A dynamic internal slow feature extraction method based on diCC-sfa for methyltin reaction process

Abstract

The application provides a dynamic internal slow feature extraction method for methyl tin reaction process based on DiCC-SFA. The method comprises the following steps: obtaining a first target function and a second target function of dynamic internal slow feature extraction of methyl tin reaction according to a methyl tin reaction process data set; determining a dynamic order of an autoregressive prediction model of methyl tin reaction, weight coefficients of the first target function and the second target function, obtaining a calculation rule of an autoregressive coefficient matrix and a calculation rule of a scalar mapping matrix; extracting slow features of methyl tin reaction from the methyl tin reaction process data set; obtaining the number of main slow features according to the extracted slow features; obtaining monitoring statistics of a plurality of preset target monitoring data from the methyl tin reaction process data set according to the slow degree of the slow features, the number of main slow features, the calculation rule of the autoregressive coefficient matrix and the calculation rule of the scalar mapping matrix; and determining an abnormal type of the monitored methyl tin reaction according to the monitoring statistics.

Description

Technical Field

[0001] This application relates to the field of monitoring technology for methyltin reaction, specifically to a method for extracting dynamic internal slow features of the methyltin reaction process based on DiCC-SFA. Background Technology

[0002] Real-time monitoring of the methyltin reaction based on measurement data is an effective means to ensure the safe and stable operation of the methyltin reaction process. However, the methyltin reaction is a complex chemical production process with data characterized by diversity, high dimensionality, nonlinearity, and coupling. Furthermore, due to the presence of numerous manipulated variables, strong continuity, and complex dynamic relationships, the operating state of the methyltin reaction process exhibits gradual changes. In the initial stages of abnormal states, data changes are small, and the time-propagation relationships of process variables are complex, making it difficult for traditional monitoring methods to detect these changes in a timely manner. Summary of the Invention

[0003] The purpose of this application is to overcome the shortcomings and deficiencies of the prior art and provide a method for extracting dynamic internal slow features of the methyltin reaction process based on DiCC-SFA, which can efficiently and accurately monitor the methyltin reaction.

[0004] The first aspect of this application provides a method for extracting dynamic internal slow features of the methyltin reaction process based on DiCC-SFA, including:

[0005] Historical data of the monitored methyltin reaction were obtained, and the historical data were standardized to obtain a methyltin reaction process dataset with zero mean and standard deviation.

[0006] Based on the methyltin reaction process dataset, dynamic-internal canonical correlation analysis and original slow feature analysis were used to analyze and model the process, resulting in the first objective function and the second objective function of the dynamic internal slow feature extraction model for the methyltin reaction.

[0007] Determine the dynamic order of the autoregressive prediction model for the methyltin reaction, as well as the first weighting coefficient of the first objective function and the second weighting coefficient of the second objective function;

[0008] Based on the dynamic internal slow feature extraction model of the methyltin reaction, the dynamic order, the first objective function, the second objective function, the first weight coefficient, and the second weight coefficient, the calculation rules for the autoregressive coefficient matrix and the scalar mapping matrix are obtained.

[0009] Potential slow features are extracted from historical or real-time monitoring data of the methyltin reaction process collected from the DCS system; based on the slow features, the number of major slow features is obtained; wherein, the major slow features are slow features that carry important information about the methyltin reaction.

[0010] Based on the degree of slowness of the slow features, the number of the main slow features, the autoregressive coefficient matrix, and the scalar mapping matrix, obtain the monitoring statistics of multiple preset target monitoring data;

[0011] Based on the monitoring statistics and preset control limits, determine the abnormal type of the methyltin reaction monitored in the methyltin reaction process dataset; or, update the methyltin reaction process dataset with real-time measurement datasets of the methyltin reaction process collected by the DCS system at equal time intervals, and determine the abnormal type of the methyltin reaction monitored in the updated methyltin reaction process dataset based on the monitoring statistics and preset control limits.

[0012] Furthermore, the steps for obtaining the calculation rules for the autoregressive coefficient matrix and the scalar mapping matrix based on the dynamic internal slow feature extraction model of the methyltin reaction, the dynamic order, the first objective function, the second objective function, the first weight coefficient, and the second weight coefficient include:

[0013] Based on the dynamic internal slow feature extraction model of the methyltin reaction, the dynamic order, the first objective function, the second objective function, the first weight coefficient, and the second weight coefficient, the multi-objective problem is transformed into a single-objective optimization problem, as shown in the following formula:

[0014] ;in, For a single-objective optimization problem, the maximum value of the objective value is... These are the weight coefficients for the first objective function. Let the first objective function be... These are the weight coefficients for the second objective function. The second objective function is... The first data set of the methyltin reaction process The scalar mapping matrix of the row is used to extract the first row. One potential feature The adjusted input matrix is ​​organized from the dataset of the methyltin reaction process. For the organization of the dataset from the methyltin reaction process The new adjusted input matrix is ​​reorganized in the middle. This is a new extended input matrix organized from the dataset of the methyltin reaction process. For the dataset of the methyltin reaction process The new extended input matrix is ​​reorganized in the middle. For the target data The autoregressive coefficient matrix of the data;

[0015] The single-objective optimization problem is solved using the Lagrange multiplier method, as shown in the following formula:

[0016] ;

[0017] in, For Kronecker product;

[0018] The Kronecker product satisfies , Scalar mapping matrix The identity matrix, Autoregressive coefficient matrix The identity matrix;

[0019] By taking the partial derivatives of the autoregressive coefficient matrix and the scalar mapping matrix respectively, and setting the partial derivatives to 0, the relationship between the objective value and the eigenvalue of the single-objective optimization problem is obtained.

[0020] Based on the single-objective optimization problem and the relationship between the objective value and the eigenvalue of the single-objective optimization problem, the calculation rules for the autoregressive coefficient matrix and the calculation rules for the scalar mapping matrix are obtained.

