Model migration based modeling method and system for pilot scale-up of continuous stirred tank reactors

Abstract

This invention discloses a model transfer-based method and system for pilot-scale modeling of continuous stirred reactors, belonging to the field of process industry modeling technology. The invention collects and preprocesses process data from laboratory and pilot-scale continuous stirred reactors to construct a general nonlinear identification model. Based on sparse Bayesian learning, it separately identifies the laboratory reactor to obtain model structure information and identifies the pilot-scale reactor to obtain independent posterior distributions of parameters. It reuses the laboratory structure information to construct the pilot-scale model's pre-posterior distribution and generates enhanced observation outputs. Using the independent posterior distribution as the ideal model, it solves the fused posterior distribution by minimizing distribution differences to determine model parameters and achieve reactant concentration prediction. This invention can reduce the cost of pilot-scale modeling and significantly improve the model identification accuracy and stability in small-sample, high-noise scenarios.

Description

Technical Field

[0001] This invention relates to the field of process industry modeling technology, and in particular to a method and system for pilot-scale modeling of a continuous stirred reactor based on model transfer. Background Technology

[0002] Continuous stirred tank reactors are core reaction equipment in fine chemical, pharmaceutical, bioreaction, and process industries, exhibiting typical characteristics of strong nonlinearity, variable coupling, and dynamic time-varying behavior. The industrialization of reaction processes must follow the path of "laboratory-scale research and development—pilot-scale verification—industrialization." First, mechanism studies, parameter identification, and operation optimization are completed in laboratory reactors, and then the feasibility and operational stability of the process are verified through pilot-scale amplification.

[0003] When a reactor is scaled up from laboratory to pilot-scale, significant changes occur in equipment volume, heat and mass transfer conditions, residence time distribution, mixing characteristics, and operating environment. The dynamic relationship between system input and output deviates significantly from the laboratory stage. The model built in the laboratory cannot be directly extrapolated to the pilot-scale scenario, and is prone to problems such as a sharp drop in prediction accuracy and model failure, which directly affects the operation evaluation and control scheme design of the pilot-scale process.

[0004] Existing pilot-scale modeling methods for continuous stirred tank reactors often employ an independent identification approach, requiring the collection of extensive pilot-scale process data for model retraining. However, the amount of effective data obtainable during the pilot-scale stage is extremely limited due to factors such as equipment constraints, high material costs, stringent safety regulations, and on-site operational disturbances, and measurement noise interference is even more significant. Relying solely on pilot-scale data for modeling makes it difficult to achieve accurate model structure identification and reliable parameter estimation, resulting in drawbacks such as high modeling costs, low prediction accuracy, and poor structural stability.

[0005] Laboratory and pilot-scale reactors share high similarities in reaction mechanisms, key variable relationships, and dynamic structures, making the structural information acquired in the laboratory highly valuable for reuse. Current technologies fail to fully utilize this similarity, hindering the transfer of effective laboratory structural information to the pilot-scale modeling process and failing to address the industry pain points of scarce data and insufficient observation quality in the early stages of pilot-scale operations. Therefore, developing a high-precision pilot-scale modeling method that reuses laboratory model structural information and incorporates observational enhancement has become a pressing technical challenge in the scale-up of process industry reaction equipment. Summary of the Invention

[0006] To address this, this invention provides a model transfer-based method and system for pilot-scale modeling of continuous stirred reactors, which solves the technical problems of high modeling cost, low prediction accuracy, and poor model stability in existing continuous stirred reactor pilot-scale modeling, where the model structure information of laboratory-scale reactors cannot be effectively reused, and the model is limited by the scarcity of effective data and large measurement noise interference in the pilot stage.

[0007] To address the aforementioned technical problems, this invention provides a modeling method for pilot-scale expansion of a continuous stirred reactor based on model transfer, comprising the following steps: Step S1: Collect historical process data of the reaction process in the laboratory-scale continuous stirred reactor and the pilot-scale continuous stirred reactor respectively, and preprocess the historical process data; wherein, the laboratory-scale continuous stirred reactor is defined as reactor a and the pilot-scale continuous stirred reactor is defined as reactor b, and the historical process data includes the input variable coolant flow rate and the output variable reactant outlet concentration; Step S2: Based on the input and output variables of the continuous stirred reactor, construct a general nonlinear identification model for the continuous stirred reactor; Step S3: Based on the sparse Bayesian learning method, the general nonlinear identification model is identified using the preprocessed process data of reactor a, and the accuracy matrix of the estimated parameters characterizing the structural information of the reactor a model is obtained. Step S4: Based on the sparse Bayesian learning method, the general nonlinear identification model is independently identified using the preprocessed process data of reactor b, and the independent posterior distribution of the reactor b model parameters and the corresponding hyperparameters are obtained. Step S5: Reuse the model structure information of reactor a, and introduce the estimated parameter accuracy matrix as a prior constraint into the model identification process of reactor b to construct the pre- and posterior distribution of the model parameters of reactor b. Step S6: Generate enhanced observation output based on the pre-posterior distribution, and use the enhanced observation output to fine-tune and correct the original observation data of reactor b; Step S7: Using the independent posterior distribution obtained in step S4 as the ideal reference model and the enhanced observation output generated in step S6 as the fixed constraint, construct the fusion identification model. By minimizing the distribution difference between the fusion identification model and the ideal reference model, solve to obtain the fusion posterior distribution of the reactor b model parameters. Step S8: Determine the final model parameters of reactor b based on the fusion posterior distribution, and predict the reactant outlet concentration of reactor b based on the final model parameters.

