CN105278520B - Based on T-KPRM complex industrial process evaluation of running status methods and application - Google Patents
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Abstract
The advantages of present invention discloses a kind of complex industrial process evaluation of running status method and its application based on T KPRM, and method combines both PRM and T KPLS further decomposes higher-dimension principal component subspace and the residual error subspace of KPLS：Part related with output is come with unrelated being partially separated of output, the part for having larger residual error and being partially separated for final noise are come；It can accurately extract and export relevant variable information, convenient for grasping situ industrial process operation state.The application of method is to establish the evaluated off-line model of operating status, introduces sliding window technique, and the on-line evaluation of complex industrial process operating status is carried out using the similarity between online data window and corresponding opinion rating.Using Euclidean distance between sliding data window and optimal opinion rating, the contribution rate of relevant variable is calculated, operating status non-optimal factor is identified, convenient for site operation personnel's adjustment in time and improved production strategy, improve production efficiency.
Description
Technical Field
The invention relates to an industrial process running state evaluation method based on T-KPRM and application thereof, belonging to the technical field of industrial production process running state evaluation.
Background
The good operation state of the industrial process is the effective guarantee of the product quality and the economic benefit of enterprises. However, in a complex industrial process, the operating state is often influenced by various uncertainties, which cause the operating state to deviate from the optimal operating point. Meanwhile, data from an industrial site is subjected to various interferences (such as sensor faults) in the acquisition process, so that outliers exist in sample data. Therefore, it is necessary to provide a robust online evaluation strategy for industrial operation status for real-time understanding of the operation conditions of complex industries. The separation of raw coal by heavy media is a complex industrial operation process. Meanwhile, the coal preparation process parameters need to be continuously detected and adjusted to ensure the stability of the quality and quantity of products and ensure the safe operation of the production process.
The online evaluation of the running state refers to further distinguishing the good and bad conditions of the production process under the condition that the industrial production is kept in normal running. And an operator can adjust production according to the evaluation result so as to ensure that the production operation process is always in an optimal state.
The dense medium coal separation process is widely applied in China, and no matter the dense medium cyclone separation process or the gravity dense medium separation process, the key point for ensuring the product quality is to measure and control the medium density. To obtain a good sorting result, it is necessary to ensure that the density of the medium is stabilized within a desired range. By evaluating the running state of the measurement and control process of the coal preparation density of the heavy medium on line, the on-site operators can know the specific condition of the running state of the measurement and control process of the medium density in time. And then, correspondingly adjusting the coal preparation process according to the evaluation result, improving the separation efficiency in the coal preparation process, and increasing the yield of clean coal, thereby improving the economic benefit of enterprises. In addition, the improvement of the separation efficiency also contributes to the development of clean energy and recycling economy.
The process flow of raw coal separation by using dense medium cyclone is shown in fig. 1, wherein raw coal and circulating medium are fed into a mixing barrel together, then are separated by two-product dense medium cyclone, the underflow and overflow are respectively subjected to medium removal, dehydration and related treatment, finally clean coal, middlings and gangue products are obtained, and the medium is recovered and concentrated by a medium system and finally recycled. The whole sorting process is divided into a coal flow process, a medium flow process and the like, and sensors related in the process mainly comprise a density meter, a magnetic substance content meter, a liquid level meter and the like. Monitoring the density in the medium combining barrel by using a density meter, and monitoring the liquid level of suspension in the medium combining barrel by using a liquid level meter; the coal slime during the separation process is monitored by utilizing the magnetic material content meter, and various electromagnetic valves are matched with the system to control the flow of media, clean water and the like. The main control object in the dense medium separation process is the density of the dense medium suspension in the dense medium barrel, the density control relates to density feedback and ash content feedback, the density feedback is used for carrying out closed-loop adjustment on the density of the suspension in the dense medium barrel, the ash content feedback is used for monitoring the quality of a separated product, and the density given value of the dense medium suspension is adjusted according to an ash content result so as to achieve the purpose of stabilizing the product quality. The quick ash test of the coal preparation plant detects the ash content of raw coal, and the ash content is a basic index of coal quality. The lower the ash content, the less coal impurities washed out, and the better the coal quality.
Currently, some researches on the evaluation of the operation state of the production process have been made by related scholars. The research on the measurement and control process of the dense-medium coal separation density, such as Hanfang, Zebra and the like, only stays in the theoretical analysis of the importance of the density measurement and control system on the whole dense-medium coal separation process, and does not provide a specific density monitoring strategy. Liu inflammation and the like, and provides an operation state evaluation strategy based on a T-KPLS algorithm. However, data in the industrial field is often nonlinear and also contains a certain number of outliers, and an evaluation model established by using the existing method (such as T-KPLS and Fisher discriminant analysis) is easily affected by the outliers, so that the accuracy of an evaluation result is affected due to the loss of the generalization capability of the method.
Disclosure of Invention
Aiming at the problems in the prior art, the invention provides the T-KPRM-based complex industrial process running state evaluation method, which can not only quickly solve the nonlinear problem of data, but also accurately extract the information of each variable in the process data, and can overcome the influence of outliers on the precision of an evaluation model; the application of the provided T-KPRM-based complex industrial process running state evaluation method (T-KPRM) refers to a kernel bias robust latent variable technology-based complex industrial process running state evaluation method, namely the method can be used for establishing an off-line evaluation model of the running state by utilizing the kernel bias robust latent variable technology; and then, introducing a sliding window technology, calculating the similarity between the online data window and the corresponding evaluation level, and performing online evaluation on the running state of the complex industrial process by using the similarity. Meanwhile, the Euclidean distance between the sliding data window and the optimal evaluation level can be utilized to calculate the contribution rate of corresponding variables, identify the non-optimal factors of the running state and provide decision basis for field operators to adjust the production strategy in real time, so that the production efficiency of enterprises is improved.
