CN113345532A - Method for estimating rapid state of polyphenylene oxide production process - Google Patents

Method for estimating rapid state of polyphenylene oxide production process Download PDF

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CN113345532A
CN113345532A CN202110608741.8A CN202110608741A CN113345532A CN 113345532 A CN113345532 A CN 113345532A CN 202110608741 A CN202110608741 A CN 202110608741A CN 113345532 A CN113345532 A CN 113345532A
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赵顺毅
李可
郭松杰
栾小丽
刘飞
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Abstract

The invention discloses a method for quickly estimating the state of a polyphenyl ether production process, which comprises the following steps: establishing a linear high-dimensional system dynamic model in the process of generating polyphenyl ether by the alkylation of phenol and methanol, dividing a high-dimensional system state vector into low-dimensional state blocks according to system characteristics, and performing state estimation on the state blocks by using a variational Bayes theory and a Kalman filtering principle. The invention can effectively reduce the calculation cost while keeping higher state estimation precision, and realizes the balance of the high-dimensional system in the estimation precision and the calculation cost.

Description

Method for estimating rapid state of polyphenylene oxide production process
Technical Field
The invention relates to the technical field of complex process state estimation and monitoring, in particular to a rapid state estimation method for a polyphenyl ether production process.
Background
The process of producing polyphenylene ether by alkylation of phenol with methanol involves numerous state variables, and is in the field of complex industrial processes, and therefore the process can be described as a high dimensional system, and state estimation of the polyphenylene ether production process can be converted into state estimation of this high dimensional system. In the prior art, the state of a high-dimensional system is estimated by using Kalman filtering, the Kalman filtering can provide optimal estimation in the meaning of minimum mean square error, but the calculation cost required when the Kalman filter is actually applied to the high-dimensional system is very high. In order to reduce the calculation cost, an ensemble kalman filtering method is also proposed, and although the calculation cost can be reduced to some extent, the reduction effect is limited. Meanwhile, the estimation precision depends on the size of the sample set, and when the sample set is large enough, the precision of state estimation can achieve a satisfactory effect, but the cost of simultaneous calculation of the large sample set is relatively high; when the sample set is small, the calculation cost can be reduced to a certain extent, but the accuracy of state estimation is difficult to achieve a satisfactory effect. At present, no good state estimation method can realize the balance between the estimation precision and the calculation cost of a high-dimensional system.
Disclosure of Invention
Therefore, the technical problem to be solved by the invention is to overcome the defects in the prior art, and provide a method for quickly estimating the state of the polyphenylene ether production process, which can reduce the calculation cost while ensuring high-precision estimation of the state of the process of producing the polyphenylene ether by alkylation of phenol and methanol, and realize the balance between the state estimation precision and the calculation cost.
In order to solve the technical problem, the invention provides a method for quickly estimating the state of a polyphenyl ether production process, which comprises the following steps:
step 1: establishing a linear high-dimensional system dynamic model of the process of generating the polyphenyl ether by the alkylation of phenol and methanol,
step 2: dividing high-dimensional system state vector into d according to system characteristicssA state block, each state block having dimension si；
And step 3: setting the initial state value of the system
Figure BDA0003095118470000021
Initial covariance matrix P0|0N measured values of the systemnProcess noise covariance matrix QnNumber of blocks dsThe total iteration times L and the total sampling times step of each moment, and the initialization time index n is 1;
and 4, step 4: calculating a state prediction value of each state block and a prediction value of covariance of each state block according to a variational Bayes theory and a Kalman filtering principle;
and 5: updating the predicted value of the covariance of each state block, and initializing the iteration number l to be 1;
step 6: updating the state prediction value of each state block;
and 7: judging whether the current iteration number L meets the condition that L is equal to L or not, and if so, executing a step 8; if not, making l equal to l +1, and skipping to execute the step 6;
and 8: outputting the estimated value of each state block at n moments;
and step 9: outputting an estimated value of the system state at the n moment and a covariance matrix of the system state at the n moment;
step 10: judging whether the time n meets n ═ steps, if not, making n ═ n +1, and skipping to execute the step 4; if yes, ending the output to obtain the state estimation of the production process of the polyphenyl ether.