[0021] Further, the steps of obtaining the calculation rules for the autoregressive coefficient matrix and the scalar mapping matrix based on the single-objective optimization problem and the relationship between the objective value and eigenvalues ​​of the single-objective optimization problem include:

[0022] Based on the relationship between the objective value and the eigenvalues ​​of the single-objective optimization problem, the objective value of the single-objective optimization problem is maximized in order to maximize the eigenvalues:

[0023]

[0024] Simplifying the above formula, we obtain the calculation rule for the autoregressive coefficient matrix:

[0025] ;in, For eigenvalues, To adjust the input matrix by incorporating a dynamic order from the target data organization, An extended input matrix with added dynamic order is formed from the target data organization.

[0026] Furthermore, based on the single-objective optimization problem and the relationship between the objective value and eigenvalues ​​of the single-objective optimization problem, the steps for deriving the calculation rules for the autoregressive coefficient matrix and the scalar mapping matrix include:

[0027] Based on the relationship between the objective value and the eigenvalues ​​of the single-objective optimization problem, the objective value of the single-objective optimization problem is maximized in order to maximize the eigenvalues:

[0028]

[0029] Simplifying the above formula, we obtain the calculation rule for the scalar mapping matrix:

[0030] ;in, For eigenvalues, The input matrix is ​​an adjustment matrix with an added dynamic order, organized from the dataset of the methyltin reaction process. This is an extended input matrix with added dynamic order, organized from the dataset of the methyltin reaction process.

[0031] Furthermore, after the step of extracting potential slow features from the historical data or real-time monitoring data of the methyltin reaction process collected from the DCS system, the method further includes: sorting the extracted slow features in ascending order of their rate of change based on the derivative values ​​of the slow features.

[0032] Further, the step of obtaining monitoring statistics for multiple preset target monitoring data based on the degree of slowness of the slow features, the number of the main slow features, the autoregressive coefficient matrix, and the scalar mapping matrix includes:

[0033] Based on the degree of slowness of the slow features and the number of the main slow features, the autoregressive coefficient matrix is ​​divided into a first type of autoregressive coefficient matrix and a second type of regression coefficient matrix, and the scalar mapping matrix is ​​divided into a first type of scalar mapping matrix and a second type of scalar mapping matrix.

[0034] Based on the first type of scalar mapping matrix, obtain the dynamic slow features inside the main space of the potential process of the methyltin reaction, the estimated value of the dynamic slow features inside the main space, and the derivative of the dynamic slow features inside the main space.

[0035] Based on the second type of scalar mapping matrix, obtain the slow dynamic features inside the residual subspace, the estimated value of the slow dynamic features inside the residual subspace, and the derivative of the slow dynamic features inside the residual subspace for the potential process of methyltin reaction.

[0036] Based on the dynamic slow features within the main space, the estimated value of the dynamic slow features within the main space, the derivative of the dynamic slow features within the main space, the dynamic slow features within the residual subspace, the estimated value of the dynamic slow features within the residual subspace, and the derivative of the dynamic slow features within the residual subspace, monitoring statistics of multiple preset target monitoring data are obtained.

[0037] Further, the step of obtaining monitoring statistics of multiple preset target monitoring data based on the slow dynamic features within the main space, the estimated value of the slow dynamic features within the main space, the derivative of the slow dynamic features within the main space, the slow dynamic features within the residual subspace, the estimated value of the slow dynamic features within the residual subspace, and the derivative of the slow dynamic features within the residual subspace includes:

[0038] The monitoring statistics for each target monitoring data can be obtained using the following formula:

[0039] ;

[0040] in, For monitoring statistics exist Monitoring values ​​at any given time for Dynamic slow features within the main space extracted from the methyltin reaction process dataset at each moment;

[0041] ;

[0042] in, For monitoring statistics The monitoring value at any given time, for Dynamic slow features within the residual subspace extracted from the methyltin reaction process dataset at each moment;

[0043] in, and This is the Hotelling statistic;

[0044] ;

[0045] in, For monitoring statistics exist The detection value at that moment, for Estimates of the dynamic slow features within the main space extracted from the methyltin reaction process dataset at each time step;

[0046] ;

[0047] in, For monitoring statistics exist Monitoring values ​​at any given time for Estimates of the dynamic slow features within the residual subspace extracted from the methyltin reaction process dataset at each time step;

[0048] in, and This is the squared prediction error statistic;

[0049] ;

[0050] in, For monitoring statistics exist Monitoring values ​​at any given time For a moment Derivatives of the slow dynamic features within the main space extracted from the methyltin reaction process dataset;

[0051] ;

[0052] in, For monitoring statistics exist Monitoring values ​​at any given time For a moment Derivatives of the slow dynamic features within the residual subspace extracted from the methyltin reaction process dataset;

[0053] in, and This is a statistical measure for similar monitoring.

[0054] Further, the step of determining the abnormal type of the monitored methyltin reaction based on the monitoring statistics includes:

[0055] exist , , and When there are monitoring statistics exceeding the corresponding control limits, if and The monitoring statistics were all less than the corresponding control limits, and the anomaly type was determined to be a steady-state anomaly; whereby, steady-state anomaly means that the disturbance has no effect on the kinetics of the methyltin reaction process;

[0056] like and The monitoring statistics were all greater than the corresponding control limits, and the anomaly type was determined to be a dynamic anomaly.

[0057] Compared with related technologies, this application extracts potential slow features from the target data of methyltin reaction. Based on the calculation rules of the autoregressive coefficient matrix and the scalar mapping matrix, the autoregressive coefficient matrix and the scalar mapping matrix are obtained respectively. Then, the feature space is divided into the main space and the residual subspace according to the degree of slowness of the slow features. The monitoring statistics of multiple target monitoring data are obtained from the target data of methyltin reaction. The monitoring statistics of the target monitoring data are used to determine the abnormal type of the monitored methyltin reaction, so as to monitor the methyltin reaction efficiently and accurately.

[0058] To provide a clearer understanding of this application, the specific embodiments of this application will be described below in conjunction with the accompanying drawings. Attached Figure Description

[0059] Figure 1 This is a flowchart of a method for extracting dynamic internal slow features of a methyltin reaction process based on DiCC-SFA according to an embodiment of this application.