In order to achieve the purpose, the invention adopts a T-KPRM-based complex industrial process running state evaluation method, and an input data matrix is assumed to be X epsilon RN×JN is the number of samples, J is the number of process variables; the output data matrix is Y ∈ RNIncluding transportingOutputting a process variable; the method for evaluating the running state of the complex industrial process based on the kernel bias robust latent variable technology comprises the following specific steps:
step one, carrying out zero mean value and unit variance processing on each column of an input data matrix X; similarly, the output data matrix Y is also subjected to standardization processing;
step two, the input data matrix X is subjected to nonlinear mapping phi: x is the number ofi∈RN→Φ(xi) E F is projected to a high-dimensional feature space F, and an kernel matrix K is calculated in the F space: k is phiTΦ；
Step three, carrying out standardization processing on the kernel matrix K;
and fourthly, operating a PRM algorithm on the kernel matrix K and the output data matrix Y, wherein the PRM algorithm specifically comprises the following steps:
a1, settingThe leverage value for the ith sample data can be represented by the following formula:
and is
Wherein, | | | |, represents the Euclidean distance, med represents the median, medL1Represents the median value of L1, tiIs the PLS score of the ith sample data, c is a constant;
setting the residual weight of ith sample dataCan be defined by the following formula:
wherein r isiRepresenting the residual between the predicted value and the actual value of the ith sample data,a robust scale estimate representing the residual may be calculated by:
the integrated weight w of the ith sample dataiThis can be determined by the following formula:initializing weight W by using equations (1), (3) and (5)i；
b1, respectively carrying out weighted calculation on the kernel matrix K and the output data matrix Y, and obtaining an input kernel matrix K after weightingWAnd the output data matrix YWThen, a PLS1 regression model is established for the weighted input and output data, and the score vector of the weighted input and output data is corrected;
c1, calculating residual error r of each sample dataiUpdating the sample weight W using the equations (1), (3) and (5)i；
d1, if the relative difference of q is less than the threshold value (e.g. 10)-2) Step five is entered, otherwise, b1 is returned;
step five, the input data matrix is changed into KWThe output data matrix becomes YWFrom the output data matrix YWExtracting the converged uiLet i equal to 1, KWi＝KW，YWi＝YW；
a2, order YWiIs equal to ui；
b2, calculating KWScore vector of (t)i＝KWiui，ti←ti/||ti||；
c2、
d2, calculate YWiScore vector u ofi＝YWiqi，ui←ui/||ui||；
e2, judgment uiWhether convergence is achieved, if yes, the step six is carried out, otherwise, the step a2 is returned;
step six, calculating KWiThe load matrix of (a):
seventhly, extracting all principal elements and calculating an input data matrix KWScore matrix T and input data matrix KWLoad matrix P, output data matrix YWScore matrix U and output data matrix YWThe load matrix Q of (2) is as follows:
a3, order
b3, making i equal to i +1, repeating the fifth step and the sixth step until A principal elements are extracted, wherein the number A of the principal elements can be determined by a cross-validation method;
c3、T＝[t1,...,tA]，P＝[p1,...,pA]，U＝[u1,...,uA]，Q＝[q1,...,qA]；
step eight, KW＝TPT+E，YW＝UQT+F；
Nine steps, to principal component TPTOperating the PCA algorithm:
step ten, operating a PCA algorithm on the residual error E:
if the output data matrix Y is a single output variable, the expression of the T-KPRM model is as follows:
the above-mentioned score vector tyShown is the neutralization of the output y in TWThe directly related part, namely the most key variable required to establish the evaluation model, can be used for establishing the off-line evaluation model of the running state; t isoIs represented in T and output yWAn orthogonal portion; t isrIs the part of the residual E with the larger variance; erIs the final residual, i.e., noise;
when a new sample k is introducednewThe score matrix will be given by:
wherein k isnewIs a new sample xnewThe kernel function of (a) can be calculated by the following formula:
knew＝Φ(X)Φ(xnew)＝[k(x1,xnew),...k(xn,xnew)]T(8)
to k is pairednewThe following are obtained by carrying out equalization:
wherein 1 ist＝1/n·[11...1]T∈Rn，The above-mentioned score vector tyThe method can be used for establishing an off-line evaluation model of the running state.
An application of a complex industrial process running state evaluation method based on T-KPRM specifically refers to establishing an off-line evaluation model of a running state, on-line evaluation of the running state of the complex industrial process and identification of non-optimal factors by utilizing a kernel bias robust latent variable technology, specifically, establishing the off-line evaluation model by utilizing the kernel bias robust latent variable technology, and scoring vectors of the off-line evaluation model corresponding to running state grades areWherein c is the number of operating state levels; then, introducing a sliding window technology, calculating the similarity between an online data window and a corresponding evaluation grade, and performing online evaluation on the running state of the complex industrial process by using the similarity; and then, calculating the contribution rate of the corresponding variable by using the Euclidean distance between the sliding data window and the optimal evaluation level, and identifying the non-optimal factors of the running state.