[0008] Preferably, the preprocessing in step S1 includes outlier removal, missing data completion, and dimensional normalization; wherein, outlier removal includes removing non-numerical sample points, abnormal operating condition data, and outliers; missing data completion uses interpolation or forward / backward imputation; and dimensional normalization is used to eliminate dimensional differences between different variables.

[0009] Preferably, the specific method for constructing the general nonlinear identification model of the continuous stirred reactor in step S2 is as follows: Step S21: Based on the material balance equation of the continuous stirred reactor, the general nonlinear identification model is set as a nonlinear autoregressive exogenous input model, with the following expression: ; In the formula, For the first The outlet concentration of the reactant at each sampling time For white measurement noise that follows a Gaussian distribution, For the regression vector, Candidate basis functions, These are the model parameters corresponding to the candidate basis functions. The total number of candidate model items; The regression vector The expression is: ; In the formula, For the first Coolant flow rate at each sampling time, The maximum lag order of the output variable. The maximum lag order of the input variable; S22: When the effective sample length is Then, the nonlinear autoregressive exogenous input model is converted into an equivalent identification model in matrix form: ; In the formula, For the output vector, For information matrix, For model parameter vectors, For the noise vector, the initial modeling time is... , This is the function for finding the maximum value.

[0010] Preferably, the sparse Bayesian learning identification method in steps S3 and S4 specifically includes the following steps: Based on the characteristic that the measurement noise follows zero-mean Gaussian white noise, an observation probability model is constructed: ; In the formula, Represents the conditional probability distribution. For the output vector, For information matrix, For model parameter vectors, For noise accuracy, , For noise variance, Indicates a Gaussian distribution. For noise variance, It is the identity matrix; For model parameter vectors Each component in the model is set to an independent Gaussian prior distribution with zero mean: ; In the formula, The diagonal matrix of the hyperparameters of the parameter accuracy. For the first The precision hyperparameters of the parameters corresponding to each candidate basis function; Solve for the model parameter vector using Bayes' theorem. The posterior distribution is a Gaussian distribution: ; In the formula, the covariance matrix of the posterior distribution is... The mean vector of the posterior distribution ; By maximizing the marginal likelihood function of the output data, the iterative update rules for parameter accuracy hyperparameters and noise accuracy are derived. Based on the iterative update rule, iterative identification is performed until the preset convergence condition is met or the maximum number of iterations is reached. The final model parameter posterior distribution, estimated parameter accuracy matrix, and noise accuracy are output. After the iteration terminates, candidate model terms with parameter accuracy hyperparameters greater than a preset threshold are removed, and the candidate model terms corresponding to the remaining non-zero parameters constitute the effective model structure.

[0011] Preferably, the step S5 of constructing the prognostic distribution of the reactor b model parameters specifically includes: Step S51: Reuse the model structure information obtained from identifying reactor a in step S3, and record the model structure information as... ,by To construct the pre- and posterior distributions of the reactor model b parameters for the prior constraints of model transfer, the expression is: ; In the formula, This represents a conditional probability distribution, with the superscript "-" indicating the prior distribution in the posterior stage. Let be the model parameter vector of reactor b. This is the information matrix of reactor b. Let b be the output vector of the reactor. The noise accuracy estimate obtained by independently identifying reactor b. Proportional to the sign, Represents the conditional probability distribution. To introduce Prior distribution of parameters in model b of the constrained reactor; Step S52: Identify the accuracy matrix of the estimated parameters output after the reactor a converges, as described in step S3. As the structural information Quantitative characterization, constructing the prior distribution of the parameters of the reactor model b: ; In the formula, Indicates a Gaussian distribution. To estimate the parameter accuracy matrix The reverse; Step S53: Using Bayes' theorem, the prognostic distribution of the parameters of reactor model b is obtained as a Gaussian distribution. ; In the formula, the covariance matrix of the posterior distribution is... The mean vector of the posterior distribution .

[0012] Preferably, the method for generating the enhanced observation output in step S6 is as follows: based on the prognostic and posterior distributions of the reactor b model parameters, the probability distribution of the enhanced observation output is derived as a Gaussian distribution: ; In the formula, To enhance the observed output, its distribution mean Distribution covariance matrix The mean of the distribution is used as the determining value for enhancing the observation output, and the original observation data of reactor b is finely adjusted and corrected.

[0013] Preferably, the step S7 of obtaining the fused posterior distribution of the reactor b model parameters specifically includes: Using the independent posterior distribution of the reactor b model parameters obtained in step S4 as the ideal reference model, and the enhanced observation output probability distribution generated in step S6... As a fixed constraint, the posterior distribution expression of the parameters of the fusion identification model is constructed as follows: ; Kullback-Leibler divergence is used as the quantification criterion for the distribution difference between the fusion identification model and the ideal reference model, and a minimization optimization objective is constructed. By solving the minimization optimization objective, the fused posterior distribution of the parameters of the reactor b model is obtained as a Gaussian distribution: ; In the formula, Let denot the fused posterior distribution, and let covariance matrix of the fused posterior distribution be denoted as ... , the mean vector of the fused posterior distribution , To independently identify the inverse of the accuracy matrix and the gain matrix of the estimated parameters output after convergence of reactor b. , It is an identity matrix.

