak,k'The following were used:
(5.2) use of the similarity γk,k'Orderly grouping the windows: for the ith operating modeAs initial windows, respectively calculatingAndsimilarity 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 conditionThe stable condition data comprises
The first condition is as follows: starting from k, 3 windows and an initial windowAre 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, whereinIs SiThe slow non-steady feature in (1), i.e. the feature for automatic division of operating conditions, is usedDenotes SiIn (1) removingOther features remaining thereafter. Next, utilizeAnd establishing a statistical model of the ith stable working condition.
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 separately definedComprises the following steps:
T2,i=TiΛ-1TiT (5)
wherein Λ representsA diagonal matrix formed by the eigenvalues of the covariance matrix,is thatThe calculation method of (2) is as follows:
wherein, T2The statistics are subjected to an F distribution with a weighting factor, whereby the control limits can be determinedAnd the control limit of the SPE statistic is subject to chi with weight coefficient2Is distributed so that the control limit can be determined
(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 statisticsAnd
(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:
wherein the content of the first and second substances,represents T under the ith stable condition2The statistical quantity is calculated by the statistical quantity,is T2The control limit of the statistical quantity is,is T2The statistical quantity is a normal conditional probability,is T2Statistics abnormal condition probabilities.
The conditional probabilities of the SPE statistics under normal and abnormal conditions are respectively:
wherein the content of the first and second substances,represents the SPE statistic for the ith steady state condition,is the control limit for the SPE statistics,to be the SPE statistic normal conditional probability,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:
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:
(9) And (3) judging a state monitoring result: binding state monitoring indexAndjudging whether the process is running normally, if soAndare respectively greater than a predetermined threshold valueAnd deltaSPE 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: 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:
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,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 asDefining two windowsAndsimilarity of middle features gammak,k'The following were used:
(5.2) use of the similarity γk,k'Orderly grouping the windows: for the ith operating modeAs initial windows, respectively calculatingAndsimilarity 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 conditionThe stable condition data comprises
The first condition is as follows: to avoid misclassification, 3 windows starting from k x and the initial windowAre all smaller than the threshold Γ.
And a second condition: in order to ensure the modeling data quantity, the number of samples contained in the current working condition is required to be larger than a 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, whereinIs SiThe slow non-steady feature in (1), i.e. the feature for automatic division of operating conditions, is usedDenotes SiIn (1) removingOther features remaining thereafter. Next, utilizeAnd establishing a statistical model of the ith stable working condition.
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)
wherein Λ representsA diagonal matrix formed by the eigenvalues of the covariance matrix,is thatThe calculation method of (2) is as follows:
wherein, T2The statistics are subjected to an F distribution with a weighting factor, whereby the control limits can be determinedAnd the control limit of the SPE statistic is subject to chi with weight coefficient2Is distributed so that the control limit can be determined
(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 statisticsAnd
(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:
wherein the content of the first and second substances,represents T under the ith stable condition2The statistical quantity is calculated by the statistical quantity,is T2The control limit of the statistical quantity is,is T2The statistical quantity is a normal conditional probability,is T2Statistics abnormal condition probabilities.
