Improved rapid estimation method for process state of polyphenyl ether production

Abstract

The present application relates to a kind of improved polyphenyl ether production process state fast estimation method, including the linear high-dimensional system dynamic model generated by phenol and methanol alkylation polyphenyl ether;The state vector of high-dimensional system is divided into multiple state blocks of low dimension, while introducing an auxiliary variable to correct the system error caused by block.This method can meet the low calculation cost of linear high-dimensional system state estimation while achieving higher accuracy requirements.

Description

Technical Field

[0001] This invention relates to the field of industrial process state estimation and monitoring technology, and in particular to an improved method for rapid estimation of the state of polyphenylene ether production process. Background Technology

[0002] The process of producing polyphenylene ether from the alkylation of phenol and methanol falls under the category of complex industrial processes. This system has a large architecture and numerous state variables, thus it can be described as a high-dimensional system. Regarding the state estimation problem of linear high-dimensional systems, the Kalman filter method can provide the optimal estimate in the sense of minimum mean square error. However, when the dimension of the system's state vector is very high, applying the Kalman filter method incurs extremely high computational costs, which severely impacts the real-time performance and effectiveness of the state estimation. To reduce computational costs, some researchers have proposed ensemble Kalman filtering, which can reduce computational costs to some extent. However, the accuracy of state estimation depends heavily on the size of the sample set. When the sample set is large enough, the accuracy of state estimation can achieve satisfactory results, but the computational cost is relatively high. Conversely, when the sample set is small, the computational cost can be reduced to some extent, but the accuracy of state estimation is still difficult to achieve satisfactory results. Therefore, some researchers have proposed dividing the system into multiple scalars. This method can significantly reduce computational costs, but the accuracy of state estimation is still difficult to achieve satisfactory results, especially in systems where the state variables are closely correlated, where the state estimation performance is very poor. Subsequently, methods for state estimation by dividing the system into blocks were developed. For example, invention patent CN113345532A discloses a rapid state estimation method for the polypropylene ether production process. This method can, to some extent, balance the accuracy of state estimation with computational cost. However, the aforementioned methods for dividing the system into blocks do not consider compensation for system errors. Therefore, methods for state estimation of high-dimensional systems still require further exploration and research. Summary of the Invention

[0003] Therefore, the technical problem to be solved by the present invention is to overcome the problems existing in the prior art and propose an improved method for rapid estimation of the state of polyphenylene ether production process, which enables the state estimation to achieve higher accuracy while keeping the computational cost at a low level.

[0004] To address the aforementioned technical problems, this invention provides an improved method for rapid estimation of the state of a polyphenylene ether (PPE) production process, comprising the following steps:

[0005] S1: Establish a linear high-dimensional dynamic model of polyphenylene ether produced by the alkylation of phenol and methanol;

[0006] S2: Divide the state vector of the high-dimensional system into multiple low-dimensional state blocks, introduce an auxiliary variable, and use the Gamma distribution to describe the probability density function of the auxiliary variable;

[0007] S3: Initialize the system settings, including the initial state values, initial covariance matrix, initial values ​​of the shape parameter of the Gamma distribution, initial values ​​of the scale parameter of the Gamma distribution, the total number of iterations L at each time step, the total number of sampling steps, and time step n;

[0008] Let n = 1;

[0009] S4: Calculate the predicted state value and the predicted covariance value for each state block;

[0010] S5: Update the shape parameters of the Gamma distribution;

[0011] Let l = 1;

[0012] S6: Update the scale parameters of the Gamma distribution;

[0013] S7: Calculate the expected value of the auxiliary variable;

[0014] S8: Update the predicted value of the covariance for each state block;

[0015] S9: Update the state prediction value for each state block;

[0016] S10: Determine whether the current iteration number l satisfies l = L. If yes, execute S11; otherwise, set l = l + 1 and jump to S6.

[0017] S11: Output the estimated value of each state block at time n, the estimated value of the system state, and the covariance matrix;

[0018] S12: Determine whether time n satisfies n = steps. If not, set n = n + 1 and jump to S4. If yes, end the process and obtain the state estimate of the polypropylene ether production process.