[0060] Figure 2 This is a flowchart illustrating the processing of historical and real-time data for a DiCC-SFA-based dynamic internal slow feature extraction method for the methyltin reaction process according to an embodiment of this application. Detailed Implementation

[0061] To make the objectives, technical solutions, and advantages of this application clearer, the embodiments of this application will be described in further detail below with reference to the accompanying drawings.

[0062] It should be understood that the described embodiments are merely some, not all, of the embodiments of this application. All other embodiments obtained by those skilled in the art based on the embodiments of this application without creative effort are within the scope of protection of the embodiments of this application.

[0063] In the following description, when referring to the accompanying drawings, unless otherwise indicated, the same numbers in different drawings represent the same or similar elements. In the description of this application, it should be understood that the terms "first," "second," "third," etc., are used only to distinguish similar objects and are not necessarily used to describe a specific order or sequence, nor should they be construed as indicating or implying relative importance. Those skilled in the art can understand the specific meaning of the above terms in this application according to the specific circumstances. The singular forms "a," "the," and "the" used in this application and the appended claims are also intended to include the plural forms, unless the context clearly indicates otherwise. The word "if" as used herein can be interpreted as "when," "when," or "in response to determination."

[0064] Furthermore, in the description of this application, unless otherwise stated, "multiple" means two or more. "And / or" describes the relationship between related objects, indicating that three relationships can exist. For example, A and / or B can represent: A alone, A and B simultaneously, or B alone. The character " / " generally indicates that the preceding and following related objects have an "or" relationship.

[0065] Please see Figure 1This is a flowchart of a method for extracting dynamic internal slow features of a methyltin reaction process based on DiCC-SFA according to an embodiment of this application. The method for extracting dynamic internal slow features of a methyltin reaction process based on DiCC-SFA disclosed in this application is applied to the methyltin reaction process, specifically to identify the abnormal types of the methyltin reaction process. Therefore, the embodiments of this application can also be understood as a method for identifying abnormal types of methyltin reaction.

[0066] DiCC-SFA refers to a dynamic internal slow feature extraction model that combines DiCCA and SFA. DiCCA is an improved version of CCA called dynamic-inner canonical correlation analysis (DiCCA), which considers both cross-correlation and autocorrelation. CCA projects the original data onto a lower-dimensional subspace to find a set of low-modulus latent variables to represent the original high-modulus data, thus capturing the maximum variance in complex data. SFA is a slow feature analysis method used to learn slowly changing time-dependent features from vector input signals, providing valuable information for distinguishing deviations from normal operating conditions and compensations for process control behaviors.

[0067] The embodiments of this application include:

[0068] S1: Obtain historical data of the monitored methyltin reaction, and standardize the historical data to obtain a methyltin reaction process dataset with zero mean and standard deviation.

[0069] Specifically, step S1 can be achieved through the following steps:

[0070] S1.1: Collect historical datasets of the methyltin reaction process using the DCS system at equal time intervals. , where J is the dimension of the historical dataset, and n is the number of samples in the historical dataset. Here, DCS system refers to a Distributed Control System (DCS).

[0071] S1.2: Using a normalization method to process historical datasets of methyltin reaction processes Preprocessing reduces the correlation between data points, resulting in a new dataset. Specifically:

[0072] S1.2.1: Calculate the mean of all variables x in the methyltin reaction process dataset: ;in Let be the n input datasets for the i-th variable (dimension), where j represents the j-th sampling point.

[0073] S1.2.2: Calculate the standard deviation of all variables in the methyltin reaction process dataset: .

[0074] S1.2.3: According to the formula The sampling data for each dimension of the methyltin reaction were standardized to zero mean and unit variance to reduce the correlation between adjacent sampling data points, resulting in a methyltin reaction process dataset with zero mean and standard deviation. .

[0075] S2: Based on the methyltin reaction process dataset, the dynamic-internal canonical correlation analysis method and the original slow feature analysis method are used for analysis and modeling to obtain the first objective function and the second objective function of the dynamic internal slow feature extraction model of the methyltin reaction.

[0076] Specifically, step S2 can be achieved through the following steps:

[0077] S2.1: Based on the fundamental principles of DiCCA and SFA, it is assumed that the latent variables extracted from the methyltin reaction process are a linear combination of the measured variables: , It is a scalar mapping matrix.

[0078] S2.1.1: Assume that past predicted measurements in the methyltin reaction can be represented by an auto-regressive (AR) model as follows: ;

[0079] S2.1.2: Estimate the current value of the latent variable from past measurements of the methyltin reaction:

[0080]

[0081] S2.1.3: Maximizing the latent variables in the methyltin reaction process and its estimated value The correlation between them ensures Best prediction :

[0082]

[0083] S2.2: Assumption Matrix From the original dataset of methyltin reaction process The matrix Y and matrix Z are organized, and the corresponding adjustment input matrices after adding the dynamic order q are respectively added. To directly map latent variables Extended input matrix Indirectly predicting latent variables .

[0084] S2.3: The time derivative of the potential slow characteristic of the extracted methyltin reaction is restated and estimated: ,in This represents the rate of change of the slowness during the methyltin reaction. This represents the internal dynamic prediction error of the methyltin reaction process.

[0085] S2.4: The following matrices are obtained by organizing matrices Y and Z: , To calculate the time derivative of the slow feature extracted from the methyltin reaction process, and Let Y and Z represent the vectors of all variables in matrices Y and Z at time h, respectively.

[0086] S2.5: The latent variable components extracted from the methyltin reaction can be directly mapped or indirectly predicted, as shown in the following model:

[0087]

[0088] so , .

