Hybrid modeling method and system for optimizing separation performance of sequential simulated moving bed

Abstract

The invention discloses a hybrid modeling method and system for optimizing the separation performance of a sequential simulated moving bed, and the method achieves the high-precision modeling of the separation process of the sequential simulated moving bed through constructing a transfer diffusion mechanism model which retains mass conservation, and embedding a dual-branch neural network to replace a conventional adsorption kinetic model. Representative data covering main operation states are obtained through low-cost double-column experimental design, joint optimization is carried out on a neural network structure and model parameters in combination with an L-SHADE algorithm and a grid search method, and the model precision and generalization ability are remarkably improved. Compared with the prior art, the method has the advantages that the physical interpretability of a mechanism model and the flexibility of a data-driven model are effectively fused, the dependence on complex adsorption kinetics experiments and large-scale historical data is reduced, and the method is suitable for performance evaluation and industrial optimization of complex separation processes such as xylooligosaccharide purification.

Description

Technical Field

[0001] This invention belongs to the field of chemical process modeling and optimization technology, and in particular relates to a hybrid modeling method and system for sequential simulation of moving bed separation performance optimization. Background Technology

[0002] The Sequential Simulated Moving Bed (SSMB) breaks down the continuous feeding mode of the traditional Simulated Moving Bed (SMB) into three sub-steps: feeding, circulation, and elution by switching the timing sequence. This increases operational flexibility and reduces eluent consumption while ensuring separation efficiency. It is suitable for separation scenarios with complex mixture composition and high eluent costs, such as xylooligosaccharide purification, xylose mother liquor separation, and alcohol mixture separation.

[0003] However, the separation performance of SSMB largely depends on the reasonable setting of process parameters (such as switching time, feed flow rate, elution flow rate, etc.). In the existing technology, parameter adjustment mainly relies on the experience judgment of engineers and a large number of trial and error experiments, which has the problems of low efficiency and high cost. In addition, since SSMB itself has multi-segment switching, periodic operation and significant nonlinear coupling characteristics, the traditional parameter adjustment method lacks systematicity and repeatability, making it difficult to ensure the consistency and optimality of the debugging effect.

[0004] In chromatographic process modeling, mechanistic modeling based on the law of conservation of mass is usually the preferred method. Commonly used mechanistic models include equilibrium diffusion models, transport diffusion models, and universal rate models. These models theoretically possess good interpretability and extrapolation capabilities, but their application presupposes the accurate acquisition of adsorption isotherms and kinetic parameters within the chromatographic system. Furthermore, in laboratory environments, due to low system concentrations and controllable operating conditions, adsorption isotherms can employ explicit assumptions, and relevant kinetic parameters can be obtained through methods such as moment analysis and pulse experiments. However, for large-scale industrial equipment, this prerequisite is often difficult to meet. Given these limitations, data-driven models are considered a viable alternative. These methods do not rely on complex physical derivations but instead directly learn system laws through operational data, establishing a nonlinear mapping between input and output. In existing technologies, deep learning and reinforcement learning have been widely applied to learn the laws governing chromatographic processes. However, the accuracy of deep learning and reinforcement learning models highly depends on a large amount of historical data, which is often difficult to achieve in the early stages of system development. Simultaneously, because the modeling process bypasses key physical mechanisms, the resulting models are usually only applicable to specific systems and lack cross-system generalization capabilities. Summary of the Invention

[0005] Purpose of the invention: This invention provides a hybrid modeling method and system for sequential simulation of moving bed separation performance optimization, aiming to solve the problems of low efficiency and high cost of SSMB parameter adjustment in existing technologies; strong dependence of mechanistic models on adsorption isotherms and kinetic parameters, making it difficult to accurately obtain these parameters on an industrial scale, resulting in difficulty in model establishment or inaccurate prediction, thus limiting their application in actual production; and the fact that most artificial intelligence models rely on a large amount of historical data, which is often difficult to achieve in the early stages of system development.