In the process of evaluating the running state, a data window with the width of H is introduced as a basic analysis unit in consideration that single sample data is not enough to represent the running state of the production process and is easy to be interfered by various factors; then, the similarity between the data window at the time k and the corresponding evaluation level is calculatedThe system is used for evaluating the process running state; meanwhile, a similarity threshold value epsilon (epsilon is more than 0.5 and less than 1) is set for distinguishing the determined operation state grade and the transition stage of the corresponding operation state grade; maximum of assumed similarityIf greater than the threshold ε, the process state level may be determined to be p; when the operating state is in the transition phase,namely, in the stage of transition from the previous operation state to the next operation state, the similarity value of the two operation states shows a slowly changing rule; assuming that the similarity is smaller than the threshold epsilon and the magnitude of the similarity satisfies the rule of sequential increasing, the process running state can be considered to be in a transition stage; if the above two assumptions are not satisfied, the operating state is considered to be disturbed by other factors, and the evaluation results are consistent with the previous ones.
The flow of online running state evaluation is as follows:
the first step is as follows: constructing an online window data matrix at time k, Xon,k＝[xon,k-H+1,...,xon,k]TH is the width of the data window;
the second step is that: standardization of Xon,kThe online window data matrix after standardization is obtained by utilizing the established offline evaluation model,
the third step: computingScore vector of
Wherein,byThe mean value is obtained through centralization;
the fourth step: the euclidean distance between the online data window and the corresponding rating c is calculated,whereinIs thatThe vector of averaging; obtained by a T-KPRM method,then
The fifth step: by usingThe similarity between the data window and the corresponding evaluation level c is calculated as follows:
suppose thatThen
Wherein
And a sixth step: judging the grade of the running state according to the similarity, wherein the evaluation criterion of the online running state is as follows:
criterion one, ifJudging that the online data window belongs to a certain determined operation state grade p;
criterion two, if the criterion one is not satisfied, the formula is satisfiedThen it is decidedThe data window is in a transition stage of the operation state, namely in a stage of converting from the previous operation state to the next operation state, wherein l is a positive integer, and the size is determined by production experience;
if the two criteria are not met, the data window is proved to be interfered by other factors, and the judgment result of the running state of the data window is consistent with that of the data window before;
through the judgment of the three criteria, whether the data window at the time k belongs to a certain operation state level or is in a transition stage between the state levels can be effectively determined.
The non-optimal operation state means all operation states except the optimal operation state, which includes a good state, a normal state, a bad state, and a transition stage between the stable states. Generally, managers of an enterprise desire that a production process be run in an optimal state. However, when the industrial production is inevitably in a non-optimal stage, it is necessary to find a suitable method to trace the reasons for the non-optimal operation, thereby providing an effective basis for production adjustment.
In the study of data-based fault diagnosis, the use of the contribution graph method is common. Particularly for linear models, the method can intuitively and effectively find out the relevant variables causing the fault. However, the conventional contribution graph method is not suitable for a model built by a kernel function. A method for identifying non-optimal factors based on kernel functions is provided: the method comprises the steps of firstly, calculating a partial derivative of a Euclidean distance between an online data window and an optimal operation state grade to obtain the contribution rate of sample data variables, wherein variables with larger contribution rates are regarded as factors causing production to be in a non-optimal operation state, and then identifying and judging the factors.
The Euclidean distance between the online data window and the optimal operating condition level is re-expressed as
In the formula,an off-line model matrix representing the optimal operating conditions,a kernel mean matrix representing an online data window corresponding to an optimal operating state;
in thatIn the formula, the contribution ratio of the jth variable is calculated by the following formula:
in the formula,is a sample data windowTr (-) as a trace of the matrix;
to find out the above equation ContrjExact expression, must be derivedThe partial derivatives of (a) and, therefore, some necessary processing is required:
a. core matrixThe partial derivatives of (a) are:
b. partial derivatives are simultaneously calculated for the two kernel matrices, and the following can be obtained:
c. calculate outPartial derivatives of the elements in row i and column q:
in the formula,n4is the number of samples of modeling data for the best operating conditions.
Compared with the prior art, the complex industrial process operation state evaluation method (T-KPRM) based on the kernel bias robust latent variable technology combines the advantages of PRM and T-KPLS, can accurately master the operation state of the field industrial process in real time, and can further decompose the high-dimensional principal element subspace and the residual error subspace of the KPLS. In the pivot subspace, output-dependent parts are separated from output-independent parts. Meanwhile, in the residual subspace, the part with the larger residual and the part with the final noise are separated. Therefore, the T-KPRM can accurately extract variable information related to output. The method can be used for establishing an off-line evaluation model of the operation state. Meanwhile, a sliding window technology is introduced, the similarity between the online data window and the corresponding evaluation level is calculated, and the online evaluation of the running state of the complex industrial process can be carried out by utilizing the similarity. And then, calculating the contribution rate of the corresponding variable by using the Euclidean distance between the sliding data window and the optimal evaluation level, and identifying the non-optimal factors of the running state. By means of simulation analysis and comparison, the operation state online evaluation and non-optimal factor identification of the coal preparation density measurement and control process of the heavy medium are very significant by utilizing an off-line evaluation model of the operation state established by a complex industrial process operation state evaluation method (T-KPRM) based on the kernel bias robust latent variable technology. By means of the evaluation and factor identification results, operators can adjust and improve the production strategy in time, and the production efficiency is improved. In addition, the online evaluation method of the running state can be suitable for the separation of the dense medium cyclone and the gravity dense medium separation process.