The conditional probabilities of the SPE statistics under normal and abnormal conditions are respectively:
wherein the content of the first and second substances,represents the SPE statistic for the ith steady state condition,is the control limit for the SPE statistics,to be the SPE statistic normal conditional probability,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:
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:
(9) And (3) judging a state monitoring result: binding state monitoring indexAndjudging whether the process is running normally, if soAndare respectively greater than a predetermined threshold valueAndthe 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. Further, a process state monitoring index is obtained according to the step (8.3), as shown in fig. 8, the solid line is an index trend, and the dotted line is a 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 element in the nth row and the jth column in (NxJ);
(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:
obtaining a matrix X (N multiplied by J) with the mean value of each column being 0 and the variance being 1;
wherein x isnjThe normalized sample is represented as a sample after normalization,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 a slow feature of X, W is a 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 characteristics in S can be considered as the characteristics which change slowly, the later characteristics are the characteristics which change quickly, 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 asDefining two windowsAndsimilarity of middle features gammak,k'The following were used:
wherein | | | purple hair2RepresentsAndthe Euclidean distance between the two, theta is a hyper-parameter;
(5.2) use of the similarity γk,k'Orderly grouping the windows: for the ith operating modeAs initial windows, respectively calculatingAndsimilarity 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 conditionThe stable condition data comprises
The first condition is as follows: starting from k, 3 windows and an initial windowAre all smaller than a threshold value gamma;
and a second condition: the number of samples contained in the current working condition is required to be larger than the threshold valueN;
(5.3) repeating the step (5.2) to obtain a 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, whereinIs SiThe slow non-steady feature in (1), i.e. the feature for automatic division of operating conditions, is usedDenotes SiIn (1) removingOther features remaining after; next, utilizeEstablishing a statistical model of the ith stable working condition;
wherein, PiIndicating the direction of projection, TiRepresenting a pivot score, I ═ 1,2, …, I being 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)
wherein Λ representsA diagonal matrix formed by the eigenvalues of the covariance matrix,is thatThe calculation method of (2) is as follows:
wherein, T2The statistics are subjected to an F distribution with a weighting factor, whereby the control limits can be determinedAnd the control limit of the SPE statistic is subject to chi with weight coefficient2Is distributed so that the control limit can be determined
(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 statisticsAnd
(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:
wherein the content of the first and second substances,represents T under the ith stable condition2The statistical quantity is calculated by the statistical quantity,is T2The control limit of the statistical quantity is,is T2The statistical quantity is a normal conditional probability,is T2Statistics abnormal condition probability;
the conditional probabilities of the SPE statistics under normal and abnormal conditions are respectively:
wherein the content of the first and second substances,represents the SPE statistic for the ith steady state condition,is the control limit for the SPE statistics,to be the SPE statistic normal conditional probability,abnormal condition probability is taken as 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:
wherein, Pr (N) and Pr (F) respectively represent the prior probability when the process is normal and abnormal;
under the ith stable working condition obtained by calculating SPE statistics, the probability of normal operation of the process is as follows:
(9) And (3) judging a state monitoring result: binding state monitoring indexAndjudging whether the process is running normally, if soAndare respectively greater than a predetermined threshold valueAnd deltaSPE,δSPE<And 1, judging that the process normally runs, otherwise, judging that the process is abnormal.
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.
Priority Applications (1)
Application Number | Priority Date | Filing Date | Title |
---|---|---|---|
CN202010103466.XA CN111208793B (en) | 2020-02-20 | 2020-02-20 | State monitoring method of non-stationary industrial process based on slow characteristic analysis |
Applications Claiming Priority (1)
Application Number | Priority Date | Filing Date | Title |
---|---|---|---|
CN202010103466.XA CN111208793B (en) | 2020-02-20 | 2020-02-20 | State monitoring method of non-stationary industrial process based on slow characteristic analysis |
Publications (2)
Publication Number | Publication Date |
---|---|
CN111208793A CN111208793A (en) | 2020-05-29 |
CN111208793B true CN111208793B (en) | 2021-01-19 |
Family
ID=70785871
Family Applications (1)
Application Number | Title | Priority Date | Filing Date |