[0006] Technical solution: This invention provides a hybrid modeling method for sequentially simulating the separation performance optimization of a moving bed, comprising:

[0007] Design multiple sets of dual-column experiments to collect effluent concentration data at different times during chromatographic separation to form a dataset;

[0008] A dual-branch neural network model was constructed, and the two branches of the dual-branch neural network model were used to replace the adsorption kinetic equations of the strongly adsorbed component and the weakly adsorbed component in the mass conservation equation of the traditional mechanism model, respectively, to obtain a hybrid model embedded in the dual-branch neural network.

[0009] In the dataset, the successful history adaptive differential evolution algorithm with linear population size reduction combined with a grid search strategy is used to jointly optimize the structure of the two-branch neural network model and the parameters of the hybrid model, with the goal of minimizing the weighted sum of squares error, to obtain the optimal hybrid model.

[0010] Discretely solve the mass conservation partial differential equation of the optimal mixing model to obtain the outlet concentrations predicted by the optimal mixing model at different times; evaluate the performance of the optimal mixing model based on the predicted outlet concentrations at different times.

[0011] The evaluation indexes for the sequential simulated moving bed are determined, and the optimal hybrid model is used for process optimization to solve for the Pareto optimal solution of the evaluation indexes for the sequential simulated moving bed.

[0012] Furthermore, the hybrid model embedding a dual-branch neural network includes:

[0013] Using a transport-diffusion model as the mechanistic framework, a mass conservation partial differential equation describing the mass transfer process between the mobile phase and the stationary phase within the chromatographic column is established. A two-branch neural network structure is employed, with the outlet concentration as input and the adsorption rates of strongly and weakly adsorbed components as output. Nonlinear mapping relationships between the adsorption rates of strongly and weakly adsorbed components and the outlet concentration are established, respectively. These nonlinear mapping relationships are then used to replace the adsorption kinetic equations of strongly and weakly adsorbed components in the transport-diffusion model, forming a hybrid model embedded in the neural network.

[0014] Furthermore, the discrete solution of the mass conservation equation of the optimal mixing model includes: using the orthogonal finite element method (OCFE) to spatially discretize the partial differential equation of mass conservation of the optimal mixing model, transforming it into a system of differential algebraic equations, and calling the ODE solver to perform time integration to obtain the outlet concentration predicted by the optimal mixing model at different times.

[0015] Furthermore, the collection of outlet concentration data under the feed and elution conditions includes:

[0016] A dual-column experimental system was constructed, consisting of two chromatographic columns connected in series, to simulate the state of the columns in the feeding and elution stages of a sequential moving bed. During the feeding stage, feed solution was continuously injected into the first column at a constant flow rate, and the outlet concentration data of the feeding stage were collected simultaneously until a complete breakthrough curve was obtained at the outlet of the first column. During the elution stage, eluent was injected into the first column at a constant elution flow rate, and the concentration data of the outlet of the second column were collected simultaneously until a complete elution curve was obtained at the outlet of the second column.

[0017] Furthermore, the joint optimization includes:

[0018] The dataset is divided into training and testing sets. The structure of the dual-branch neural network model is enumerated using a grid search strategy. For each candidate structure, the first objective function is to minimize the weighted sum of squares error of the training set exit concentration. The L-SHADE success history adaptive differential evolution algorithm with linear population size reduction is used to iteratively optimize the parameters of the hybrid model. If the number of iterations is reached or the optimization condition is met, the iterative optimization of the candidate structure is stopped, and the optimal parameters of each candidate structure are obtained.

[0019] The second objective function is to minimize the weighted sum of squares error of the export concentration on the dataset. Candidate structures that satisfy the second objective function are selected from the candidate structures with optimal parameters and taken as the optimal candidate structures. The hybrid model that uses the optimal candidate structures and the optimal parameters of the optimal candidate structures is taken as the optimal hybrid model.

[0020] Furthermore, the evaluation of the performance of the optimal mixing model includes: using the coefficient of determination R² and the normalized root mean square error NRMSE as performance evaluation indicators of the optimal mixing model, and evaluating the outlet concentrations obtained by the optimal mixing model at different times on the test set.