Drawings
FIG. 1 is a process flow diagram for raw coal separation using a dense medium cyclone;
FIG. 2 is a flow chart of the present invention for online evaluation of operating conditions and identification of non-optimal factors based on T-KPRM;
FIG. 3 is a schematic diagram of the online evaluation result of the similarity and density measurement and control operation state;
FIG. 4 is a graph of prior art method (T-KPLS) density measurement and control operation status evaluation results without strong noise and outliers;
FIG. 5 is a graph of the evaluation of the density measurement and control operating conditions of the proposed method (T-KPRM) without strong noise and outliers;
FIG. 6 is a diagram showing the evaluation result of the operation state of the density measurement and control process of the prior art method (T-KPLS) with strong noise and outliers;
FIG. 7 shows the evaluation results of the density measurement and control operation status of the proposed method (T-KPRM) with strong noise and outliers;
FIG. 8 is a non-optimal factor identification for a status level of "poor";
FIG. 9 is a non-optimal factor identification for the transition phase between "poor" to "medium";
FIG. 10 is a non-optimal factor identification for the status level "medium";
FIG. 11 is a non-optimal factor identification for the transition phase between "medium" to "good";
FIG. 12 is a non-optimal factor identification for the status level "good";
FIG. 13 is a non-optimal factor identification for the transition phase between "good" to "good".
Detailed Description
The invention is further described below with reference to the figures and simulation analysis.
A complex industrial process running state evaluation method based on T-KPRM assumes that an input data matrix is X belongs to RN ×JN is the number of samples, J is the number of process variables; the output data matrix is Y ∈ RNIncluding an output process variable; the method for evaluating the running state of the complex industrial process based on the kernel bias robust latent variable technology comprises the following specific steps:
step one, carrying out zero mean value and unit variance processing on each column of an input data matrix X; similarly, the output data matrix Y is also subjected to standardization processing;
step two, the input data matrix X is subjected to nonlinear mapping phi: x is the number ofi∈RN→Φ(xi) E F is projected to a high-dimensional feature space F, and an kernel matrix K is calculated in the F space: k is phiTΦ；
Step three, carrying out standardization processing on the kernel matrix K;
and fourthly, operating a PRM algorithm on the kernel matrix K and the output data matrix Y, wherein the PRM algorithm specifically comprises the following steps:
a1, settingThe leverage value for the ith sample data can be represented by the following formula:
and is
Wherein, | | | |, represents the Euclidean distance, med represents the median, medL1Represents the median value of L1, tiIs the PLS score of the ith sample data, c is a constant;
setting the residual weight of ith sample dataCan be defined by the following formula:
wherein r isiRepresenting the residual between the predicted value and the actual value of the ith sample data,a robust scale estimate representing the residual may be calculated by:
the integrated weight w of the ith sample dataiThis can be determined by the following formula:
initializing weight W by using equations (1), (3) and (5)i；
b1, respectively aligning the kernel matrix K and the output dataWeighting the matrix Y to obtain an input kernel matrix KWAnd the output data matrix YWThen, a PLS1 regression model is established for the weighted input and output data, and the score vector of the weighted input and output data is corrected;
c1, calculating residual error r of each sample dataiUpdating the sample weight W using the equations (1), (3) and (5)i；
d1, if the relative difference of q is less than the threshold value (e.g. 10)-2) Step five is entered, otherwise, b1 is returned;
step five, the input data matrix is changed into KWThe output data matrix becomes YWFrom the output data matrix YWExtracting the converged uiLet i equal to 1, KWi＝KW，YWi＝YW；
a2, order YWiIs equal to ui；
b2, calculating KWScore vector of (t)i＝KWiui，ti←ti/||ti||；
c2、
d2, calculate YWiScore vector u ofi＝YWiqi，ui←ui/||ui||；
e2, judgment uiWhether convergence is achieved, if yes, the step six is carried out, otherwise, the step a2 is returned;
step six, calculating KWiThe load matrix of (a):
step seven, extracting all principal elements and calculating the inputInto a data matrix KWScore matrix T and input data matrix KWLoad matrix P, output data matrix YWScore matrix U and output data matrix YWThe load matrix Q of (2) is as follows:
a3, order
b3, making i equal to i +1, repeating the fifth step and the sixth step until A principal elements are extracted, wherein the number A of the principal elements can be determined by a cross-validation method;
c3、T＝[t1,...,tA]，P＝[p1,...,pA]，U＝[u1,...,uA]，Q＝[q1,...,qA]；
step eight, KW＝TPT+E，YW＝UQT+F；
Nine steps, to principal component TPTOperating the PCA algorithm:
step ten, operating a PCA algorithm on the residual error E:
if the output data matrix Y is a single output variable, the expression of the T-KPRM model is as follows:
the above-mentioned score vector tyShown is the neutralization of the output y in TWThe directly related part, namely the most key variable required to establish the evaluation model, can be used for establishing the off-line evaluation model of the running state; t isoIs represented in T and output yWOrthogonal partDividing; t isrIs the part of the residual E with the larger variance; erIs the final residual, i.e., noise;
when a new sample k is introducednewThe score matrix will be given by:
wherein k isnewIs a new sample xnewThe kernel function of (a) can be calculated by the following formula:
knew＝Φ(X)Φ(xnew)＝[k(x1,xnew),...k(xn,xnew)]T(8)
to k is pairednewThe following are obtained by carrying out equalization:
wherein 1 ist＝1/n·[11...1]T∈Rn，The above-mentioned score vector tyThe method can be used for establishing an off-line evaluation model of the running state.