[0089] S2.6: Construct the DiCC-SFA model based on the objective function of the DiCCA model and the mathematical expression of the basic principles of SFA. Based on the methyltin reaction process dataset, obtain the calculation rules for the scalar mapping matrix W and the autoregressive coefficient matrix β:

[0090] S2.6.1: The goal of the original SFA is to find the input-output function. This makes the output signal To extract the potential slow internal dynamics of the methyltin reaction while ensuring the changes are as slow as possible, and still retain some information about the input signal, this application first considers minimizing the derivative change of the original SFA algorithm as the primary objective, resulting in the first objective function:

[0091]

[0092] S2.6.2: To ensure that the prediction error remains relatively constant when the methyltin reaction exhibits a potentially slow characteristic, DiCCA is used to maximize the latent variable. Rather than predicting The correlation between them is the second objective, to capture and , ... The dynamic relationship between them keeps the prediction error relatively constant, resulting in the second objective function, which has the following specific form:

[0093]

[0094] S2.6.3: Under the condition that the first and second objectives mentioned above are satisfied simultaneously, the organization obtains the following multi-objective optimization problem:

[0095]

[0096] S2.6.3: Rewrite the first objective function:

[0097]

[0098] Minimize Equivalent to maximizing .

[0099] S3: Determine the dynamic order of the autoregressive prediction model for the methyltin reaction, as well as the first weight coefficient of the first objective function and the second weight coefficient of the second objective function.

[0100] S4: Based on the dynamic internal slow feature extraction model of the methyltin reaction, the dynamic order, the first objective function, the second objective function, the first weight coefficient, and the second weight coefficient, obtain the calculation rules for the autoregressive coefficient matrix and the calculation rules for the scalar mapping matrix.

[0101] S5: Extract potential slow features from historical data or real-time monitoring data of the methyltin reaction process collected from the DCS system; obtain the number of main slow features based on the slow features; wherein the main slow features are slow features that carry important information about the methyltin reaction.

[0102] S6: Based on the degree of slowness of the slow features, the number of the main slow features, the autoregressive coefficient matrix, and the scalar mapping matrix, obtain the monitoring statistics of multiple preset target monitoring data.

[0103] S7: Based on the monitoring statistics and preset control limits, determine the abnormal type of the methyltin reaction monitored in the methyltin reaction process dataset; or, update the methyltin reaction process dataset with real-time measurement datasets of the methyltin reaction process collected by the DCS system at equal time intervals, and determine the abnormal type of the methyltin reaction monitored in the updated methyltin reaction process dataset based on the monitoring statistics and preset control limits.

[0104] Please see Figure 2 The dynamic internal slow feature extraction method for the methyltin reaction process based on DiCC-SFA in the embodiments of this application can be implemented by an offline modeling module and an online monitoring module. The offline modeling module is used to execute steps S1-S7, and the online monitoring module is used to update the methyltin reaction process dataset with the real-time measurement dataset of the methyltin reaction process collected by the DCS system at equal time intervals, and then monitor the types of anomalies that occur in the real-time methyltin reaction process according to the dynamic internal slow feature extraction model established in the above steps.

[0105] In step S7, updating the methyltin reaction process dataset with real-time measurement datasets collected by the DCS system at equal time intervals, and determining the abnormal type of the methyltin reaction monitored in the updated methyltin reaction process dataset based on the monitoring statistics and preset control limits, includes:

[0106] Step 7.1: Collect real-time measurement datasets of the new methyltin reaction process from the DCS system at equal time intervals. (Where J is the dimension of the measurement dataset, and n is the number of samples in the dataset) Perform the standardization preprocessing shown in Step 1 to obtain a new dataset of the methyltin reaction process with zero mean and standard deviation. ;

[0107] Step 7.2: Apply the methyltin reaction process dataset obtained in Step 7.1 to Step S3 to first obtain the dynamic order q of the autoregressive prediction model based on the real-time measurement dataset of the methyltin reaction process and the first weight coefficient of the objective function. Second weighting coefficients of the second objective function ;

[0108] Step 7.3: Data set of the methyltin reaction process in Step 7.1 By adding historical data points of the methyltin reaction process at the first q time points, we obtain... augmented data matrix ;

[0109] Step 7.4: Execute the established DiCC-SFA model to update the scalar mapping matrix W and autoregressive coefficient matrix β of the historical dataset, extract all potential slow features SFs in the real-time dataset of the methyltin reaction process, and sort them in ascending order of change rate;

[0110] Step 7.5: Apply all the extracted potential slow features to Step 4 to obtain the number A of potential main slow features in the real-time measurement dataset of the methyltin reaction process, and extract the main slow features SFs;

[0111] Step 7.6: Monitor the real-time reaction process of methyltin to see if any abnormalities occur. If an abnormality occurs, determine the type of abnormality.

[0112] In a feasible embodiment, step S4: obtaining the calculation rules for the calculation rules of the autoregressive coefficient matrix and the scalar mapping matrix based on the dynamic internal slow feature extraction model of the methyltin reaction, the dynamic order, the first objective function, the second objective function, the first weight coefficient, and the second weight coefficient includes:

[0113] S41: Based on the dynamic internal slow feature extraction model of the methyltin reaction, the dynamic order, the first objective function, the second objective function, the first weighting coefficient, and the second weighting coefficient, the multi-objective problem is transformed into a single-objective optimization problem, as shown in the following formula:

[0114] ;in, For a single-objective optimization problem, the maximum value of the objective value is... These are the weight coefficients for the first objective function. Let the first objective function be... These are the weight coefficients for the second objective function. The second objective function is... The first data set of the methyltin reaction process The scalar mapping matrix of the row is used to extract the first row. One potential feature The adjusted input matrix is ​​organized from the dataset of the methyltin reaction process. For the organization of the dataset from the methyltin reaction process The new adjusted input matrix is ​​reorganized in the middle. This is a new extended input matrix organized from the dataset of the methyltin reaction process. For the dataset of the methyltin reaction process The new extended input matrix is ​​reorganized in the middle. For the target data The autoregressive coefficient matrix of the data;

[0115] S42: The single-objective optimization problem is solved using the Lagrange multiplier method, as shown in the following formula:

[0116] ;

[0117] in, For Kronecker product;

[0118] The Kronecker product satisfies , Scalar mapping matrix The identity matrix, Autoregressive coefficient matrix The identity matrix;

[0119] S43: Take the partial derivatives of the autoregressive coefficient matrix and the scalar mapping matrix respectively, and set the partial derivatives to 0 to obtain the relationship between the objective value and the eigenvalue of the single-objective optimization problem;

[0120] S44: Based on the single-objective optimization problem and the relationship between the objective value and the eigenvalue of the single-objective optimization problem, the calculation rules for the autoregressive coefficient matrix and the calculation rules for the scalar mapping matrix are obtained.