Further, the linear high-dimensional system dynamic model established in step 1 is:
xn+1＝Fnxn+wn，
yn＝Hnxn+vn；
wherein n represents a time index, xn+1Represents the system state at time n +1, xnIndicating the state of the system at time n, FnIn order to be a state transition matrix,
Figure BDA0003095118470000031
subject to a mean of 0 and a covariance matrix of QnThe process noise of (1); y isnRepresenting measured values of the system at time n, HnIn order to measure the matrix of the measurements,
Figure BDA0003095118470000032
subject to a mean of 0 and a covariance matrix of RnThe measurement noise of (2).
Further, in the step 2, a high-dimensional system state vector is divided into d according to the system characteristicssThe status block specifically comprises: setting the number d of state blocks according to actual needssAnalyzing the physical meaning and the relation between the system state variables and putting the closely related system state vectors into the same state block to obtain dsStatus block
Figure BDA0003095118470000033
Further, the calculation formula of the state prediction value of each state block in step 4 is as follows:
Figure BDA0003095118470000034
wherein,
Figure BDA0003095118470000035
indicating the state prediction value for the ith state block at time n,
Figure BDA0003095118470000036
represents the state transition matrix FnOf (i) th si×dxSubmatrix of dimension, dxIn order to be a dimension of the state vector,
Figure BDA0003095118470000037
representing an estimate of the state of the system at time n-1.
Further, the calculation formula of the predicted value of the covariance of each state block in step 4 is as follows:
Figure BDA0003095118470000038
wherein
Figure BDA0003095118470000039
Representing the predicted value of the covariance for the ith state block at time n,
Figure BDA00030951184700000310
represents the state transition matrix FnThe ith diagonal block matrix of the block matrix,
Figure BDA00030951184700000311
representing an estimate of the covariance of the ith state block at time n-1,
Figure BDA00030951184700000312
to represent
Figure BDA00030951184700000313
The transpose of (a) is performed,
Figure BDA00030951184700000314
representing process noise covariance matrix QnThe ith diagonal block matrix.
Further, the update formula of the prediction value of the covariance of each state block in step 5 is as follows:
Figure BDA0003095118470000041
wherein,
Figure BDA0003095118470000042
a predictor representing the covariance of the ith state block at time n,
Figure BDA0003095118470000043
represents the state transition matrix FnS of middle jj×siSubmatrix of dimension, sjFor the dimension of the jth state block,
Figure BDA0003095118470000044
representing process noise covariance matrix QnThe jth diagonal block matrix of (a) is,
Figure BDA0003095118470000045
to represent
Figure BDA0003095118470000046
The transpose of (a) is performed,
Figure BDA0003095118470000047
representing a measurement matrix HnOf (i) th dy×siSubmatrix of dimension, dyThe dimensions of the measurement vector are represented by,
Figure BDA0003095118470000048
to represent
Figure BDA0003095118470000049
The transpose of (a) is performed,
Figure BDA00030951184700000410
representing a measurement noise covariance matrix RnThe inverse of (a) is,
Figure BDA00030951184700000411
representing the inverse of the covariance prediction for the ith state block at time n.
Further, the update formula of the state prediction value of each state block in step 6 is as follows:
Figure BDA00030951184700000412
wherein,
Figure BDA00030951184700000413
representing the state estimate for the ith state block at time n for the ith iteration,
Figure BDA00030951184700000414
representing a measurement matrix HnOf (i) th dy×siSubmatrix of dimension, dyThe dimensions of the measurement vector are represented by,
Figure BDA00030951184700000415
to represent
Figure BDA00030951184700000416
Transposing;
Figure BDA00030951184700000417
representing a measurement noise covariance matrix RnThe inverse of (a) is,
Figure BDA00030951184700000418
representing the inverse of the covariance prediction for the ith state block at time n, ynRepresenting the measured value of the system at the n moment;
Figure BDA00030951184700000419
representing a measurement matrix HnThe sub-matrix matching the 1 st state block to the (i-1) th state block dimension,
Figure BDA00030951184700000420
representing the 1 st state block to the i-1 st state block in the estimated value of the system state vector at the l step iteration at the time n,
Figure BDA00030951184700000421
representing a measurement matrix HnAnd (i + 1) th to (d) th status blockssA sub-matrix that matches the dimensions of the individual state blocks,
Figure BDA00030951184700000422
i +1 th state block to d-th state block representing system state estimation value in l-1 th iterationsThe status of each of the status blocks is,
Figure BDA00030951184700000423
and the predicted value of the ith state block at the moment n is shown.