[0019] In one embodiment of the present invention, the dynamic model of the linear high-dimensional system established in step S1 is as follows:

[0020] x n+1 =F n x n +w n

[0021] y n =H n x n +v n

[0022] Where n represents time, xn+1 Let x represent the system state at time n+1. n F represents the system state at time n. n H is the state transition matrix. n For the measurement matrix, y n Represents the system measurement value at time n. To follow a pattern with a mean of 0 and a covariance matrix of Q n Process noise, To follow a pattern with a mean of 0 and a covariance matrix of R n Measurement noise.

[0023] In one embodiment of the present invention, the probability density function of the auxiliary variable described in step S2 using the Gamma distribution is:

[0024]

[0025] Where, ξ n Represents auxiliary variables. Let α represent the probability density function of the Gamma distribution. n and β n These represent the shape parameter and scale parameter describing the Gamma distribution, respectively.

[0026] In one embodiment of the present invention, the formula for calculating the predicted state value and the predicted covariance value of each state block in step S4 is as follows:

[0027]

[0028]

[0029] in, This represents the predicted state value of the i-th state block at time n. Represents the state transition matrix F n The i-th s i ×d x A submatrix of dimension d x Let be the dimension of the state vector. This represents the estimated state of the system at time n-1. Let represent the predicted value of the covariance matrix for the i-th state block at time n. Represents the state transition matrix F n The i-th diagonal block matrix in the matrix, Let represent the estimated value of the covariance matrix of the i-th state block at time n-1. express transpose, The process noise covariance matrix Q represents n The i-th diagonal block matrix.

[0030] In one embodiment of the present invention, the formula for updating the shape parameter of the Gamma distribution in step S5 is:

[0031]

[0032] Where, d x λ represents the dimension of the system state vector, and λ1 represents the initial value of the shape parameter of the Gamma distribution.

[0033] In one embodiment of the present invention, the formula for updating the scale parameter of the Gamma distribution in step S6 is:

[0034]

[0035] in, This represents the scaling parameter value of the Gamma distribution at time n and the l-th iteration. Let the covariance matrix be the value at time n and the (l-1)th iteration. P represents the state estimate at time n, in the (l-1)th iteration. n|n-1 This represents the predicted value of the covariance matrix at time n.

[0036] In one embodiment of the present invention, the auxiliary variable ξ in step S7 n The formula for calculating the expected value is:

[0037]

[0038] Where, ξ n Represents auxiliary variables. ξ represents the l-th iteration at time n. n The expected value.

[0039] In one embodiment of the present invention, the formula for updating the predicted value of the covariance of each state block in step S8 is as follows:

[0040]

[0041] in, This represents the estimated value of the covariance matrix of the i-th state block at time n during the l-th iteration. Represents the state transition matrix F n The jth s j ×s i A submatrix of dimension s j Let the dimension be the j-th state block. The process noise covariance matrix Q represents n The j-th diagonal block matrix, express transpose, Represents the measurement matrix H n The i-th d y ×s i A submatrix of dimension, express transpose, R represents the measurement noise covariance matrix. n The reverse, It represents the inverse of the predicted value of the covariance matrix of the i-th state block at time n.

[0042] In one embodiment of the present invention, the formula for updating the state value of each state block in step S9 is as follows:

[0043]

[0044] in, This represents the state estimate of the i-th state block at time n in the l-th iteration. This represents the estimated value of the covariance matrix of the i-th state block at time n in the (l-1)-th iteration. Represents the measurement matrix H n The submatrix that matches the dimensions of the first to (i-1)th state blocks. This represents the first to the (i-1)th state blocks in the estimated system state vector at time n and the l-th iteration. Represents the measurement matrix H n From the (i+1)th state block to the dth state block s A submatrix that matches the dimensions of each state block. This represents the (i+1)th to dth state blocks of the system state estimate at the (l-1)th iteration. s A state block.

[0045] In one embodiment of the present invention, the formulas for calculating the estimated value of each state block, the estimated value of the system state, and the covariance matrix in step S11 are as follows:

[0046]

[0047]

[0048]

[0049] in, Let represent the estimated value of the i-th state block at time n and the L-th iteration. This represents the estimated state of the system at time n. This represents the transpose of the estimated value of the first state block at the Lth iteration. Indicates the dth s The transpose of the estimated values ​​of the state blocks at the Lth iteration, Pn|n Let represent the estimated value of the covariance matrix of the system state at time n, and blkdiag(·) denote the block diagonal matrix operator. This represents the covariance matrix corresponding to the first state block. Indicates the dth s The covariance matrix corresponding to each state block.