[0121] In a feasible embodiment, step S44: obtaining the calculation rules for the autoregressive coefficient matrix and the scalar mapping matrix based on the single-objective optimization problem and the relationship between the objective value and eigenvalues ​​of the single-objective optimization problem, includes:

[0122] S441: Based on the relationship between the objective value and the eigenvalues ​​of the single-objective optimization problem, maximize the objective value of the single-objective optimization problem to maximize the eigenvalues.

[0123]

[0124] S442: Simplifying the above formula, we obtain the calculation rule for the autoregressive coefficient matrix:

[0125] ;in, For eigenvalues, To adjust the input matrix by incorporating a dynamic order from the target data organization, An extended input matrix with added dynamic order is formed from the target data organization.

[0126] In a feasible embodiment, step S44: obtaining the calculation rules for the autoregressive coefficient matrix and the scalar mapping matrix based on the single-objective optimization problem and the relationship between the objective value and eigenvalues ​​of the single-objective optimization problem, includes:

[0127] S443: Based on the relationship between the objective value and the eigenvalues ​​of the single-objective optimization problem, maximize the objective value of the single-objective optimization problem to maximize the eigenvalues:

[0128]

[0129] S444: Simplifying the above formula, we obtain the calculation rule for the scalar mapping matrix:

[0130] ;in, For eigenvalues, The input matrix is ​​an adjustment matrix with an added dynamic order, organized from the dataset of the methyltin reaction process. This is an extended input matrix with added dynamic order, organized from the dataset of the methyltin reaction process.

[0131] To facilitate the examiner's understanding of step S4, the specific steps of step S4 are explained below:

[0132] S4.1.1: Solving the target optimization problem of the potential slow features in the extraction of methyltin reaction process in this application using the Lagrange multiplier method:

[0133]

[0134] And the Kronecker product satisfies .

[0135] S4.1.2: For the autoregressive coefficient matrix respectively and scalar mapping matrix Find the partial derivative and set it equal to 0:

[0136] ,

[0137] S4.1.3: Equivalence and Right multiplication respectively , :

[0138] ,

[0139] so , ,Right now .

[0140] S4.1.4: Maximizing a single-objective optimization problem is equivalent to maximizing eigenvalues. :

[0141] ,

[0142] Simplification can be obtained , Calculation rules:

[0143] Rules for calculating the autoregressive coefficient matrix:

[0144] ;

[0145] Rules for calculating scalar mapping matrices:

[0146] .

[0147] S4.2: Because , The optimization problem based on the methyltin reaction process dataset is mutually coupled and has no analytical solution. Therefore, an iterative method is used to calculate until the objective function converges.

[0148] S4.2.1: Initialize using a row of the identity matrix .

[0149] S4.2.2: Will Substituting the simplified autoregressive coefficient matrix into the calculation rules yields... .

[0150] S4.2.3: Substitution Solve the eigenvalue decomposition problem of the simplified scalar mapping matrix computation rule, and update the eigenvector corresponding to the largest eigenvalue obtained. This process continues until all J*q potential eigenvalues ​​during the methyltin reaction are extracted, yielding the scalar mapping matrix. eigenvalue matrix .

[0151] S4.2.4: Extracting the scalar mapping matrix The absolute value of the largest eigenvalue (spectral radius) is determined, and it is checked whether it is less than 1. If it is less than 1, then... If convergence is achieved, proceed to the next step; otherwise, return to S4.2.2 and continue iterating until convergence is achieved.

[0152] S4.2.4: The autoregressive coefficient matrix β is obtained by using the calculation rule of the simplified autoregressive coefficient matrix.

[0153] S4.3: Combining the AR model's judgment method and cumulative contribution method, determine the dynamic order (lag variable) q of the autoregressive prediction model based on the methyltin reaction process data.

[0154] S4.3.1: The partial autocorrelation function (PACF) of the AR model has a truncation property, that is, PACF(k) becomes 0 when k>p, or fluctuates in a small range near 0 after a delay of p. Therefore, a large dynamic order p can be roughly determined based on the PACF plot of the input data X of the methyltin reaction process after standardization.

[0155] S4.3.2: Determine the dynamic order q of the autoregressive prediction model based on methyltin reaction process data using the cumulative contribution method:

[0156]

[0157] This ensures that the q-order autocorrelation contains 95% of the autocorrelation information for the entire methyltin reaction process.

[0158] S4.4: To achieve the goal of "extracting a set of latent features with slowly changing rates and explicit dynamic autoregressive representations in the methyltin reaction, for monitoring steady-state and dynamic anomalies in the dynamic process of the methyltin reaction," the importance of the sub-objective function within the overall objective function needs to be considered. If Therefore, the single-objective optimization problem described in S2.6.4 is the same as the original SFA, and under the new derivative estimation formula (S2.3), it cannot be guaranteed that the potential characteristics of the extracted methyltin reaction process are slowly changing. Therefore, the optimization problem described in S31 only considers the internal dynamic autocorrelation of the methyltin reaction process. Since the extracted slow dynamic features within the methyltin reaction process are time-dependent, potentially changing features that change as slowly as possible, the first and second objectives are considered to have equal importance. Therefore, the following settings are made: .

[0159] S4.5: Combine the dynamic order q and weight coefficients. and Substituting these into the calculation rules for the autoregressive coefficient matrix and the scalar mapping matrix, W and β are obtained by solving based on the new mapping relationship.

[0160] In a feasible embodiment, after the step of extracting potential slow features from the historical data or real-time monitoring data of the methyltin reaction process collected from the DCS system, the method further includes: sorting the extracted slow features in ascending order of their rate of change based on the derivative values ​​of the slow features.