The T-KPRM combines the advantages of the PRM and the T-KPLS, and can accurately master the running state of the field industrial process in real time. The T-KPPM may further decompose the high-dimensional principal component subspace and residual subspace of KPLS. In the pivot subspace, output-dependent parts are separated from output-independent parts. Meanwhile, in the residual subspace, the part with the larger residual and the part with the final noise are separated. Therefore, the T-KPRM can accurately extract variable information related to output.
An application of a complex industrial process running state evaluation method based on T-KPRM, in particular to an off-line evaluation model for establishing a running state by utilizing a kernel-bias robust latent variable technologyThe method comprises the steps of firstly utilizing a kernel-bias robust latent variable technology to establish an offline evaluation model, and scoring vectors of the offline evaluation model corresponding to the operation state grades intoWherein c is the number of operating state levels; then, introducing a sliding window technology, calculating the similarity between an online data window and a corresponding evaluation grade, and performing online evaluation on the running state of the complex industrial process by using the similarity; and then, calculating the contribution rate of the corresponding variable by using the Euclidean distance between the sliding data window and the optimal evaluation level, and identifying the non-optimal factors of the running state.
In the process of evaluating the running state, a data window with the width of H is introduced as a basic analysis unit in consideration that single sample data is not enough to represent the running state of the production process and is easy to be interfered by various factors; then, the similarity between the data window at the time k and the corresponding evaluation level is calculatedThe system is used for evaluating the process running state; meanwhile, a similarity threshold value epsilon (epsilon is more than 0.5 and less than 1) is set for distinguishing the determined operation state grade and the transition stage of the corresponding operation state grade; maximum of assumed similarityIf greater than the threshold ε, the process state level may be determined to be p; when the operation state is in a transition stage, namely a stage of transition from the previous operation state to the next operation state, the similarity value of the operation state shows a slowly changing rule; assuming that the similarity is smaller than the threshold epsilon and the magnitude of the similarity satisfies the rule of sequential increasing, the process running state can be considered to be in a transition stage; if the above two assumptions are not satisfied, the operating state is considered to be disturbed by other factors, and the evaluation results are consistent with the previous ones.
The flow of online running state evaluation is as follows:
the first step is as follows: constructing an online window data matrix at time k, Xon,k＝[xon,k-H+1,...,xon,k]TH is the width of the data window;
the second step is that: standardization of Xon,kThe online window data matrix after standardization is obtained by utilizing the established offline evaluation model,
the third step: computingScore vector of
Wherein,byThe mean value is obtained through centralization;
the fourth step: the euclidean distance between the online data window and the corresponding rating c is calculated,whereinIs thatThe vector of averaging; obtained by a T-KPRM method,then
The fifth step: by usingThe similarity between the data window and the corresponding evaluation level c is calculated as follows:
suppose thatThen
Wherein
And a sixth step: judging the grade of the running state according to the similarity, wherein the evaluation criterion of the online running state is as follows:
criterion one, ifJudging that the online data window belongs to a certain determined operation state grade p;
criterion two, if the criterion one is not satisfied, the formula is satisfiedDetermining that the data window is in a transition stage of the operating state, namely in a stage of transition from a previous operating state to a next operating state, wherein l is a positive integer, and the size is determined by production experience;
if the two criteria are not met, the data window is proved to be interfered by other factors, and the judgment result of the running state of the data window is consistent with that before;
through the judgment of the three criteria, whether the window data at the time k belongs to a certain operation state level or is in a transition stage between the state levels can be effectively determined.
The non-optimal operation state means all operation states except the optimal operation state, including a good state, a general state, a bad state, and an excessive stage of the state. Generally, managers of an enterprise desire that a production process be run in an optimal state. However, when the industrial production is inevitably in a non-optimal stage, it is necessary to find a suitable method to trace the reasons for the non-optimal operation, thereby providing an effective basis for production adjustment.
In the study of data-based fault diagnosis, the use of the contribution graph method is common. Particularly for linear models, the method can intuitively and effectively find out the relevant variables causing the fault. However, the conventional contribution graph method is not suitable for a model built by a kernel function. A method for identifying non-optimal factors based on kernel functions is provided: the method comprises the steps of firstly, calculating a partial derivative of a Euclidean distance between an online data window and an optimal operation state grade to obtain the contribution rate of sample data variables, wherein variables with larger contribution rates are regarded as factors causing production to be in a non-optimal operation state, and then identifying and judging the factors.
The Euclidean distance between the online data window and the optimal operating condition level is re-expressed as
In the formula,an off-line model matrix representing the optimal operating conditions,a kernel mean matrix representing an online data window corresponding to an optimal operating state;
in thatIn the formula, the contribution ratio of the jth variable is calculated by the following formula:
in the formula,is a sample data windowTr (-) as a trace of the matrix;
to find out the above equation ContrjExact expression, must be derivedThe partial derivatives of (a) and, therefore, some necessary processing is required:
a. core matrixThe partial derivatives of (a) are:
b. partial derivatives are simultaneously calculated for the two kernel matrices, and the following can be obtained:
c. calculate outPartial derivatives of the elements in row i and column q:
in the formula,n4is the number of samples of modeling data for the best operating conditions.