[0050] The technical solution of the present invention has the following advantages compared with the prior art:

[0051] The present invention discloses an improved method for rapid state estimation in the production process of polyphenylene ether. Based on the alkylation of phenol and methanol to produce polyphenylene ether, a linear high-dimensional state-space model is constructed. The high-dimensional system state vector is divided into multiple low-dimensional state blocks. At the same time, an auxiliary variable is introduced to correct the system error caused by the block division, so that the state estimation can achieve higher accuracy while the computational cost remains at a low level. Attached Figure Description

[0052] To make the content of this invention easier to understand, the invention will be further described in detail below with reference to specific embodiments and accompanying drawings, wherein...

[0053] Figure 1 This is a flowchart illustrating an improved method for rapid estimation of the state of a polyphenylene ether production process proposed in this invention.

[0054] Figure 2 The graph shows the root mean square error of the state estimation system for the five separation sections in the polyphenylene ether (PPE) production process over time.

[0055] Figure 3 To calculate the cost as a function of the system state vector dimension (d) x (The change graph). Detailed Implementation

[0056] The present invention will be further described below with reference to the accompanying drawings and specific embodiments, so that those skilled in the art can better understand and implement the present invention. However, the embodiments described are not intended to limit the present invention.

[0057] Reference Figure 1 As shown in the figure, this invention provides an improved method for rapid estimation of the state of a polyphenylene ether (PPE) production process. The method includes the following steps:

[0058] S1: Establish a linear high-dimensional dynamic model of polyphenylene ether produced by the alkylation of phenol and methanol;

[0059] S2: Divide the state vector of the high-dimensional system into multiple state blocks with low dimensions, introduce an auxiliary variable, and use the Gamma distribution to describe the probability density function of the auxiliary variable;

[0060] S3: Initialize the system settings, including the initial state values, initial covariance matrix, initial values ​​of the shape parameter of the Gamma distribution, initial values ​​of the scale parameter of the Gamma distribution, the total number of iterations L at each time step, the total number of sampling steps, and time step n;

[0061] Let n = 1;

[0062] S4: Calculate the predicted state value and the predicted covariance value for each state block;

[0063] S5: Update the shape parameters of the Gamma distribution;

[0064] Let l = 1;

[0065] S6: Update the scale parameters of the Gamma distribution;

[0066] S7: Calculate the expected value of the auxiliary variable;

[0067] S8: Update the predicted value of the covariance for each state block;

[0068] S9: Update the state prediction value for each state block;

[0069] S10: Determine whether the current iteration number l satisfies l = L. If yes, execute S11; otherwise, set l = l + 1 and jump to S6.

[0070] S11: Output the estimated value of each state block at time n, the estimated value of the system state, and the covariance matrix;

[0071] S12: Determine whether time n satisfies n = steps. If not, set n = n + 1 and jump to S4. If yes, end the process and obtain the state estimate of the polypropylene ether production process.

[0072] The present invention discloses an improved method for rapid state estimation in the production process of polyphenylene ether. Based on the alkylation of phenol and methanol to produce polyphenylene ether, a linear high-dimensional state-space model is constructed. The high-dimensional system state vector is divided into multiple low-dimensional state blocks. At the same time, an auxiliary variable is introduced to correct the system error caused by the block division, so that the state estimation can achieve higher accuracy while the computational cost remains at a low level.

[0073] Specifically, an improved method for rapid estimation of the state of a polyphenylene ether production process according to the present invention includes the following steps:

[0074] S1: The following is a linear high-dimensional dynamic model of the polyphenylene ether produced by the alkylation of phenol and methanol:

[0075] xn+1 =F n x n +w n (1)

[0076] y n =H n x n +v n (2)

[0077] Where n represents time, x n+1 Let x represent the system state at time n+1. n F represents the system state at time n. n H is the state transition matrix. n For the measurement matrix, y n This represents the measurement value at time n. To follow a pattern with a mean of 0 and a covariance matrix of Q n Process noise, To follow a pattern with a mean of 0 and a covariance matrix of R n Measurement noise.