[0161] Specifically, after sorting the extracted slow features in ascending order of their rate of change, the number of major slow features can be obtained based on these slow features through the following steps:

[0162] S5.1: Assume variables in the methyltin reaction process Through linear mapping Accurate recovery from SFs, where Represents the reconstructed weight coefficient matrix The jth line in the middle.

[0163] S5.2: To achieve dimensionality reduction, a small number of slow features (SFs) are selected to derive a "denoised" reconstructed vector. ,in It is The reconstructed vector is formed by replacing some components with zero. ( (representing the k-th unit vector), and k satisfies ,therefore The speed of reconstructing vectors becomes slower.

[0164] S5.3: Utilizing empirical strategies: Variables in the methyltin reaction process slowness ( () is a weighted sum of the slowness levels of potential slow feature SFs in all extracted methyltin reaction processes. ,in .like It has more variable reaction process than methyltin. Faster potential slow features driven by SFs Faster; if It has more variable reaction process than methyltin. Slower potential slow features driven by SFs Slower. Therefore, in order to eliminate the influence of noise, potentially slow-featured SFs are sequentially excluded from the extracted methyltin reaction process. The slow nature of this process continuously drives down the reconstruction speed.

[0165] S5.4: Using quantile statistics to estimate the number of potential slow-feature SFs in the methyltin reaction, which changes faster than all input variables: ,in This represents the number of elements in a set. , Represents a set The q-upper quantile.

[0166] S5.5: Calculate the number of potential primary slow features (SFs) in the methyltin reaction process dataset: .

[0167] In a feasible embodiment, S6: the step of obtaining monitoring statistics of multiple preset target monitoring data based on the degree of slowness of the slow features, the number of the main slow features, the autoregressive coefficient matrix, and the scalar mapping matrix includes:

[0168] S61: Based on the degree of slowness of the slow features and the number of the main slow features, the autoregressive coefficient matrix is ​​divided into a first type of autoregressive coefficient matrix and a second type of regression coefficient matrix, and the scalar mapping matrix is ​​divided into a first type of scalar mapping matrix and a second type of scalar mapping matrix.

[0169] Specifically, based on the degree of slowness of change of the slow features extracted from the methyltin reaction dataset and the number A of the main slow features, the scalar mapping matrix and the autoregressive coefficient matrix can be further divided into two groups: , , , .

[0170] S62: Based on the first type of scalar mapping matrix, obtain the dynamic slow feature inside the main space of the potential process of the methyltin reaction, the estimated value of the dynamic slow feature inside the main space, and the derivative of the dynamic slow feature inside the main space.

[0171] Specifically, the slow dynamic characteristics within the master space of the potential process of the methyltin reaction can be obtained by the following formula:

[0172] ;

[0173] The estimated value of the slow dynamic features within the main space can be obtained by the following formula:

[0174] ;

[0175] The derivative of the slow dynamic feature within the main space can be obtained using the following formula:

[0176] .

[0177] S63: Based on the second type of scalar mapping matrix, obtain the slow dynamic feature inside the residual subspace of the potential process of the methyltin reaction, the estimated value of the slow dynamic feature inside the residual subspace, and the derivative of the slow dynamic feature inside the residual subspace.

[0178] Specifically, the slow dynamic characteristics within the residual subspace of the potential process of the methyltin reaction can be obtained by the following formula:

[0179] ;

[0180] The estimate of the dynamic slow feature within the residual subspace can be obtained by the following formula:

[0181] ;

[0182] The derivative of the slow dynamic feature within the residual subspace can be obtained using the following formula:

[0183] .

[0184] S64: Based on the dynamic slow features inside the main space, the estimated value of the dynamic slow features inside the main space, the derivative of the dynamic slow features inside the main space, the dynamic slow features inside the residual subspace, the estimated value of the dynamic slow features inside the residual subspace, and the derivative of the dynamic slow features inside the residual subspace, obtain the monitoring statistics of multiple preset target monitoring data.

[0185] In a feasible embodiment, the step of obtaining monitoring statistics of a plurality of preset target monitoring data based on the slow dynamic features within the main space, the estimated value of the slow dynamic features within the main space, the derivative of the slow dynamic features within the main space, the slow dynamic features within the residual subspace, the estimated value of the slow dynamic features within the residual subspace, and the derivative of the slow dynamic features within the residual subspace includes:

[0186] The monitoring statistics for each target monitoring data can be obtained using the following formula:

[0187] ;

[0188] in, For monitoring statistics exist Monitoring values ​​at any given time for Dynamic slow features within the main space extracted from the methyltin reaction process dataset at each moment;

[0189] ;

[0190] in, For monitoring statistics The monitoring value at any given time, for Dynamic slow features within the residual subspace extracted from the methyltin reaction process dataset at each moment;

[0191] in, and This is the Hotling statistic.

[0192] ;

[0193] in, For monitoring statistics exist The detection value at that moment, for Estimates of the dynamic slow features within the main space extracted from the methyltin reaction process dataset at each time step;

[0194] ;

[0195] in, For monitoring statistics exist Monitoring values ​​at any given time for Estimates of the dynamic slow features within the residual subspace extracted from the methyltin reaction process dataset at each time step;

[0196] in, and This is the squared prediction error statistic.

[0197] ;

[0198] in, For monitoring statistics exist Monitoring values ​​at any given time For a moment Derivatives of the slow dynamic features within the main space extracted from the methyltin reaction process dataset;

[0199] ;

[0200] in, For monitoring statistics exist Monitoring values ​​at any given time For a moment Derivatives of the slow dynamic features within the residual subspace extracted from the methyltin reaction process dataset;

[0201] in, and This is a statistical measure for similar monitoring.

[0202] Kernel density estimation can be used to calculate the control limits of the static index and time statistics in the methyltin reaction, and then analyze and evaluate the corresponding monitoring statistics of the methyltin reaction process. The probability density function of the kernel estimator is: ,in This represents the statistical quantity of the methyltin reaction process dataset. Represents the statistics of the methyltin reaction process dataset. The k-th value, where l represents the number of samples in the methyltin reaction process dataset, and h represents the window width. , This refers to the kernel function; here, the Gaussian kernel function is used. Ultimately, the standard normal density function was chosen. It is the variance of the statistical sample.