---|---|---|---|
CN202010103466.XA Active CN111208793B (en) | 2020-02-20 | 2020-02-20 | State monitoring method of non-stationary industrial process based on slow characteristic analysis |
Country Status (1)
Country | Link |
---|---|
CN (1) | CN111208793B (en) |
Families Citing this family (7)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
CN111814325B (en) * | 2020-07-01 | 2023-12-29 | 浙江浙能台州第二发电有限责任公司 | Single-variable alarm threshold optimization method for non-stationary operation of coal-fired power generation equipment |
CN112651444B (en) * | 2020-12-29 | 2022-08-02 | 山东科技大学 | Self-learning-based non-stationary process anomaly detection method |
CN112801978A (en) * | 2021-01-28 | 2021-05-14 | 新疆大学 | Multispectral remote sensing image change detection method and device and storage medium |
CN113030726A (en) * | 2021-03-24 | 2021-06-25 | 河南中烟工业有限责任公司 | Motor state monitoring method and system based on data driving |
CN113238543B (en) * | 2021-04-14 | 2022-09-23 | 东北大学 | Modal division method and fault monitoring method for multi-modal characteristic industrial process |
CN114527731B (en) * | 2022-02-22 | 2023-12-26 | 中国矿业大学 | Industrial process operation state evaluation method based on supervision probability slow feature analysis |
CN117524337B (en) * | 2023-10-30 | 2024-05-07 | 江南大学 | CO based on double-flow slow-non-steady fast feature extraction2Content prediction method |
Family Cites Families (3)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
CN106647718B (en) * | 2017-01-20 | 2019-01-11 | 中国石油大学(华东) | Nonlinear industrial processes fault detection method based on the slow signature analysis of Bayes's core |
CN108803531B (en) * | 2018-07-17 | 2019-10-15 | 浙江大学 | Closed-loop system process monitoring method based on sound feature Cooperative Analysis and orderly Time segments division |
CN110262450B (en) * | 2019-06-17 | 2020-06-05 | 浙江浙能嘉华发电有限公司 | Fault prediction method for cooperative analysis of multiple fault characteristics of steam turbine |
-
2020
- 2020-02-20 CN CN202010103466.XA patent/CN111208793B/en active Active
Also Published As
Publication number | Publication date |
---|---|
CN111208793A (en) | 2020-05-29 |
Similar Documents
Publication | Publication Date | Title |
---|---|---|
CN111208793B (en) | State monitoring method of non-stationary industrial process based on slow characteristic analysis | |
CN109034260B (en) | Desulfurization tower oxidation fan fault diagnosis system and method based on statistical principle and intelligent optimization | |
CN110033141B (en) | Method for establishing desulfurization system operation condition database | |
CN112904810B (en) | Process industry nonlinear process monitoring method based on effective feature selection | |
CN112860183B (en) | Multisource distillation-migration mechanical fault intelligent diagnosis method based on high-order moment matching | |
CN105955214A (en) | Batch process fault detection method based on sample timing sequence and neighborhood similarity information | |
CN108830006B (en) | Linear-nonlinear industrial process fault detection method based on linear evaluation factor | |
CN112907561A (en) | Notebook appearance flaw detection method based on deep learning | |
CN106933211A (en) | It is a kind of to recognize the industrial process dynamically interval method and apparatus of adjustment | |
CN115112372A (en) | Bearing fault diagnosis method and device, electronic equipment and storage medium | |
CN106845825B (en) | Strip steel cold rolling quality problem tracing and control method based on improved PCA | |
CN115294109A (en) | Real wood board production defect identification system based on artificial intelligence, and electronic equipment | |
CN110717602A (en) | Machine learning model robustness assessment method based on noise data | |
CN113177578A (en) | Agricultural product quality classification method based on LSTM | |
CN110910528B (en) | Method and device for predicting tensile strength of paper sheet | |
CN112434739A (en) | Chemical process fault diagnosis method of support vector machine based on multi-core learning | |
CN115861672B (en) | Foam flotation operation performance evaluation method based on image feature joint distribution | |
CN110347579B (en) | Deep learning test case selection method based on neuron output behavior pattern | |
CN115983534A (en) | Method and system for evaluating state of sewage treatment process | |
CN114139643B (en) | Monoglyceride quality detection method and system based on machine vision | |
CN116226693A (en) | Gaussian mixture model nuclear power operation condition division method based on density peak clustering | |
Wang et al. | Identification of abnormal conditions for gold flotation process based on multivariate information fusion and double‐channel convolutional neural network | |
CN113033683A (en) | Industrial system working condition monitoring method and system based on static and dynamic joint analysis | |
Wu et al. | Research on fuzzy clustering method for working status of mineral flotation process | |
CN113378956B (en) | Equipment degradation data convenient labeling method based on secondary relaxation clustering |
Legal Events
Date | Code | Title | Description |
---|---|---|---|
PB01 | Publication | ||
PB01 | Publication | ||
SE01 | Entry into force of request for substantive examination | ||
SE01 | Entry into force of request for substantive examination | ||
GR01 | Patent grant | ||
GR01 | Patent grant |