Simulation analysis:
in the process of dense medium coal separation, the coal separation process parameters need to be continuously detected and adjusted to ensure the stability of the quality and quantity of products and ensure the safe operation of the production process, so the detection and adjustment of the density and rheological property of the dense medium suspension liquid are the key points for the measurement and control of the dense medium coal separation process parameters. In actual production, the operation state of the dense-medium suspension density measurement and control process is often influenced by factors such as process parameter drift and environmental disturbance, and deviates from the optimal operation state. The separation of raw coal by heavy media is a complex industrial operation process. In order to master the running state of production in time, the method can be used for the on-line evaluation of the running state of the dense-medium coal separation density measurement and control process based on process data.
By deeply analyzing the dense-medium coal separation density measurement and control process and considering the actual production process on site, 5 process variables and 1 output variable can be selected for the online evaluation of the running state of the dense-medium coal separation density measurement and control process. The 5 process variables are respectively: main separation density, main separation liquid level, main separation pressure, magnetic substance concentration and coal slime content; the 1 output variable is: and (5) grading with ash. The input and output variables are shown in table 1:
TABLE 1 input/output variables table
1) Establishment of density measurement and control process off-line evaluation model
9900 groups of samples can be collected according to field data of a density measurement and control process of a certain coal preparation plant and used for modeling, evaluating and classifying running states. According to long-term practical production experience, the dense medium density measurement and control process is divided into 4 state grades and gradual change operation states among different grades according to grey scales (fast grey data), and as shown in table 2:
TABLE 2 Process State partition criteria
Wherein the data set (X) is modeled1,y1)，(X2,y2)，(X3,y3)，(X4,y4) Respectively corresponding to 4 classes of excellent, medium and poor running states. Meanwhile, an evaluation model of each operation state grade is established by using a T-KPRM method
2) On-line running state evaluation of density measurement and control process based on T-KPRM
640 test data sets can be randomly collected in the actual production process and used for online evaluation of the running state. As shown in table 3, the test data contained 4 state levels of excellent and medium difference and 3 kinds of gradual operation state data between different levels. Setting a similarity threshold value as epsilon 0.8, setting the width of a sliding window as H4, setting the step length l as 1 and setting the similarity continuous increment number as 3. The production process follows a time sequence and transitions according to the order of poor, medium, good and excellent.
TABLE 3 number of test sample sets at each stage
As shown in fig. 3, the four graphs (a), (b), (c), and (d) in fig. 3 show the variation of the similarity between the sliding data window and the four state levels of poor, medium, good, and good, respectively. And between the 1 st sampling time and the 103 th sampling time, the similarity between the data of the sliding time window and the grade difference is greater than the similarity threshold value of 0.85, and the production process runs in a difference state at the moment as judged by the first evaluation criterion. Similarly, at the 127 th to 355 th sampling moments, at the 380 th to 509 th sampling moments, and between the 529 th to 640 th sampling moments, the similarity between the data of the line data window and the states "in", "good" and "good" is greater than the similarity threshold value of 0.85, so that it can be determined that the production process is respectively operated in the "in", "good" and "good" states at this time. Fig. 3 (e) is a diagram showing the online evaluation result of the operation state of the whole measurement and control process, and the ordinate 1, 2, 3 and 4 in the diagram respectively represent four state levels of poor, medium, good and excellent.
Except for four determined-level operation states, the rest sampling moment area is a transition stage between two adjacent stable states. For example, from the sampling time 104 to 106, the similarity between the online window data and each state level is less than the threshold value, and the similarity with "medium" gradually increases. Namely satisfyJudging according to the evaluation criterion two, if the number of the incremental increases before and after the satisfaction of the similarity is 3, indicating that the similarity between the data of the sliding time window and the difference grade is smaller than the similarity threshold value between the sampling time 104 and the sampling time 126, and the similarity between the preceding time and the subsequent time is gradually decreasedAnd (4) potential. The production run is now in the "poor" to "medium" transition phase. Similarly, the sampling times 356 to 379,510 to 528 can also be determined that the production process is in the "medium" to "good" transition phase and the "good" to "good" transition phase, respectively. In the diagram (e) of fig. 3, the ordinates 1.5, 2.5 and 3.5 respectively represent the transition phases between the operating states.
3) Comparison of evaluation models in the presence of strong noise and outliers
It is considered that industrial field data often suffers from various interferences (such as sensor faults, process disturbances and the like) in the acquisition process, so that outliers exist in sample data. The existence of these outliers often causes the modeling analysis method to lose its proper generalization capability, thereby affecting the accuracy of the model. The complex industrial process running state evaluation method (T-KPRM) based on the kernel bias robust latent variable technology combines the advantages of two algorithms of PRM and T-KPLS, so that the nonlinear problem of data can be rapidly solved, and the influence of outliers on the accuracy of an evaluation model can be overcome. Although the conventional method (such as T-KPLS, FDA, etc.) can also be used for establishing an operating state evaluation model, when the modeling sample data contains outliers, the accuracy of the evaluation model is affected, and the operating state cannot be accurately evaluated and identified.