[0203] In one feasible embodiment, the step of determining the abnormal type of the monitored methyltin reaction based on the monitoring statistics includes:

[0204] exist , , and When there are monitoring statistics exceeding the corresponding control limits, if and The monitoring statistics were all less than the corresponding control limits, and the anomaly type was determined to be a steady-state anomaly; whereby, steady-state anomaly means that the disturbance has no effect on the kinetics of the methyltin reaction process;

[0205] like and The monitoring statistics were all greater than the corresponding control limits, and the anomaly type was determined to be a dynamic anomaly.

[0206] The significance level of the control limits corresponding to each target monitoring data was set to 0.01, meaning the confidence level of the probability density function of the kernel estimator was set to 99%. The control limits for evaluating each statistic in the methyltin reaction process can be determined based on the probability density function of the kernel estimator. , , , , and .

[0207] Compared with related technologies, this application extracts potential slow features from the target data of methyltin reaction. Based on the calculation rules of the autoregressive coefficient matrix and the scalar mapping matrix, the autoregressive coefficient matrix and the scalar mapping matrix are obtained respectively. Then, the feature space is divided into the main space and the residual subspace according to the degree of slowness of the slow features. The monitoring statistics of multiple target monitoring data are obtained from the target data of methyltin reaction. The monitoring statistics of the target monitoring data are used to determine the abnormal type of the monitored methyltin reaction, so as to monitor the methyltin reaction efficiently and accurately.

[0208] 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 The 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 selected in one or more boxes.

[0209] 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 selected in one or more boxes.

[0210] In a typical configuration, a computing device includes one or more processors (CPU), input / output interfaces, network interfaces, and memory.

[0211] Memory may include non-persistent memory in computer-readable media, such as random access memory (RAM) and / or non-volatile memory, such as read-only memory (ROM) or flash RAM. Memory is an example of computer-readable media.

[0212] Computer-readable media includes both permanent and non-permanent, removable and non-removable media that can store information using any method or technology. Information can be computer-readable instructions, data structures, modules of programs, or other data. Examples of computer storage media include, but are not limited to, phase-change memory (PRAM), static random access memory (SRAM), dynamic random access memory (DRAM), other types of random access memory (RAM), read-only memory (ROM), electrically erasable programmable read-only memory (EEPROM), flash memory or other memory technologies, CD-ROM, digital versatile optical disc (DVD) or other optical storage, magnetic tape, magnetic magnetic disk storage or other magnetic storage devices, or any other non-transferable medium that can be used to store information accessible by a computing device. As defined herein, computer-readable media does not include transient computer-readable media, such as modulated data signals and carrier waves.

[0213] It should also be noted that the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such process, method, article, or apparatus. Unless otherwise specified, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes that element.

[0214] The above are merely embodiments of this application and are not intended to limit the scope of this application. Various modifications and variations can be made to this application by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of this application should be included within the scope of the claims of this application.

Claims

1. A DiCC-SFA-based dynamic internal slow feature extraction method for methyltin reaction process, characterized in that, include: Historical data of the monitored methyltin reaction were obtained, and the historical data were standardized to obtain a methyltin reaction process dataset with zero mean and standard deviation. Based on the methyltin reaction process dataset, dynamic-internal canonical correlation analysis and original slow feature analysis were used to analyze and model the process, resulting in the first objective function and the second objective function of the dynamic internal slow feature extraction model for the methyltin reaction. Determine the dynamic order of the autoregressive prediction model for the methyltin reaction, as well as the first weighting coefficient of the first objective function and the second weighting coefficient of the second objective function; Based on the dynamic internal slow feature extraction model of the methyltin reaction, the dynamic order, the first objective function, the second objective function, the first weight coefficient, and the second weight coefficient, the calculation rules for the autoregressive coefficient matrix and the scalar mapping matrix are obtained. Potential slow features are extracted from historical or real-time monitoring data of the methyltin reaction process collected from the DCS system; based on the slow features, the number of major slow features is obtained; wherein, the major slow features are slow features that carry important information about the methyltin reaction. Based on the degree of slowness of the slow features, the number of the main slow features, the autoregressive coefficient matrix, and the scalar mapping matrix, obtain the monitoring statistics of multiple preset target monitoring data; Based on the monitoring statistics and preset control limits, determine the abnormal type of the methyltin reaction monitored in the methyltin reaction process dataset; or, update the methyltin reaction process dataset with real-time measurement datasets of the methyltin reaction process collected by the DCS system at equal time intervals, and determine the abnormal type of the methyltin reaction monitored in the updated methyltin reaction process dataset based on the monitoring statistics and preset control limits.

2. The DiCC-SFA based dynamic internal slow feature extraction method for methyltin reaction process according to claim 1, characterized in that, The steps for obtaining the calculation rules for the autoregressive coefficient matrix and the scalar mapping matrix based on the dynamic internal slow feature extraction model of the methyltin reaction, the dynamic order, the first objective function, the second objective function, the first weight coefficient, and the second weight coefficient include: Based on the dynamic internal slow feature extraction model of the methyltin reaction, the dynamic order, the first objective function, the second objective function, the first weighting coefficient, and the second weighting coefficient, the multi-objective problem is transformed into a single-objective optimization problem, as shown in the following formula: ;in, For a single-objective optimization problem, the maximum value of the objective value is... These are the weight coefficients for the first objective function. Let the first objective function be... These are the weight coefficients for the second objective function. The second objective function is... The first data set of the methyltin reaction process The scalar mapping matrix of the row is used to extract the first row. One potential feature The adjusted input matrix is ​​organized from the dataset of the methyltin reaction process. For the organization of the dataset from the methyltin reaction process A new, reorganized adjustment input matrix, This is a new extended input matrix organized from the dataset of the methyltin reaction process. For the dataset of the methyltin reaction process A new extended input matrix that has been reorganized. For the target data The autoregressive coefficient matrix of the data; The single-objective optimization problem is solved using the Lagrange multiplier method, as shown in the following formula: ； in, For Kronecker product; The Kronecker product satisfies , Scalar mapping matrix The identity matrix, Autoregressive coefficient matrix The identity matrix; By taking the partial derivatives of the autoregressive coefficient matrix and the scalar mapping matrix respectively, and setting the partial derivatives to 0, the relationship between the objective value and the eigenvalue of the single-objective optimization problem is obtained. Based on the single-objective optimization problem and the relationship between the objective value and the eigenvalue of the single-objective optimization problem, the calculation rules for the autoregressive coefficient matrix and the calculation rules for the scalar mapping matrix are obtained.