[0078] S2: Divide the high-dimensional system state vector into d based on system characteristics and the relationships between state variables. s There are _ ... i Introduce an auxiliary variable ξ n And its probability density function is described using the Gamma distribution:

[0079]

[0080] in, Let α represent the probability density function of the Gamma distribution. n and β n These are the shape parameter and scale parameter describing the Gamma distribution, respectively.

[0081] S3: Set initial values P 0|0 y n Q n R n d s λ1, λ2, L and steps, where, Let P be the initial state value. 0|0 Let d be the initial covariance matrix. s λ1 is the number of blocks, λ2 is the initial value of the shape parameter of the Gamma distribution, L is the total number of iterations at each time step, and steps is the total number of samplings.

[0082] Let n = 1;

[0083] S4: Calculate the predicted value of each state block and its covariance using the following formula:

[0084]

[0085]

[0086] in, This represents the predicted state value of the i-th state block at time n. Represents the state transition matrix F n The i-th s i ×d x A submatrix of dimension d x Let be the dimension of the state vector. This represents the estimated state of the system at time n-1. Let represent the predicted value of the covariance matrix for the i-th state block at time n. Represents the state transition matrix F n The i-th diagonal block matrix in the matrix, Let represent the estimated value of the covariance matrix of the i-th state block at time n-1. express transpose, The process noise covariance matrix Q represents n The i-th diagonal block matrix.

[0087] S5: Update the shape parameters of the Gamma distribution using the following formula:

[0088]

[0089] Where, d x is the dimension of the system state vector.

[0090] Let l = 1;

[0091] S6: Update the scale parameter of the Gamma distribution using the following formula:

[0092]

[0093] in, This represents the scaling parameter value of the Gamma distribution at time n and the l-th iteration. Let the covariance matrix be the value at time n and the (l-1)th iteration. P represents the state estimate at time n, in the (l-1)th iteration. n|n-1 This represents the predicted value of the covariance matrix at time n.

[0094] S7: Calculate the auxiliary variable ξ n The expected value is calculated using the following formula:

[0095]

[0096] in, ξ represents the l-th iteration at time n. n The expected value.

[0097] S8: Update the covariance of each state block using the following formula:

[0098]

[0099] in, This represents the estimated value of the covariance matrix of the i-th state block at time n during the l-th iteration. Represents the state transition matrix F n The jth s j ×s i A submatrix of dimension s j Let the dimension be the j-th state block. The process noise covariance matrix Q represents n The j-th diagonal block matrix, express transpose, Represents the measurement matrix H n The i-th d y ×s i A submatrix of dimension, express The transpose of R n -1 R represents the measurement noise covariance matrix. n The reverse, It represents the inverse of the predicted value of the covariance matrix of the i-th state block at time n.

[0100] S9: Update the state value of each state block using the following formula:

[0101]

[0102] in, This represents the state estimate of the i-th state block at time n in the l-th iteration. This represents the estimated value of the covariance matrix of the i-th state block at time n in the (l-1)-th iteration. Represents the measurement matrix H n The submatrix that matches the dimensions of the first to (i-1)th state blocks. This represents the first to the (i-1)th state blocks in the estimated system state vector at time n and the l-th iteration. Represents the measurement matrix H n From the (i+1)th state block to the dth state blocks A submatrix that matches the dimensions of each state block. This represents the (i+1)th to dth state blocks of the system state estimate at the (l-1)th iteration. s A state block.

[0103] S10: Determine whether the current iteration number l satisfies l = L. If yes, execute S11; otherwise, set l = l + 1 and jump to S6.

[0104] S11: Output the estimated value of each state block, the estimated value of the system state, and the covariance matrix at time n. The formulas for calculating the estimated value of each state block, the estimated value of the system state, and the covariance matrix are as follows:

[0105]

[0106]

[0107]

[0108] in, Let represent the estimated value of the i-th state block at time n and the L-th iteration. This represents the estimated state of the system at time n. This represents the transpose of the estimated value of the first state block at the Lth iteration. Indicates the dth s The transpose of the estimated values ​​of the state blocks at the Lth iteration, P n|n Let represent the estimated value of the covariance matrix of the system state at time n, and blkdiag(·) denote the block diagonal matrix operator. This represents the covariance matrix corresponding to the first state block. Indicates the dth s The covariance matrix corresponding to each state block.