Further, the estimated value of each state block at the time n in the step 8
Figure BDA00030951184700000424
Comprises the following steps:
Figure BDA00030951184700000425
wherein
Figure BDA00030951184700000426
Representing the estimate for the ith state block at time n for the lth iteration.
Further, the estimated value of the system state at the time n in the step 9
Figure BDA0003095118470000051
Comprises the following steps:
Figure BDA0003095118470000052
wherein
Figure BDA0003095118470000053
Representing the transpose of the estimate of the 1 st state block at the L-th iteration,
Figure BDA0003095118470000054
denotes the d-thsThe transpose of the estimated values of the state blocks at the iteration of the L-th step.
Further, the covariance matrix P of the system state at time n in step 9n|nComprises the following steps:
Figure BDA0003095118470000055
where blkdiag (-) represents the block diagonal matrix operator,
Figure BDA0003095118470000056
represents the covariance matrix corresponding to the 1 st state block,
Figure BDA0003095118470000057
denotes the d-thsCovariance of each state block.
Compared with the prior art, the technical scheme of the invention has the following advantages:
the method for quickly estimating the state of the polyphenyl ether production process establishes a linear high-dimensional system dynamic model of the polyphenyl ether production process by the alkylation of phenol and methanol, divides a high-dimensional system state vector into a plurality of low-dimensional state blocks according to system characteristics, and estimates the state of the state blocks by a variational Bayesian theory and a Kalman filtering principle. The segmented system state estimation method avoids the direct calculation of the state covariance matrix at each moment, so that the calculation cost is obviously reduced, the calculation cost can be effectively reduced while the state estimation precision is ensured, and the balance of a high-dimensional system in the estimation precision and the calculation cost is realized.
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In order that the present disclosure may be more readily and clearly understood, reference will now be made in detail to the present disclosure, examples of which are illustrated in the accompanying drawings.
FIG. 1 is a flow chart of the present invention.
FIG. 2 is a graph showing the results of comparison of the state estimation root mean square error of five separation section systems in a polyphenylene ether production process with KF, EnKF and SKF using the invention in the example of the invention with time.
FIG. 3 is a diagram of the results of comparing the computational cost with the dimension of the system state vector using the present invention with KF, EnKF and SKF in an embodiment of the present invention.
Detailed Description
The present invention is further described below in conjunction with the following figures and specific examples so that those skilled in the art may better understand the present invention and practice it, but the examples are not intended to limit the present invention.
In the description of the present invention, it should be understood that the term "comprises/comprising" is intended to cover a non-exclusive inclusion, such that a process, method, system, article, or apparatus that comprises a list of steps or elements is not limited to the listed steps or elements but may alternatively include other steps or elements not expressly listed or inherent to such process, method, article, or apparatus.
Referring to the flowchart of FIG. 1, an embodiment of a method for rapid state estimation in a polyphenylene ether production process according to the present invention comprises the steps of:
step 1: a linear high dimensional system dynamic model of the process of producing polyphenylene ether from the alkylation of phenol and methanol is established. The high-dimensional system dynamic model is used for describing a high-dimensional system, and the linear high-dimensional system dynamic model in the embodiment is a state space model.