[0014] Preferably, in step S8, predicting the reactant outlet concentration of reactor b based on the final model parameters specifically involves: merging the mean vector of the posterior distribution... As the final model parameter vector of reactor b Substituting the input into a nonlinear autoregressive exogenous model, the predicted values ​​of reactant outlet concentrations are calculated: ; In the formula, For reactor b The outlet concentration of the reactant at each sampling time For the final model parameter vector, the first... One element, For the first The candidate basis functions at the th... The value at each sampling time, For the regression vector, This represents the total number of candidate model terms.

[0015] This invention also provides a model transfer-based continuous stirred reactor pilot-scale modeling system for implementing the aforementioned model transfer-based continuous stirred reactor pilot-scale modeling method. The system includes: The data acquisition and preprocessing module is used to acquire historical process data of the reaction process in the laboratory-scale continuous stirred reactor and the pilot-scale continuous stirred reactor, respectively, and to preprocess the historical process data; wherein, the laboratory-scale continuous stirred reactor is defined as reactor a and the pilot-scale continuous stirred reactor is defined as reactor b, and the historical process data includes the input variable coolant flow rate and the output variable reactant outlet concentration; The general model building module is used to build a general nonlinear identification model of a continuous stirred reactor based on the input and output variables of the reactor. The laboratory model identification module is used to identify the general nonlinear identification model based on the sparse Bayesian learning method using the preprocessed process data of reactor a, and obtain the estimation parameter accuracy matrix characterizing the structural information of the reactor a model. The pilot-scale model independent identification module is used to independently identify the general nonlinear identification model based on the sparse Bayesian learning method using the preprocessed process data of reactor b, and obtain the independent posterior distribution of the reactor b model parameters and the corresponding hyperparameters. The model transfer and prognostic construction module is used to reuse the model structure information of reactor a, introduce the estimated parameter accuracy matrix as a prior constraint into the model identification process of reactor b, and construct the prognostic distribution of the model parameters of reactor b. An observation enhancement module is used to generate enhanced observation output based on the pre-posterior distribution, and to fine-tune and correct the original observation data of reactor b using the enhanced observation output. The fusion modeling module is used to construct a fusion identification model with the independent posterior distribution as the ideal reference model and the enhanced observation output as the fixed constraint. By minimizing the distribution difference between the fusion identification model and the ideal reference model, the fusion posterior distribution of the reactor b model parameters is obtained. The concentration prediction module is used to determine the final model parameters of reactor b based on the fusion posterior distribution, and to predict the reactant outlet concentration of reactor b based on the final model parameters.

[0016] This invention also provides a computer storage medium storing a computer software product, the computer software product including several instructions to cause a computer device to execute the above-described model transfer-based continuous stirred reactor pilot-scale modeling method.

[0017] As can be seen from the above technical solutions, this invention application has the following beneficial effects: First, this invention reuses the model structure information obtained by sparse Bayesian learning from a laboratory-scale continuous stirred reactor, and introduces the identification process of a pilot-scale reactor with the parameter accuracy matrix as a prior constraint. This eliminates the need to collect a large amount of high-cost experimental data in the pilot stage to complete model construction, significantly reducing the material, equipment, and time costs of pilot-scale scale-up. At the same time, relying on the effective structural information constraints verified in the laboratory, it solves the industry pain point of model overfitting and inaccurate structure identification caused by the scarcity of effective samples in the early stage of pilot-scale testing, and greatly improves the stability of model identification under small sample conditions.

[0018] Secondly, this invention generates enhanced observation output based on the pre-posterior distribution constructed by reusing structural information, which fine-tunes and corrects the original noisy observation data of the pilot-scale test, effectively supplementing the effective observation information in the pilot-scale test scenario and reducing the interference of on-site measurement noise on the identification results. At the same time, using the parameter posterior distribution independently identified by the pilot-scale reactor as an ideal reference model, the parameter fusion solution is achieved by minimizing the KL divergence. This not only fully preserves the input-output dynamic characteristics of the pilot-scale reactor itself, but also makes up for the information defects of the pilot-scale test data by using laboratory structural information, which greatly improves the prediction accuracy of reactant outlet concentration and ensures the generalization performance of the model under complex working conditions.

[0019] Third, this invention constructs a nonlinear autoregressive exogenous input general model framework based on the material balance characteristics of a continuous stirred reactor, and combines sparse Bayesian learning to achieve full-process data-driven model identification and transfer. It does not rely on the precise mechanistic equations of the reaction process, avoiding complex mechanism modeling and parameter fitting processes. At the same time, the method is modular and the steps are standardized, which can be adapted to pilot-scale modeling scenarios of continuous stirred reactors with different reaction systems and different scale-up ratios. The output dynamic model can be directly connected to the operational status evaluation, operation optimization and advanced control design of the pilot-scale process, and has strong engineering scalability and application value. Attached Figure Description

[0020] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the embodiments will be briefly described below. Referring to the drawings will make the features and advantages of the present invention clearer. The drawings are illustrative and should not be construed as limiting the present invention in any way. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort. Wherein: Figure 1 This is a flowchart of a pilot-scale modeling method for a continuous stirred reactor based on model transfer, provided by the present invention. Figure 2 This is a schematic diagram of the coolant flow rate and reactant outlet concentration data curves for the continuous stirred reactor a in this invention; Figure 3 This is a schematic diagram of the coolant flow rate and reactant outlet concentration data curves of the continuous stirred reactor b in this invention; Figure 4 This is a schematic diagram of the reactant outlet concentration prediction curve of the continuous stirred reactor a in this invention; Figure 5 This is a schematic diagram of the reactant outlet concentration prediction curve in the continuous stirred reactor b of this invention; Figure 6 This is a block diagram of a continuous stirred reactor pilot-scale modeling system based on model transfer, provided by the present invention. Detailed Implementation