[0109] S12: Determine whether time n satisfies n = steps. If not, set n = n + 1 and jump to S4. If yes, end the process and obtain the state estimate of the polypropylene ether production process.

[0110] The following examples and simulations illustrate the beneficial effects of the improved method for rapid estimation of the state of the polyphenylene ether production process according to the present invention.

[0111] The method proposed in this invention was used to simulate and verify five separation stages in the polyphenylene ether (PPE) production process, which together contain 60 state variables. Based on the system characteristics, these 60 state variables were divided into five state blocks: the first block contains 9 state variables, the second and fourth blocks each contain 13 state variables, the third block contains 11 state variables, and the fifth block contains 14 state variables. The process noise covariance matrix and measurement noise covariance matrix of the system are as follows: and The simulation was based on 20 Monte Carlo runs with a time of 100 seconds. The proposed method (denoted as BtKF) was compared with existing methods for handling state estimation problems of high-dimensional systems: (1) Kalman filtering method (denoted as KF), (2) ensemble Kalman filtering method (denoted as EnKF), (3) method of dividing the system state vector into multiple scalars (denoted as SKF), and (4) method of dividing the system into blocks without compensating for system errors (denoted as BKF). The root mean square error (RMSE) of the system state estimation over time and the computational cost of the algorithm over the dimension of the state vector are compared as shown in the figure. Figure 2 and Figure 3 As shown.

[0112] from Figure 2 and Figure 3 As can be seen, the method of this invention (i.e., the BtKF method) can maintain higher estimation accuracy (compared to the BKF method) when estimating the state of high-dimensional systems, while ensuring that the computational cost remains at a low level. Therefore, the improved rapid state estimation method for polyphenylene ether production processes proposed in this invention can meet the requirements of low computational cost and higher accuracy in estimating the state of linear high-dimensional systems.

[0113] Those skilled in the art will understand that embodiments of this application can be provided as methods, systems, or computer program products. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this application can 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, etc.) containing computer-usable program code.

[0114] This application is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this application. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can 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, generate instructions for implementing the flowchart... Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0115] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0116] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0117] Obviously, the above embodiments are merely illustrative examples for clear explanation and are not intended to limit the implementation. Those skilled in the art will recognize that other variations or modifications can be made based on the above description. It is neither necessary nor possible to exhaustively list all possible implementations here. However, obvious variations or modifications derived therefrom are still within the scope of protection of this invention.

Claims

1. An improved method for rapid estimation of the state of a polyphenylene ether (PPE) production process, characterized in that: Includes the following steps: S1: Establish a linear high-dimensional dynamic model of polyphenylene ether produced by the alkylation of phenol and methanol; S2: Divide the state vector of the high-dimensional system into multiple low-dimensional state blocks, introduce an auxiliary variable, and use the Gamma distribution to describe the probability density function of the auxiliary variable; The probability density function of the auxiliary variable, described using the Gamma distribution, is: ;in, Represents auxiliary variables. This represents the probability density function of the Gamma distribution. and These represent the shape parameter and scale parameter describing the Gamma distribution, respectively; S3: Initialize the system, including setting the initial system state values, initial covariance matrix, initial values ​​for the shape parameter of the Gamma distribution, initial values ​​for the scale parameter of the Gamma distribution, and the total number of iterations at each time step. Total number of samplings and time n; make ; S4: Calculate the predicted state value and the predicted covariance value for each state block; S5: Update the shape parameters of the Gamma distribution; make ; S6: Update the scale parameters of the Gamma distribution; S7: Calculate the expected value of the auxiliary variable. The formula for calculating the expected value is: in, Represents auxiliary variables. express Time of the first step-by-step iteration Expected value; S8: Update the predicted value of the covariance for each state block; S9: Update the state prediction value for each state block. The formula for updating the state value of each state block is: ； in, express Time of the first The state block in the ... State estimates for each iteration express Time of the first The state block in the ... The estimated value of the covariance matrix after one iteration. Representation of measurement matrix In the middle of the first state block to the first A submatrix that matches the dimensions of each state block. express Time of the first During step iteration, the estimated state vector values ​​of the system from the first state block to the second state block are obtained. A state block, Representation of measurement matrix Middle and the first The state block to the 1st A submatrix that matches the dimensions of each state block. Indicates the first The system state estimate at the first iteration The state block to the 1st One state block; Represents the state transition matrix The Middle indivual A submatrix of dimension, For the first The dimension of each state block, Represents the process noise covariance matrix The Middle A diagonal block matrix, express transpose, Representation of measurement matrix The Middle indivual A submatrix of dimension, express transpose, Represents the measurement noise covariance matrix The reverse, express Time of the first The inverse of the predicted covariance matrix of each state block. express System measurements at time; S10: Determine the current iteration number Does it meet the requirements? If yes, then execute S11; otherwise, execute... And jump to S6; S11: Output The estimated value of each state block at each time step, the estimated value of the system state, and the covariance matrix; S12: Determine whether time n satisfies the condition. Otherwise If the condition is met, proceed to S4; otherwise, the process ends, yielding an estimated state of the polypropylene ether production process.