xn+1＝Fnxn+wn，
yn＝Hnxn+vn；
Wherein n represents a time index, xn+1Represents the system state at time n +1, xnIndicating the state of the system at time n, FnIn order to be a state transition matrix,
Figure BDA0003095118470000061
subject to a mean of 0 and a covariance matrix of QnThe process noise of (1); y isnRepresenting measured values of the system at time n, HnIn order to measure the matrix of the measurements,
Figure BDA0003095118470000062
subject to a mean of 0 and a covariance matrix of RnThe measurement noise of (2);
step 2: dividing high-dimensional system state vector into d according to system characteristicssA state block, each state block having dimension si。
Setting the shape according to actual needsNumber of state blocks dsThe high-dimensional system comprises thousands of state variables with physical significance, the system characteristics refer to the relationship among the state variables in the system, the physical significance and the relationship among the state variables of the system are analyzed, and closely-related system state vectors (such as the close association among the speed, the acceleration and the displacement) are put into the same state block to obtain dsStatus block
Figure BDA0003095118470000071
And step 3: setting the initial state value of the system
Figure BDA0003095118470000072
Initial covariance matrix P0|0N measured value y of the time systemnProcess noise covariance matrix QnNumber of blocks dsThe total iteration times L and the total sampling times steps of each moment;
initializing a time index n to 1;
and 4, step 4: calculating the state prediction value of each state block and the prediction value of the covariance of each state block, wherein the calculation formula is as follows:
Figure BDA0003095118470000073
Figure BDA0003095118470000074
wherein,
Figure BDA0003095118470000075
indicating the state prediction value for the ith state block at time n,
Figure BDA0003095118470000076
represents the state transition matrix FnOf (i) th si×dxSubmatrix of dimension, dxIs a dimension of the state vector of the system,
Figure BDA0003095118470000077
an estimated value representing a system state at the n-1 th time;
Figure BDA0003095118470000078
representing the predicted value of the covariance for the ith state block at time n,
Figure BDA0003095118470000079
represents the state transition matrix FnThe ith diagonal block matrix of the block matrix,
Figure BDA00030951184700000710
representing an estimate of the covariance of the ith state block at time n-1,
Figure BDA00030951184700000711
to represent
Figure BDA00030951184700000712
The transpose of (a) is performed,
Figure BDA00030951184700000713
representing process noise covariance matrix QnThe ith diagonal block matrix;
and 5: updating the predicted value of the covariance of each state block, wherein the updating formula is as follows:
Figure BDA00030951184700000714
wherein,
Figure BDA00030951184700000715
a predictor representing the covariance of the ith state block at time n,
Figure BDA00030951184700000716
represents the state transition matrix FnS of middle jj×siSubmatrix of dimension, sjFor the dimension of the jth state block,
Figure BDA00030951184700000717
representing process noise covariance matrix QnThe jth diagonal block matrix of (a) is,
Figure BDA0003095118470000081
to represent
Figure BDA0003095118470000082
The transpose of (a) is performed,
Figure BDA0003095118470000083
representing a measurement matrix HnOf (i) th dy×siSubmatrix of dimension, dyThe dimensions of the measurement vector are represented by,
Figure BDA0003095118470000084
to represent
Figure BDA0003095118470000085
The transpose of (a) is performed,
Figure BDA0003095118470000086
representing a measurement noise covariance matrix RnThe inverse of (a) is,
Figure BDA0003095118470000087
representing the inverse of the covariance prediction value of the ith state block at time n;
initializing the iteration number l as 1;
step 6: updating the state prediction value of each state block, wherein the updating formula is as follows:
Figure BDA0003095118470000088
wherein,
Figure BDA0003095118470000089
representing the state estimate for the ith state block at time n for the ith iteration,
Figure BDA00030951184700000810
representing a measurement matrix HnOf (i) th dy×siSubmatrix of dimension, dyThe dimensions of the measurement vector are represented by,
Figure BDA00030951184700000811
to represent
Figure BDA00030951184700000812
Transposing;
Figure BDA00030951184700000813
representing a measurement noise covariance matrix RnThe inverse of (a) is,
Figure BDA00030951184700000814
representing the inverse of the covariance prediction for the ith state block at time n, ynRepresenting the measured value of the system at the n moment;
Figure BDA00030951184700000815
representing a measurement matrix HnThe sub-matrix matching the 1 st state block to the (i-1) th state block dimension,
Figure BDA00030951184700000816
representing the 1 st state block to the i-1 st state block in the estimated value of the system state vector at the l step iteration at the time n,
Figure BDA00030951184700000817
representing a measurement matrix HnAnd (i + 1) th to (d) th status blockssA sub-matrix that matches the dimensions of the individual state blocks,
Figure BDA00030951184700000818
i +1 th state block to d-th state block representing system state estimation value in l-1 th iterationsThe status of each of the status blocks is,
Figure BDA00030951184700000819
the predicted value of the ith state block at the moment of n is shown;
and 7: judging whether the current iteration number L meets the condition that L is equal to L or not, and if so, executing a step 8; if not, making l equal to l +1, and skipping to execute the step 6;
and 8: outputting the estimated value of each state block at n time
Figure BDA00030951184700000820
Figure BDA00030951184700000821
Wherein,
Figure BDA00030951184700000822
representing the estimated value of the ith state block at the time of the L-th iteration at the time of n;
and step 9: outputting an estimated value and a covariance matrix of the system state at n moments, wherein the formulas are respectively
Figure BDA0003095118470000091
Figure BDA0003095118470000092
Wherein,
Figure BDA0003095118470000093
an estimate representing the state of the system at time n,
Figure BDA0003095118470000094
representing the transpose of the estimate of the 1 st state block at the L-th iteration,
Figure BDA0003095118470000095
denotes the d-thsTransposing the estimation value of each state block in the L-th iteration step; pn|nAn estimate of the covariance matrix representing the state of the system at time n, blkdiag (-) represents the block diagonal matrix operator,
Figure BDA0003095118470000096
represents the covariance matrix corresponding to the 1 st state block,
Figure BDA0003095118470000097
denotes the d-thsCovariance corresponding to each state block;
step 10: judging whether the time n meets n ═ steps, if not, making n ═ n +1, and skipping to execute the step 4; if yes, ending the output to obtain the state estimation of the production process of the polyphenyl ether.