[0021] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0022] This invention discloses a model transfer-based modeling method and system for pilot-scale amplification of continuous stirred reactors. Addressing industry pain points such as the difficulty in directly extrapolating laboratory models during pilot-scale amplification of continuous stirred reactors, the limited number of pilot-scale reactor samples, and insufficient observation quality, this method reuses the sparse structural information of laboratory-scale reactor models and supplements the observation information from the pilot-scale stage with observation enhancement techniques. Ultimately, it achieves the fusion solution of model parameters by minimizing distribution differences. This alleviates the identification difficulties caused by limited data and high noise in the early stages of pilot-scale amplification, and improves the accuracy of structural identification and the reliability of parameter estimation for pilot-scale reactor models. It enables high-precision prediction of reactant concentrations during the pilot-scale amplification stage.

[0023] Example 1: This embodiment provides a pilot-scale modeling method for continuous stirred reactors based on structural information reuse and observation enhancement, such as... Figure 1 As shown, the process includes the following steps S1 to S8, and the specific implementation process is as follows: Step S1: Collect historical process data of the reaction process in the laboratory-scale continuous stirred reactor and the pilot-scale continuous stirred reactor respectively, and preprocess the historical process data; wherein, the laboratory-scale continuous stirred reactor is defined as reactor a and the pilot-scale continuous stirred reactor is defined as reactor b, and the historical process data includes the input variable coolant flow rate and the output variable reactant outlet concentration.

[0024] Specifically, in this step, the preprocessing includes outlier removal, missing data completion, and dimensional normalization. The specific implementation methods for each step are as follows: 1. Outlier Removal: This includes removing non-numerical sample points, obviously abnormal operating condition data, and outliers. Specifically, removing non-numerical sample points involves deleting null values, character records, duplicate records, and non-numerical sample points caused by sensor communication errors. For obviously abnormal operating condition data, screening is performed using process mechanism constraints, equipment operating limits, steady-state operating ranges, or empirical thresholds. For outliers, methods such as box plots, the 3σ criterion, Z-scores, MAD based on median absolute deviation, local outlier factor methods, density clustering, or isolated forest methods can be used for identification and removal. For continuous time series data, sliding window statistics, constraints on the rate of change between adjacent sampling times, or first-order difference mutation criteria can also be used for outlier identification.

[0025] 2. Missing data imputation: For missing values ​​in process data, any one of the following methods can be used: mean imputation, median imputation, forward imputation, backward imputation, linear interpolation, spline interpolation, Lagrange interpolation, K-nearest neighbor-based missing value imputation, regression model-based estimation imputation, and time series prediction model-based reconstruction imputation.

[0026] 3. Dimensional normalization: This is used to eliminate dimensional differences between different variables. Any one of the following methods can be used: min-max normalization, Z-score standardization, mean centering, interval scaling, or normalization to rated operating conditions.

[0027] After performing the above preprocessing on the process data of reactor a, the coolant flow rate and reactant outlet concentration data are obtained as follows: Figure 2 As shown; after completing the above preprocessing of the process data of reactor b, the coolant flow rate and reactant outlet concentration data are obtained as follows. Figure 3 As shown.

[0028] Step S2: Based on the input and output variables of the continuous stirred reactor, construct a general nonlinear identification model for the continuous stirred reactor.

[0029] Specifically, in this step, the method for constructing a general nonlinear identification model for a continuous stirred reactor is as follows: Step S21: Based on the material balance equation of the continuous stirred reactor, the general nonlinear identification model of the continuous stirred reactor is set as a nonlinear autoregressive exogenous input model, with the following expression: ; In the formula, For the first The outlet concentration of the reactant at each sampling time For white measurement noise that follows a Gaussian distribution, For the regression vector, Candidate basis functions, These are the model parameters corresponding to the candidate basis functions. The total number of candidate model items; The regression vector The expression is: ; In the formula, For the first Coolant flow rate at each sampling time, The maximum lag order of the output variable. The maximum lag order of the input variable; S22: For the aforementioned nonlinear autoregressive exogenous input model, with an effective sample length of... When defining the output vector Information matrix Parameter vector and noise vector They are respectively: ; ; ; ; Wherein, the initial modeling time is ,in This is the function for finding the maximum value.

[0030] The nonlinear autoregressive exogenous input model of the continuous stirred reactor can then be written as the following equivalent identification model: .

[0031] Step S3: Based on the sparse Bayesian learning method, the general nonlinear identification model is identified using the preprocessed process data of reactor a, and the accuracy matrix of the estimated parameters representing the structural information of reactor a model is obtained.

[0032] Specifically, this step includes the following steps: Step S31: Based on the noise vector It is Gaussian white noise, i.e. ,in Let V be the noise variance, and let be the noise accuracy. , For an identity matrix of appropriate dimensions, the observation probability model is constructed as follows: .

[0033] Step S32: For the parameter vector Each component is given an independent zero-mean Gaussian prior. ; In the formula, The diagonal matrix of the hyperparameters of the parameter accuracy. For the first The precision hyperparameters corresponding to the parameters of each candidate basis function.