2. The improved method for rapid estimation of the state of a polyphenylene ether production process according to claim 1, characterized in that: The dynamic model of the linear high-dimensional system established in step S1 is as follows: in, Indicates time, express The system state at any given moment. express The system state at any given moment. Here is the state transition matrix. For the measurement matrix, express System measurements at time [time] To conform to the mean The covariance matrix is Process noise, To conform to the mean The covariance matrix is Measurement noise.

3. The improved method for rapid estimation of the state of a polyphenylene ether production process according to claim 2, characterized in that: The formulas for calculating the predicted state value and its predicted covariance of each state block in step S4 are as follows: ； in, express Time for the first The state prediction value of each state block. Represents the state transition matrix The Middle indivual A submatrix of dimension, Let be the dimension of the state vector. Indicates the first The estimated value of the system state at time t. express Time for the first The predicted values ​​of the covariance matrix of each state block. Represents the state transition matrix The Middle A diagonal block matrix, Indicates the first Time of the first Estimates of the covariance matrix of each state block. express transpose, Represents the process noise covariance matrix The Middle A diagonal block matrix.

4. The improved method for rapid estimation of the state of a polyphenylene ether production process according to claim 1, characterized in that: The formula for updating the shape parameter of the Gamma distribution in step S5 is: in, The dimension of the system state vector. This represents the initial value of the shape parameter of the Gamma distribution.

5. As described in claim 1, characterized in that: According to claim 2, the improved method for rapid estimation of the state of a polyphenylene ether production process is characterized in that: the formula for updating the scale parameter of the Gamma distribution in step S6 is: ； in, express Time of the first Iterate through the scale parameter values ​​of the Gamma distribution step by step. express Time of the first The covariance matrix of the step iterations, express Time of the first State estimates for each iteration express The predicted value of the covariance matrix at time 1.

6. The improved method for rapid estimation of the state of a polyphenylene ether production process according to claim 1, characterized in that: The formula for updating the predicted covariance of each state block in step S8 is as follows: ； in, express Time of the first The state block in the ... The estimated value of the covariance matrix during step iteration. Represents the state transition matrix The Middle indivual A submatrix of dimension, For the first The dimension of each state block, Represents the process noise covariance matrix The Middle A diagonal block matrix, express transpose, Representation of measurement matrix The Middle indivual A submatrix of dimension, express transpose, Represents the measurement noise covariance matrix The reverse, express Time of the first The inverse of the predicted covariance matrix of each state block.

7. The improved method for rapid estimation of the state of a polyphenylene ether production process according to claim 2, characterized in that: The formulas for calculating the estimated value of each state block, the estimated value of the system state, and the covariance matrix in step S11 are as follows: ； ； ； in, express Time of the first During the first iteration, for the first The estimated value of each state block, express The estimated value of the system state at time t. This indicates that the first state block is in the... Transpose of the estimated value during step iteration Indicates the first The state block in the ... Transpose of the estimated value during step iteration express The estimated value of the covariance matrix of the system state at time t. Represents a block diagonal matrix operator. This represents the covariance matrix corresponding to the first state block. Indicates the first The covariance matrix corresponding to each state block.

Images