To further illustrate the beneficial effects of the present invention, five separation sections of a polyphenylene ether production process were selected for simulation verification in this example, which in total contained 60 state variables. The 60 state variables are divided into five state blocks according to system characteristics, the first state block contains 9 state variables, the second and fourth state blocks both have 13 state variables, the third state block has 11 state variables, and the fifth state block has 14 state variables. Process noise covariance Q of systemnEach time is the same
Figure BDA0003095118470000098
Measuring noise covariance RnEach time is the same
Figure BDA0003095118470000099
dxDimension of the system state vector, dyValue 60, set d in this examples5, 3 and 200. The simulation was based on 20 Monte Carlo runs and time was 200 s. The method (denoted as BKF) is combined with the existing Kalman filtering method (see the detail in the document Simon D. optimal state estimation: Kalman, H ∞, and nonlinearer apoache. John Wiley and Sons,2006. ", denoted as KF), the collective Kalman filtering method (see the detail in the document" even G. ocean Dynamics,2003,53(4):343 and 367 ", denoted as EnKF), the method for dividing the system state vector into a plurality of scalars (see the detail in the document" air-El-Fquick B, Hoteit I. IEEE Transactions on nal Processing,2015,63(21):58535867 ", SKF) of the three methods of dealing with high-dimensional system state estimation problems. The comparison of the state estimation root mean square error of a system in five separation sections in the production process of polyphenyl ether along with the change of Time is shown in figure 2, the abscissa Time in figure 2 represents Time, the ordinate RMSE represents the state estimation root mean square error of the system, and the smaller the value of the root mean square error is, the higher the estimation precision is. Comparison of the variation of the computation cost with the dimension of the system state vector is shown in FIG. 3, in which the abscissa d in FIG. 3xThe dimension of the state vector is represented, the ordinate Cost represents the calculation Cost, and the smaller the calculation Cost value is, the lower the calculation Cost is. As can be seen from FIG. 2 and FIG. 3, when the method BKF of the invention is used for estimating the system state, the higher estimation precision can be kept, and meanwhile, the calculation cost can be effectively reduced. Simulation experiments prove that the invention is a rapid state estimation method which can realize the balance between the calculation cost and the state estimation precision of a linear high-dimensional system, and further illustrates the beneficial effects of the invention.
Compared with the prior art, the technical scheme of the invention has the following advantages: the method for quickly estimating the state of the polyphenyl ether production process establishes a linear high-dimensional system dynamic model of the polyphenyl ether production process by the alkylation of phenol and methanol, divides a high-dimensional system state vector into a plurality of low-dimensional state blocks according to system characteristics, and estimates the state of the state blocks by a variational Bayesian theory and a Kalman filtering principle. The segmented system state estimation method avoids the direct calculation of the state covariance matrix at each moment, so that the calculation cost is obviously reduced, the calculation cost can be effectively reduced while the state estimation precision is ensured, and the balance of a high-dimensional system in the estimation precision and the calculation cost is realized.
As will be appreciated by one skilled in the art, embodiments of the present application may be provided as a method, system, or computer program product. Accordingly, the present application may take the form of an entirely hardware embodiment, an entirely software embodiment or an embodiment combining software and hardware aspects. Furthermore, the present application may take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, and the like) having computer-usable program code embodied therein.