[0034] Step S33: According to Bayes' theorem, the parameter vector The posterior distribution can be expressed as: ; The calculated posterior distribution is a Gaussian distribution: ; Wherein, the covariance matrix of the posterior distribution and mean vector They are respectively: ; .

[0035] Step S34: Maximize the logarithmic form of the marginal likelihood function of the output data as follows: ; Obtain the hyperparameters of parameter accuracy and noise accuracy The update rules are as follows: ; ; ; in, Hyperparameters that indicate the precision of the updated parameters. This indicates the updated noise accuracy. express Norm. Introduction To achieve a concise representation of the update process, The posterior mean is the first One element, The posterior covariance is the first One diagonal element.

[0036] Step S35: Based on the posterior distribution and hyperparameter update rules, perform identification iterations until convergence, specifically including: Step 1: Set the iteration count index ,initialization , At the same time, set the maximum number of iterations. and preset convergence threshold ; Step Two: In the first In the next iteration, the current and Substitute into the calculation to obtain the parameter vector The posterior distribution is: ; Wherein, the covariance matrix of the posterior distribution and mean vector They are respectively: ; .

[0037] Step 3: Based on the posterior mean vector Covariance Matrix Calculate intermediate variables: ; in, for The diagonal elements, for The Each element; then calculate the updated hyperparameters: ; ; And thus construct the updated hyperparameter matrix. .

[0038] Step 4: Verify the convergence condition and determine whether the posterior mean vectors obtained from two consecutive iterations satisfy the preset convergence condition: ; If the convergence condition is not met and Then let Return to step two and continue execution; If the convergence condition is met or the maximum number of iterations is reached, the iteration stops, and the estimated values ​​of each parameter in the current iteration are output and denoted as follows. , , , ,in This is the accuracy matrix of the estimated parameters that characterizes the structural information of reactor model a.

[0039] After the iteration terminates, for those that satisfy Candidate model terms with values ​​greater than a preset threshold are considered to have parameters approaching zero, and are therefore removed from the model structure with their corresponding parameter values ​​set to zero. The candidate model terms corresponding to the non-zero parameter positions in the parameter vector are the valid model structures. The predicted reactant outlet concentration of the continuous stirred reactor a obtained through this step is as follows: Figure 4 As shown.

[0040] Step S4: Based on the sparse Bayesian learning method, the general nonlinear identification model is independently identified using the preprocessed process data of reactor b, and the independent posterior distribution of the reactor b model parameters and the corresponding hyperparameters are obtained.

[0041] Specifically, the sparse Bayesian learning identification method in this step is completely consistent with step S3, and the specific implementation steps are as follows: Step S41: Based on the preprocessed data from reactor b, the corresponding observation probability model is constructed as follows: ; In the formula, Let b be the output vector of the reactor. This is the information matrix of reactor b. Let be the model parameter vector of reactor b. For the noise accuracy of reactor b, It is an identity matrix.

[0042] Step S42: Model parameter vector for reactor b Each component is given an independent Gaussian prior with zero mean: ; In the formula, is the hyperparameter diagonal matrix for the accuracy of parameter b of the reactor.

[0043] Step S43: According to Bayes' theorem, the independent posterior distribution of the parameters of the reactor b model is obtained as a Gaussian distribution: ; Wherein, the covariance matrix of the independent posterior distribution and mean vector They are respectively: ; .

[0044] Step S44: Consistent with step S34, the iterative update rules for the parameter accuracy hyperparameters and noise accuracy of reactor b are derived by maximizing the marginal likelihood function. Iterative identification is performed until convergence, and finally, the independent posterior distribution of the reactor b model parameters and the estimated parameter accuracy matrix are output. With noise accuracy This independent posterior distribution is used as an ideal reference model for subsequent fusion modeling.

[0045] Step S5: Reuse the model structure information of reactor a, and introduce the estimated parameter accuracy matrix as a prior constraint into the model identification process of reactor b to construct the pre- and posterior distribution of the model parameters of reactor b.

[0046] Specifically, this step includes the following steps: Step S51: Reuse the model structure information obtained from identifying reactor a in step S3, and record the model structure information as... ,by To construct the pre- and posterior distributions of the reactor model b parameters for the prior constraints of model transfer, the expression is: ; In the formula, This represents a conditional probability distribution, with the superscript "-" indicating the prior distribution in the posterior stage. Let be the model parameter vector of reactor b. This is the information matrix of reactor b. Let b be the output vector of the reactor. The noise accuracy estimate obtained by independently identifying reactor b. Proportional to the sign, Represents the conditional probability distribution. To introduce Prior distribution of parameters for the constrained reactor model b.

[0047] Step S52: Identify the accuracy matrix of the estimated parameters output after the reactor a converges, as described in step S3. As the structural information Quantitative characterization, constructing the prior distribution of the parameters of the reactor model b: ; In the formula, Indicates a Gaussian distribution. To estimate the parameter accuracy matrix The reverse.

[0048] Step S53: Using Bayes' theorem, the prognostic distribution of the parameters of reactor model b is obtained as a Gaussian distribution. ; In the formula, the covariance matrix of the posterior distribution is... The mean vector of the posterior distribution .

[0049] Step S6: Generate enhanced observation output based on the pre-posterior distribution, and use the enhanced observation output to fine-tune and correct the original observation data of reactor b.