3. The method for extracting dynamic internal slow features of the methyltin reaction process based on DiCC-SFA according to claim 2, characterized in that, The step of obtaining the calculation rules for the autoregressive coefficient matrix and the scalar mapping matrix based on the single-objective optimization problem and the relationship between the objective value and eigenvalues ​​of the single-objective optimization problem includes: Based on the relationship between the objective value and the eigenvalues ​​of the single-objective optimization problem, the objective value of the single-objective optimization problem is maximized in order to maximize the eigenvalues: Simplifying the above formula, we obtain the calculation rule for the autoregressive coefficient matrix: ;in, These are the eigenvalues.

4. The method for extracting dynamic internal slow features of the methyltin reaction process based on DiCC-SFA according to claim 2, characterized in that, The steps of obtaining the calculation rules for the autoregressive coefficient matrix and the scalar mapping matrix based on the single-objective optimization problem and the relationship between the objective value and eigenvalues ​​of the single-objective optimization problem include: Based on the relationship between the objective value and the eigenvalues ​​of the single-objective optimization problem, the objective value of the single-objective optimization problem is maximized in order to maximize the eigenvalues: Simplifying the above formula, we obtain the calculation rule for the scalar mapping matrix: ;in, These are the eigenvalues.

5. The method for extracting dynamic internal slow features of the methyltin reaction process based on DiCC-SFA according to any one of claims 1-4, characterized in that, After the step of extracting potential slow features from the historical data or real-time monitoring data of the methyltin reaction process collected from the DCS system, the method further includes: sorting the extracted slow features in ascending order of their rate of change based on the derivative values ​​of the slow features.

6. The method for extracting dynamic internal slow features of the methyltin reaction process based on DiCC-SFA according to any one of claims 1-4, characterized in that, The step of obtaining monitoring statistics for multiple preset target monitoring data based on the degree of slowness of the slow features, the number of the main slow features, the autoregressive coefficient matrix, and the scalar mapping matrix includes: Based on the degree of slowness of the slow features and the number of the main slow features, the autoregressive coefficient matrix is ​​divided into a first type of autoregressive coefficient matrix and a second type of autoregressive coefficient matrix, and the scalar mapping matrix is ​​divided into a first type of scalar mapping matrix and a second type of scalar mapping matrix. Based on the first type of scalar mapping matrix, obtain the dynamic slow features inside the main space of the potential process of the methyltin reaction, the estimated value of the dynamic slow features inside the main space, and the derivative of the dynamic slow features inside the main space. Based on the second type of scalar mapping matrix, obtain the slow dynamic features inside the residual subspace, the estimated value of the slow dynamic features inside the residual subspace, and the derivative of the slow dynamic features inside the residual subspace for the potential process of methyltin reaction. Based on the dynamic slow features within the main space, the estimated value of the dynamic slow features within the main space, the derivative of the dynamic slow features within the main space, the dynamic slow features within the residual subspace, the estimated value of the dynamic slow features within the residual subspace, and the derivative of the dynamic slow features within the residual subspace, monitoring statistics of multiple preset target monitoring data are obtained.

7. The method for extracting dynamic internal slow features of the methyltin reaction process based on DiCC-SFA according to claim 6, characterized in that, The step of obtaining monitoring statistics of multiple preset target monitoring data based on the slow dynamic features inside the main space, the estimated value of the slow dynamic features inside the main space, the derivative of the slow dynamic features inside the main space, the slow dynamic features inside the residual subspace, the estimated value of the slow dynamic features inside the residual subspace, and the derivative of the slow dynamic features inside the residual subspace includes: The monitoring statistics for each target monitoring data can be obtained using the following formula: ； in, For monitoring statistics exist Monitoring values ​​at any given time for Dynamic slow features within the main space extracted from the methyltin reaction process dataset at each moment; ； in, For monitoring statistics The monitoring value at any given time, for Dynamic slow features within the residual subspace extracted from the methyltin reaction process dataset at each moment; in, and This is the Hotelling statistic; ； in, For monitoring statistics exist The detection value at that moment, for Estimates of the dynamic slow features within the main space extracted from the methyltin reaction process dataset at each time step; ； in, For monitoring statistics exist Monitoring values ​​at any given time for Estimates of the dynamic slow features within the residual subspace extracted from the methyltin reaction process dataset at each time step; in, and This is the squared prediction error statistic; ； in, For monitoring statistics exist Monitoring values ​​at any given time For a moment Derivatives of the slow dynamic features within the main space extracted from the methyltin reaction process dataset; ； in, For monitoring statistics exist Monitoring values ​​at any given time For a moment Derivatives of the slow dynamic features within the residual subspace extracted from the methyltin reaction process dataset; in, and This is a statistical measure for similar monitoring.

8. The method for extracting dynamic internal slow features of the methyltin reaction process based on DiCC-SFA according to claim 7, characterized in that, The step of determining the abnormal type of the monitored methyltin reaction based on the monitoring statistics includes: exist , , and When there are monitoring statistics exceeding the corresponding control limits, if and The monitoring statistics were all less than the corresponding control limits, and the anomaly type was determined to be a steady-state anomaly; whereby, steady-state anomaly means that the disturbance has no effect on the kinetics of the methyltin reaction process; like and The monitoring statistics were all greater than the corresponding control limits, and the anomaly type was determined to be a dynamic anomaly.

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