The present application is described with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the application. It will be understood that each flow and/or block of the flow diagrams and/or block diagrams, and combinations of flows and/or blocks in the flow diagrams and/or block diagrams, can be implemented by computer program instructions. These computer program instructions may be provided to a processor of a general purpose computer, special purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be stored in a computer-readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instruction means which implement the function specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
It should be understood that the above examples are only for clarity of illustration and are not intended to limit the embodiments. Other variations and modifications will be apparent to persons skilled in the art in light of the above description. And are neither required nor exhaustive of all embodiments. And obvious variations or modifications of the invention may be made without departing from the spirit or scope of the invention.

Claims (10)

1. A method for rapid state estimation in a polyphenylene ether production process, comprising the steps of:
step 1: establishing a linear high-dimensional system dynamic model of the process of generating the polyphenyl ether by the alkylation of phenol and methanol,
step 2: dividing high-dimensional system state vector into d according to system characteristicssA state block, each state block having dimension si；
And step 3: setting the initial state value of the system
Figure FDA0003095118460000011
Initial covariance matrix P0|0N measured values of the systemnProcess noise covariance matrix QnNumber of blocks dsThe total iteration times L and the total sampling times step of each moment, and the initialization time index n is 1;
and 4, step 4: calculating a state prediction value of each state block and a prediction value of covariance of each state block according to a variational Bayes theory and a Kalman filtering principle;
and 5: updating the predicted value of the covariance of each state block, and initializing the iteration number l to be 1;
step 6: updating the state prediction value of each state block;
and 7: judging whether the current iteration number L meets the condition that L is equal to L or not, and if so, executing a step 8; if not, making l equal to l +1, and skipping to execute the step 6;
and 8: outputting the estimated value of each state block at n moments;
and step 9: outputting an estimated value of the system state at the n moment and a covariance matrix of the system state at the n moment;
step 10: judging whether the time n meets n ═ steps, if not, making n ═ n +1, and skipping to execute the step 4; if yes, ending the output to obtain the state estimation of the production process of the polyphenyl ether.
2. The method for rapid state estimation in polyphenylene ether production process according to claim 1, characterized in that: the linear high-dimensional system dynamic model established in the step 1 is as follows:
xn+1＝Fnxn+wn，
yn＝Hnxn+vn；
wherein n represents a time index, xn+1Represents the system state at time n +1, xnIndicating the state of the system at time n, FnIn order to be a state transition matrix,
Figure FDA0003095118460000021
subject to a mean of 0 and a covariance matrix of QnThe process noise of (1); y isnRepresenting measured values of the system at time n, HnIn order to measure the matrix of the measurements,
Figure FDA0003095118460000022
subject to a mean of 0 and a covariance matrix of RnThe measurement noise of (2).
3. The method for rapid state estimation in polyphenylene ether production process according to claim 1, characterized in that: in the step 2, the high-dimensional system state vector is divided into d according to the system characteristicssThe status block specifically comprises: setting the number d of state blocks according to actual needssAnalyzing the physical meaning and the relation between the system state variables and putting the closely related system state vectors into the same state block to obtain dsStatus block
Figure FDA0003095118460000023
4. The method for rapid state estimation in polyphenylene ether production process according to claim 1, characterized in that: the calculation formula of the state prediction value of each state block in the step 4 is as follows:
Figure FDA0003095118460000024
wherein,
Figure FDA0003095118460000025
indicating the state prediction value for the ith state block at time n,
Figure FDA0003095118460000026
represents the state transition matrix FnOf (i) th si×dxSubmatrix of dimension, dxIn order to be a dimension of the state vector,
Figure FDA0003095118460000027
representing an estimate of the state of the system at time n-1.
5. The method for rapid state estimation in polyphenylene ether production process according to claim 1, characterized in that: the calculation formula of the predicted value of the covariance of each state block in the step 4 is as follows:
Figure FDA0003095118460000028
wherein
Figure FDA0003095118460000029
Representing the predicted value of the covariance for the ith state block at time n,
Figure FDA00030951184600000210
represents the state transition matrix FnThe ith diagonal block matrix of the block matrix,
Figure FDA00030951184600000211
representing an estimate of the covariance of the ith state block at time n-1,
Figure FDA00030951184600000212
to represent
Figure FDA0003095118460000031
The transpose of (a) is performed,
Figure FDA0003095118460000032
representing process noise covariance matrix QnThe ith diagonal block matrix.