[0050] Specifically, in this step, the method for generating the enhanced observation output is based on the prognostic distribution of the parameters of the reactor b model, specifically: ; The probability distribution of the enhanced observation output is derived to be a Gaussian distribution: ; In the formula, To enhance the observed output, its distribution mean Distribution covariance matrix The mean of the distribution is used as the determining value for the enhanced observation output to fine-tune and correct the original observation data of reactor b, supplement the observation information characterizing reactor b, and improve the quality of the measurement data of reactor b.

[0051] Step S7: Using the independent posterior distribution obtained in step S4 as the ideal reference model and the enhanced observation output generated in step S6 as the fixed constraint, construct the fusion identification model. By minimizing the distribution difference between the fusion identification model and the ideal reference model, solve for the fusion posterior distribution of the reactor b model parameters.

[0052] Specifically, in this step, the fused posterior distribution of the parameters of the reactor model b is obtained by solving, which includes: Step S71: Take the independent posterior distribution of the reactor b model parameters obtained in step S4 as the ideal reference model, and its expression is: .

[0053] Step S72: Using the enhanced observation output distribution generated in step S6 As a fixed constraint, the posterior distribution expression of the parameters of the fusion identification model is constructed as follows: .

[0054] Step S73: Using the Kullback-Leibler divergence (KL divergence) between the fusion identification model and the ideal reference model as the difference criterion, construct a minimization optimization objective. The expression for the KL divergence is: ; in, Indicates from distribution To distribution Kullback-Leibler divergence between them express for Expectations It is a logarithmic function.

[0055] Step S74: Minimize the Kullback-Leibler divergence between the fused identification model and the ideal reference model to obtain the fused posterior distribution of the reactor b model parameters. Its expression is: ; in, It is an exponential function; The calculated posterior distribution of the fusion is a Gaussian distribution: ; Among them, the mean of the fusion posterior distribution Covariance for: ; ; In the formula, the gain matrix The expression is: .

[0056] Step S8: Determine the final model parameters of reactor b based on the fusion posterior distribution, and predict the reactant outlet concentration of reactor b based on the final model parameters.

[0057] Specifically, in this step, the reactant outlet concentration of reactor b is predicted based on the final model parameters, as follows: The mean vector of the fused posterior distribution obtained in step S7 As the final model parameter vector of reactor b, i.e. Substituting the input into the nonlinear autoregressive exogenous input model constructed in step S2, the predicted value of the reactant outlet concentration is calculated: ; In the formula, For reactor b The outlet concentration of the reactant at each sampling time For the final model parameter vector, the first... One element, For the first The candidate basis functions at the th... The value at each sampling time, For the regression vector, This represents the total number of candidate model terms.

[0058] The predicted reactant outlet concentration of the continuous stirred reactor b obtained through this step is as follows: Figure 5 As shown.

[0059] Example 2: like Figure 6 As shown, this invention provides a model transfer-based pilot-scale modeling system for continuous stirred reactors. This system is used to implement the model transfer-based pilot-scale modeling method for continuous stirred reactors described in Embodiment 1 above, specifically including: The data acquisition and preprocessing module 100 is used to acquire historical process data of the reaction process in the laboratory-scale continuous stirred reactor and the pilot-scale continuous stirred reactor, respectively, and to preprocess the historical process data; wherein, the laboratory-scale continuous stirred reactor is defined as reactor a and the pilot-scale continuous stirred reactor is defined as reactor b, and the historical process data includes the input variable coolant flow rate and the output variable reactant outlet concentration; The general model building module 200 is used to build a general nonlinear identification model of the continuous stirred reactor based on the input and output variables of the continuous stirred reactor. The laboratory model identification module 300 is used to identify the general nonlinear identification model based on the sparse Bayesian learning method using the preprocessed process data of reactor a, and obtain the estimation parameter accuracy matrix characterizing the structural information of the reactor a model. The pilot-scale model independent identification module 400 is used to independently identify the general nonlinear identification model based on the sparse Bayesian learning method using the preprocessed process data of reactor b, and obtain the independent posterior distribution of the reactor b model parameters and the corresponding hyperparameters. The model transfer and prognostic construction module 500 is used to reuse the model structure information of reactor a, introduce the estimated parameter accuracy matrix as a prior constraint into the model identification process of reactor b, and construct the prognostic distribution of the model parameters of reactor b. The observation enhancement module 600 is used to generate enhanced observation output based on the pre-posterior distribution, and to fine-tune and correct the original observation data of reactor b using the enhanced observation output. The fusion modeling module 700 is used to construct a fusion identification model with the independent posterior distribution as the ideal reference model and the enhanced observation output as the fixed constraint. By minimizing the distribution difference between the fusion identification model and the ideal reference model, the fusion posterior distribution of the reactor b model parameters is obtained. The concentration prediction module 800 is used to determine the final model parameters of reactor b based on the fusion posterior distribution, and to predict the reactant outlet concentration of reactor b based on the final model parameters.

[0060] This embodiment presents a model transfer-based continuous stirred reactor pilot-scale modeling system for implementing the aforementioned model transfer-based continuous stirred reactor pilot-scale modeling method. Therefore, the specific implementation of the model transfer-based continuous stirred reactor pilot-scale modeling system can be found in the previous embodiment section of the model transfer-based continuous stirred reactor pilot-scale modeling method. To avoid redundancy, it will not be repeated here.

[0061] Example 3: This invention provides a computer storage medium storing a computer software product, which includes several instructions to cause a computer device to execute the above-described model transfer-based continuous stirred reactor pilot-scale modeling method.