And aiming at the density measurement and control process of the dense-medium coal separation, 603 groups of test data are randomly acquired and used for verifying the good robustness of the T-KPRM method. As shown in table 4, the good-medium-poor 4-state grades and 3 kinds of gradual-change operation state data between different grades are still included in the test data. While the modeling dataset still took four groups of the previous section, which were (X) respectively1,y1)，(X2,y2)，(X3,y3)，(X4,y4). Meanwhile, an evaluation model of each operation state grade is established by utilizing a T-KPRM methodThe evaluation of each operating state class is also established using the existing method (T-KPLS)Model (model)
TABLE 4 test data for method comparisons
Here we choose to model outliers and strong noise by adding perturbations to the modeling data. Considering the actual acquisition condition of production data, the modeling data of the 'good' grade and the 'good' grade are less than the modeling data of the 'medium' grade and the 'poor' grade, so that 5% of sample data are randomly selected from the modeling data of the 'good' grade and the 'good' grade respectively to add disturbance. Mode of disturbance addition: the selected 5% samples (outliers) are equally divided into two portions of data, with 30% of the perturbation added to the input of one portion of data and 30% of the perturbation added to the output of the other portion of data in equal amounts. Meanwhile, 10% of sample data is randomly selected from the modeling data of the 'middle' level and the 'difference' level respectively and added with disturbance. Mode of disturbance addition: the selected 10% samples (outliers) are averaged into two portions of data, with 30% perturbation added to the input of one portion of data and 30% perturbation added to the output of the other portion of data in equal amounts.
When the modeling data is normal data, namely no disturbance is added, the running state of the density measurement and control process is evaluated by using the conventional method (T-KPLS) and the proposed method (T-KPRM), and the evaluation results of the two methods are compared, as shown in fig. 4 and 5.
When the modeling data contains outliers and strong noise, namely disturbance is added according to the previous expression, the running state of the density measurement and control process is evaluated by using the conventional method (T-KPLS) and the proposed method (T-KPRM), and the evaluation results of the two methods are compared, as shown in fig. 6 and 7.
The evaluation and recognition accuracy of the two methods are compared below. As shown in tables 5 and 6, the similarity threshold value ranges are: 0.6 to 0.9.
TABLE 5 evaluation of recognition accuracy by Prior Art method (T-KPLS)
| Similarity threshold | Difference (D) | In | Good wine | Superior food |
| ε≥0.6 | 21％ | 13％ | 59％ | 12％ |
| ε≥0.7 | 17％ | 9％ | 41％ | 6％ |
| ε≥0.8 | 10％ | 7％ | 19％ | 4％ |
| ε≥0.9 | 4％ | 2％ | 11％ | 3％ |
Evaluation and identification accuracy of the method (T-KPRM) provided in Table 6
| Similarity threshold | Difference (D) | In | Good wine | Superior food |
| ε≥0.6 | 99％ | 72％ | 99％ | 99％ |
| ε≥0.7 | 99％ | 55％ | 98％ | 96％ |
| ε≥0.8 | 96％ | 30％ | 79％ | 87％ |
| ε≥0.9 | 88％ | 15％ | 9％ | 62％ |
As can be seen from the analysis in the table, the evaluation and identification accuracy of the T-KPRM method is obviously superior to that of the existing method (T-KPLS method).
Therefore, the comparison result of the comprehensive evaluation model diagram and the identification accuracy rate shows that the existing method (T-KPLS) loses the original generalization capability due to the fact that the modeling data contains given outliers and strong noise, the evaluation result diagrams of the four types of states established by the existing method (T-KPLS) lose the evaluation accuracy and cannot keep higher evaluation identification accuracy, and the anti-noise capability of the existing method (T-KPLS) is weak. Although a few disturbances appear in an evaluation model established by the method (T-KPRM), the simulation outline of an evaluation result under the noise-free condition is basically kept, the higher evaluation identification accuracy is kept, and the method has strong noise resistance and better robustness than the existing method (T-KPLS).
4) Non-optimal factor identification for density measurement and control process
The non-optimal state refers to other stable states or transitional states of the industrial operation state besides the 'excellent' state. When the dense medium coal preparation density measurement and control process is operated in a certain determined non-optimal state or in a transition stage of two stable states, the non-optimal factors are kept unchanged. That is, changes in non-optimal factors may lead to different evaluation results.
As shown in fig. 8, 9, 10, 11, 12, and 13, the ordinate of fig. 8 to 13 represents the contribution ratio, and 1, 2, 3, 4, and 5 in the abscissa correspond to five variables: main separation density, main separation liquid level, main separation pressure, magnetic substance concentration and coal slime content. The sampling instants taken by the identification process are randomly chosen from the various state levels and the transition phases between the state levels. Fig. 8 shows that the contribution ratio of the master density and the master pressure is higher at this time, and therefore the main factors causing the non-optimal state at the 50 th sampling time are the master density and the master pressure. It can be seen from fig. 9 that the main selection pressure and main selection level are the main factors that are in a non-optimal state at the 115 th sampling instant. Similarly, the main factors of the non-optimal state can be derived from fig. 10, 11, 12, and 13, respectively, and are not described in detail herein.
According to the simulation results, the operation state off-line evaluation model established by the complex industrial process operation state evaluation method (T-KPRM) based on the nuclear bias robust latent variable technology is of practical significance for the operation state evaluation and non-optimal factor identification of the coal dressing density measurement and control process of the heavy medium. By means of the evaluation and factor identification results, field operators can adjust and improve the production strategy in time, and the production efficiency is improved. The operation state evaluation method is suitable for the heavy medium cyclone separation and gravity heavy medium separation process.