6. The method for rapid state estimation in polyphenylene ether production process according to claim 1, characterized in that: the updating formula of the predicted value of the covariance of each state block in the step 5 is as follows:
Figure FDA0003095118460000033
wherein,
Figure FDA0003095118460000034
a predictor representing the covariance of the ith state block at time n,
Figure FDA0003095118460000035
represents the state transition matrix FnS of middle jj×siSubmatrix of dimension, sjFor the dimension of the jth state block,
Figure FDA0003095118460000036
representing process noise covariance matrix QnThe jth diagonal block matrix of (a) is,
Figure FDA0003095118460000037
to represent
Figure FDA0003095118460000038
The transpose of (a) is performed,
Figure FDA0003095118460000039
representing a measurement matrix HnOf (i) th dy×siSubmatrix of dimension, dyThe dimensions of the measurement vector are represented by,
Figure FDA00030951184600000310
to represent
Figure FDA00030951184600000311
The transpose of (a) is performed,
Figure FDA00030951184600000312
representing a measurement noise covariance matrix RnThe inverse of (a) is,
Figure FDA00030951184600000313
representing the inverse of the covariance prediction for the ith state block at time n.
7. The method for rapid state estimation in polyphenylene ether production process according to claim 1, characterized in that: the update formula of the state prediction value of each state block in the step 6 is as follows:
Figure FDA00030951184600000314
wherein,
Figure FDA00030951184600000315
representing the state estimate for the ith state block at time n for the ith iteration,
Figure FDA00030951184600000316
representing a measurement matrix HnOf (i) th dy×siSubmatrix of dimension, dyThe dimensions of the measurement vector are represented by,
Figure FDA00030951184600000317
to represent
Figure FDA00030951184600000318
Transposing;
Figure FDA00030951184600000319
representing a measurement noise covariance matrix RnThe inverse of (a) is,
Figure FDA00030951184600000320
representing the inverse of the covariance prediction for the ith state block at time n, ynRepresenting the measured value of the system at the n moment;
Figure FDA00030951184600000321
representing a measurement matrix HnThe sub-matrix matching the 1 st state block to the (i-1) th state block dimension,
Figure FDA00030951184600000322
representing the 1 st state block to the i-1 st state block in the estimated value of the system state vector at the l step iteration at the time n,
Figure FDA00030951184600000323
representing a measurement matrix HnAnd (i + 1) th to (d) th status blockssA sub-matrix that matches the dimensions of the individual state blocks,
Figure FDA00030951184600000324
i +1 th state block to d-th state block representing system state estimation value in l-1 th iterationsThe status of each of the status blocks is,
Figure FDA00030951184600000325
and the predicted value of the ith state block at the moment n is shown.
8. The method for rapid state estimation in polyphenylene ether production process according to claim 1, characterized in that: the estimated value of each state block at the n time in the step 8
Figure FDA0003095118460000041
Comprises the following steps:
Figure FDA0003095118460000042
wherein
Figure FDA0003095118460000043
Representing the estimate for the ith state block at time n for the lth iteration.
9. The method for rapid state estimation in polyphenylene ether production process according to claim 1, characterized in that: the estimated value of the system state at the time n in the step 9
Figure FDA0003095118460000044
Comprises the following steps:
Figure FDA0003095118460000045
wherein
Figure FDA0003095118460000046
Representing the transpose of the estimate of the 1 st state block at the L-th iteration,
Figure FDA0003095118460000047
denotes the d-thsThe transpose of the estimated values of the state blocks at the iteration of the L-th step.
10. The method for rapid state estimation in polyphenylene ether production process according to any one of claims 1 to 9, characterized in that: the covariance matrix P of the system state at the time n in the step 9n|nComprises the following steps:
Figure FDA0003095118460000048
where blkdiag (-) represents the block diagonal matrix operator,
Figure FDA0003095118460000049
represents the covariance matrix corresponding to the 1 st state block,
Figure FDA00030951184600000410
denotes the d-thsCovariance of each state block.
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