[0062] 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.

[0063] 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.

[0064] 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 functions specified in one or more boxes. These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable apparatus 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.

[0065] 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. However, obvious variations or modifications derived therefrom are still within the scope of protection of this invention.

Claims

1. A model transfer-based method for pilot-scale modeling of a continuous stirred reactor, characterized in that, Includes the following steps: Step S1: Collect historical process data of the reaction process in the laboratory-scale continuous stirred reactor and the pilot-scale continuous stirred reactor respectively, and preprocess the historical process data; wherein, the laboratory-scale continuous stirred reactor is defined as reactor a and the pilot-scale continuous stirred reactor is defined as reactor b, and the historical process data includes the input variable coolant flow rate and the output variable reactant outlet concentration; Step S2: Based on the input and output variables of the continuous stirred reactor, construct a general nonlinear identification model for the continuous stirred reactor; Step S3: Based on the sparse Bayesian learning method, the general nonlinear identification model is identified using the preprocessed process data of reactor a, and the accuracy matrix of the estimated parameters characterizing the structural information of the reactor a model is obtained. Step S4: Based on the sparse Bayesian learning method, the general nonlinear identification model is independently identified using the preprocessed process data of reactor b, and the independent posterior distribution of the reactor b model parameters and the corresponding hyperparameters are obtained. Step S5: Reuse the model structure information of reactor a, and introduce the estimated parameter accuracy matrix as a prior constraint into the model identification process of reactor b to construct the pre- and posterior distribution of the model parameters of reactor b. Step S6: Generate enhanced observation output based on the pre-posterior distribution, and use the enhanced observation output to fine-tune and correct the original observation data of reactor b; Step S7: Using the independent posterior distribution obtained in step S4 as the ideal reference model and the enhanced observation output generated in step S6 as the fixed constraint, construct the fusion identification model. By minimizing the distribution difference between the fusion identification model and the ideal reference model, solve to obtain the fusion posterior distribution of the reactor b model parameters. Step S8: Determine the final model parameters of reactor b based on the fusion posterior distribution, and predict the reactant outlet concentration of reactor b based on the final model parameters.

2. The model transfer-based pilot-scale modeling method for continuous stirred reactors according to claim 1, characterized in that, The preprocessing in step S1 includes outlier removal, missing data completion, and dimensional normalization. Outlier removal includes removing non-numerical sample points, abnormal operating condition data, and outliers. Missing data completion uses interpolation or forward / backward imputation. Dimensional normalization is used to eliminate dimensional differences between different variables.

3. The model transfer-based pilot-scale modeling method for continuous stirred reactors according to claim 1, characterized in that, The specific method for constructing the general nonlinear identification model of the continuous stirred reactor in step S2 is as follows: Step S21: Based on the material balance equation of the continuous stirred reactor, the general nonlinear identification model is set as a nonlinear autoregressive exogenous input model, with the following expression: ； In the formula, For the first The outlet concentration of the reactant at each sampling time For white measurement noise that follows a Gaussian distribution, For the regression vector, Candidate basis functions, These are the model parameters corresponding to the candidate basis functions. The total number of candidate model items; The regression vector The expression is: ； In the formula, For the first Coolant flow rate at each sampling time, The maximum lag order of the output variable. The maximum lag order of the input variable; S22: When the effective sample length is Then, the nonlinear autoregressive exogenous input model is converted into an equivalent identification model in matrix form: ； In the formula, For the output vector, For information matrix, For model parameter vectors, For the noise vector, the initial modeling time is... , This is the function for finding the maximum value.

4. The model transfer-based pilot-scale modeling method for continuous stirred reactors according to claim 1, characterized in that, The sparse Bayesian learning identification method in steps S3 and S4 specifically includes the following steps: Based on the characteristic that the measurement noise follows zero-mean Gaussian white noise, an observation probability model is constructed: ； In the formula, Represents the conditional probability distribution. For the output vector, For information matrix, For model parameter vectors, For noise accuracy, , For noise variance, Indicates a Gaussian distribution. For noise variance, It is the identity matrix; For model parameter vectors Each component in the model is set to an independent Gaussian prior distribution with zero mean: ； In the formula, The diagonal matrix of the hyperparameters of the parameter accuracy. For the first The precision hyperparameters of the parameters corresponding to each candidate basis function; Solve for the model parameter vector using Bayes' theorem. The posterior distribution is a Gaussian distribution: ； In the formula, the covariance matrix of the posterior distribution is... The mean vector of the posterior distribution ; By maximizing the marginal likelihood function of the output data, the iterative update rules for parameter accuracy hyperparameters and noise accuracy are derived. Based on the iterative update rule, iterative identification is performed until the preset convergence condition is met or the maximum number of iterations is reached. The final model parameter posterior distribution, estimated parameter accuracy matrix, and noise accuracy are output. After the iteration terminates, candidate model terms with parameter accuracy hyperparameters greater than a preset threshold are removed, and the candidate model terms corresponding to the remaining non-zero parameters constitute the effective model structure.