In conclusion, the T-KPRM method provided by the invention combines the advantages of PRM and T-KPLS, not only can effectively solve the non-linear problem of density measurement and control process data, but also can effectively overcome the influence of outliers on the accuracy of an evaluation model. The invention provides the method application aiming at the problem of evaluating the running state of the complex industrial production process, in particular to a T-KPRM-based method for evaluating the running state of the complex industrial process, and the method is applied to the dense medium coal dressing density measurement and control process to obtain a good evaluation effect. The method comprises the steps of accurately extracting information of each variable of field data, establishing an evaluation model of historical process data, and then carrying out online running state evaluation on a density measurement and control process by using three evaluation criteria. And finally, identifying the non-optimal factors of the running state through the evaluation result, and providing a decision basis for operators to adjust the production strategy in real time, thereby improving the production efficiency and economic benefit of enterprises.
Claims (2)
1. A complex industrial process running state evaluation method based on T-KPRM is characterized in that an input data matrix is assumed to be X belongs to RN×JN is the number of samples, J is the number of process variables; the output data matrix is Y ∈ RNIncluding an output process variable; the method for evaluating the running state of the complex industrial process based on the T-KPRM comprises the following specific steps:
step one, carrying out zero mean value and unit variance processing on each column of an input data matrix X; similarly, the output data matrix Y is also subjected to standardization processing;
step twoAnd carrying out nonlinear mapping on the input data matrix X: x is the number ofi∈RN→Φ(xi) E F is projected to a high-dimensional feature space F, and an kernel matrix K is calculated in the F space: k is phiTΦ；
Step three, carrying out standardization processing on the kernel matrix K;
and fourthly, operating a PRM algorithm on the kernel matrix K and the output data matrix Y, wherein the PRM algorithm specifically comprises the following steps:
a1, settingThe leverage value for the ith sample data can be represented by the following formula:
and is
Wherein, | | | |, represents the Euclidean distance, med represents the median, medL1Represents the median value of L1, tiIs the PLS score of the ith sample data, c is a constant;
setting the residual weight of ith sample dataCan be defined by the following formula:
wherein r isiRepresenting the residual between the predicted value and the actual value of the ith sample data,a robust scale estimate representing the residual may be calculated by:
the integrated weight w of the ith sample dataiThis can be determined by the following formula:initializing weight W by using equations (1), (3) and (5)i；
b1, respectively carrying out weighted calculation on the kernel matrix K and the output data matrix Y, and obtaining an input kernel matrix K after weightingWAnd the output data matrix YWThen, a PLS1 regression model is established for the weighted input and output data, and the score vector of the weighted input and output data is corrected;
c1, calculating residual error r of each sample dataiUpdating the sample weight W using the equations (1), (3) and (5)i；
d1, if the relative difference value of q obtained by two successive calculations is smaller than the threshold value, entering the step five, otherwise, returning to the step b 1;
step five, the input data matrix is changed into KWThe output data matrix becomes YWFrom the output data matrix YWExtracting the converged uiLet i equal to 1, KWi＝KW，YWi＝YW；
a2, order YWiIs equal to ui；
b2, calculating KWScore vector of (t)i＝KWiui，ti←ti/||ti||；
c2、
d2, calculate YWiScore vector u ofi＝YWiqi，ui←ui/||ui||；
e2, judgment uiWhether convergence is achieved, if yes, the step six is carried out, otherwise, the step a2 is returned;
step six, calculating KWiThe load matrix of (a):
seventhly, extracting all principal elements and calculating an input data matrix KWScore matrix T and input data matrix KWLoad matrix P, output data matrix YWScore matrix U and output data matrix YWThe load matrix Q of (2) is as follows:
a3, order
b3, making i equal to i +1, repeating the fifth step and the sixth step until A principal elements are extracted, wherein the number A of the principal elements can be determined by a cross-validation method;
c3、T＝[t1,...,tA]，P＝[p1,...,pA]，U＝[u1,...,uA]，Q＝[q1,...,qA]；
step eight, inputting a data matrix KW＝TPT+ E, output data matrix YW＝UQT+F；
Nine steps, to principal component TPTOperating the PCA algorithm:
step ten, operating a PCA algorithm on the residual error E:
if the output data matrix Y is a single output variable, the expression of the T-KPRM model is as follows:
the above-mentioned score vector tyShown is the neutralization of the output y in TWThe directly related part, namely the most key variable required to establish the evaluation model, can be used for establishing the off-line evaluation model of the running state; t isoIs represented in T and output yWOrthogonal part；TrIs the part of the residual E with the larger variance; erIs the final residual, i.e., noise;
when a new sample k is introducednewThe score matrix will be given by:
wherein k isnewIs a new sample xnewThe kernel function of (a) can be calculated by the following formula:
knew＝Φ(X)Φ(xnew)＝[k(x1,xnew),...k(xn,xnew)]T(8)，
to k is pairednewThe following are obtained by carrying out equalization:
wherein 1 ist＝1/n·[11...1]T∈Rn。
2. The application of the method for evaluating the running state of the complex industrial process based on the T-KPRM as claimed in claim 1, wherein the application of the method for evaluating the running state of the complex industrial process based on the T-KPRM means that the nuclear bias robust latent variable technology is used to establish an off-line evaluation model of the running state, the on-line evaluation of the running state of the complex industrial process and the recognition of non-optimal factors, specifically, the nuclear bias robust latent variable technology is used to establish the off-line evaluation model, and the off-line evaluation model of the corresponding running state grade has the score vector ofWherein c is the number of operating state levels; then, introducing a sliding window technology, calculating the similarity between the online data window and the corresponding evaluation level, and performing online evaluation on the operation state of the industrial process by using the similarity; and then calculating the contribution rate of corresponding variables by using the Euclidean distance between the sliding data window and the optimal evaluation level, and calculating the running stateNon-optimal factors of the states are identified.
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