5. The model transfer-based pilot-scale modeling method for continuous stirred reactors according to claim 1, characterized in that, The step S5, which involves constructing the prognostic distribution of the parameters of the reactor b model, specifically includes: Step S51: Reuse the model structure information obtained from identifying reactor a in step S3, and record the model structure information as... ,by To construct the pre- and posterior distributions of the reactor model b parameters for the prior constraints of model transfer, the expression is: ； In the formula, This represents a conditional probability distribution, with the superscript "-" indicating the prior distribution in the posterior stage. Let be the model parameter vector of reactor b. This is the information matrix of reactor b. Let b be the output vector of the reactor. The noise accuracy estimate obtained by independently identifying reactor b. Proportional to the sign, Represents the conditional probability distribution. To introduce Prior distribution of parameters in model b of the constrained reactor; Step S52: Identify the accuracy matrix of the estimated parameters output after the reactor a converges, as described in step S3. As the structural information Quantitative characterization, constructing the prior distribution of the parameters of the reactor model b: ； In the formula, Indicates a Gaussian distribution. To estimate the parameter accuracy matrix The reverse; Step S53: Using Bayes' theorem, the prognostic distribution of the parameters of reactor model b is obtained as a Gaussian distribution. ； In the formula, the covariance matrix of the posterior distribution is... The mean vector of the posterior distribution .

6. The model transfer-based pilot-scale modeling method for continuous stirred reactors according to claim 5, characterized in that, The method for generating the enhanced observation output in step S6 is as follows: based on the prognostic distribution of the parameters of the reactor b model, the probability distribution of the enhanced observation output is derived as a Gaussian distribution. ； In the formula, To enhance the observed output, its distribution mean Distribution covariance matrix The mean of the distribution is used as the determining value for enhancing the observation output, and the original observation data of reactor b is finely adjusted and corrected.

7. The model transfer-based pilot-scale modeling method for continuous stirred reactors according to claim 6, characterized in that, The step S7, which involves solving for the fused posterior distribution of the parameters of the reactor b model, specifically includes: Using the independent posterior distribution of the reactor b model parameters obtained in step S4 as the ideal reference model, and the enhanced observation output probability distribution generated in step S6... As a fixed constraint, the posterior distribution expression of the parameters of the fusion identification model is constructed as follows: ； Kullback-Leibler divergence is used as the quantification criterion for the distribution difference between the fusion identification model and the ideal reference model, and a minimization optimization objective is constructed. By solving the minimization optimization objective, the fused posterior distribution of the parameters of the reactor b model is obtained as a Gaussian distribution: ； In the formula, Let denot the fused posterior distribution, and let covariance matrix of the fused posterior distribution be denoted as ... , the mean vector of the fused posterior distribution , To independently identify the inverse of the accuracy matrix and the gain matrix of the estimated parameters output after convergence of reactor b. , It is an identity matrix.

8. The model transfer-based pilot-scale modeling method for continuous stirred reactors according to claim 7, characterized in that, In step S8, the reactant outlet concentration of reactor b is predicted based on the final model parameters. Specifically, this involves: merging the mean vector of the posterior distribution... As the final model parameter vector of reactor b Substituting the input into a nonlinear autoregressive exogenous model, the predicted values ​​of reactant outlet concentrations are calculated: ； In the formula, For reactor b The outlet concentration of the reactant at each sampling time For the final model parameter vector, the first... One element, For the first The candidate basis functions at the th... The value at each sampling time, For the regression vector, This represents the total number of candidate model terms.

9. A pilot-scale modeling system for a continuous stirred reactor based on model transfer, characterized in that, The system is used to implement the model transfer-based pilot-scale modeling method for continuous stirred reactors according to any one of claims 1 to 8, the system comprising: The data acquisition and preprocessing module is used to acquire historical process data of the reaction process in the laboratory-scale continuous stirred reactor and the pilot-scale continuous stirred reactor, respectively, and to preprocess the historical process data; wherein, the laboratory-scale continuous stirred reactor is defined as reactor a and the pilot-scale continuous stirred reactor is defined as reactor b, and the historical process data includes the input variable coolant flow rate and the output variable reactant outlet concentration; The general model building module is used to build a general nonlinear identification model of a continuous stirred reactor based on the input and output variables of the reactor. The laboratory model identification module is used to identify the general nonlinear identification model based on the sparse Bayesian learning method using the preprocessed process data of reactor a, and obtain the estimation parameter accuracy matrix characterizing the structural information of the reactor a model. The pilot-scale model independent identification module is used to independently identify the general nonlinear identification model based on the sparse Bayesian learning method using the preprocessed process data of reactor b, and obtain the independent posterior distribution of the reactor b model parameters and the corresponding hyperparameters. The model transfer and prognostic construction module is used to reuse the model structure information of reactor a, introduce the estimated parameter accuracy matrix as a prior constraint into the model identification process of reactor b, and construct the prognostic distribution of the model parameters of reactor b. An observation enhancement module is used to generate enhanced observation output based on the pre-posterior distribution, and to fine-tune and correct the original observation data of reactor b using the enhanced observation output. The fusion modeling module is used to construct a fusion identification model with the independent posterior distribution as the ideal reference model and the enhanced observation output as the fixed constraint. By minimizing the distribution difference between the fusion identification model and the ideal reference model, the fusion posterior distribution of the reactor b model parameters is obtained. The concentration prediction module is used to determine the final model parameters of reactor b based on the fusion posterior distribution, and to predict the reactant outlet concentration of reactor b based on the final model parameters.

10. A computer storage medium, characterized in that, The computer storage medium stores a computer software product, which includes several instructions to cause a computer device to execute the model transfer-based continuous stirred reactor pilot-scale modeling method according to any one of claims 1 to 8.

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