[0021] Furthermore, the process of determining the evaluation index of the sequential simulated moving bed and using an optimal hybrid model for process optimization to solve for the Pareto optimal solution of the evaluation index of the sequential simulated moving bed includes:

[0022] Product purity and recovery rate are used as evaluation indicators for sequential simulated moving bed;

[0023] By setting both product purity and recovery rate as objective functions, a multi-objective optimization problem is established.

[0024] The non-dominated sorting genetic algorithm NSGA-II is used to iteratively solve the multi-objective optimization problem. In each iteration, a hybrid model is called to indirectly calculate the product purity and recovery rate until a non-dominated front covering the entire target space is generated.

[0025] From the non-dominated frontier, select the product purity-recovery combination that meets production requirements as the Pareto optimal operating scheme for product purity and recovery.

[0026] This invention also provides a hybrid modeling system for sequential simulation of moving bed separation performance optimization, comprising:

[0027] The data acquisition module is used to design multiple sets of dual-column experiments and collect effluent concentration data at different times during the chromatographic separation process to form a dataset.

[0028] The hybrid model building module is used to construct a dual-branch neural network model. The two branches of the dual-branch neural network model are used to replace the adsorption kinetic equations of the strongly adsorbed component and the weakly adsorbed component in the mass conservation equation of the traditional mechanism model, respectively, to obtain a hybrid model embedded with the dual-branch neural network.

[0029] The parameter structure tuning module is used to jointly optimize the structure of the dual-branch neural network model and the parameters of the hybrid model in the dataset by combining the success history adaptive differential evolution algorithm with linear population size reduction and grid search strategy, with the goal of minimizing the weighted sum of squares error, to obtain the optimal hybrid model.

[0030] The evaluation module is used to discretize and solve the mass conservation partial differential equation of the optimal mixing model to obtain the outlet concentrations predicted by the optimal mixing model at different times; based on the predicted outlet concentrations at different times, the performance of the optimal mixing model is evaluated.

[0031] The process optimization module is used to determine the evaluation index of the sequential simulated moving bed and to optimize the process using the optimal hybrid model to find the Pareto optimal solution of the evaluation index of the sequential simulated moving bed.

[0032] The present invention also provides a computer device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the steps of the above-described method.

[0033] The present invention also provides a computer-readable storage medium having a computer program stored thereon, wherein the computer program, when executed by a processor, implements the steps of the above-described method.

[0034] Beneficial effects: This invention provides a hybrid modeling method and system for sequential simulation of moving bed separation performance optimization. Compared with the prior art, this invention avoids the high dependence on adsorption isotherms and kinetic parameters in traditional mechanistic models by directly utilizing easily obtainable column outlet concentration information and simplifying the modeling process by using neural networks to replace adsorption kinetic models. On the other hand, to address the dependence of data-driven models on a large amount of historical data, this invention proposes to generate training data through a small number of carefully designed dual-column experiments to ensure that the data covers the main operating states of the system. Attached Figure Description

[0035] Figure 1 This is a schematic diagram illustrating the operation of the sequential simulated moving bed of the present invention.

[0036] Figure 2 This is a schematic diagram of the operation of the dual-column experiment of the present invention.

[0037] Figure 3 This describes the solution process for the hybrid model of this invention.

[0038] Figure 4 This describes the training process for the hybrid model of the present invention.

[0039] Figure 5 This is the result of the screening of the network structure of this invention.

[0040] Figure 6 This is the concentration fitting curve of the hybrid model in the training set during the experiment of this invention.

[0041] Figure 7 This is the concentration prediction curve of the hybrid model in the interpolation test in the experiment of this invention.

[0042] Figure 8 This is the concentration prediction curve of the hybrid model in the extrapolation test of the present invention.

[0043] Figure 9 This is the Pareto front for the multi-objective optimization of the SSMB process in the experiments of this invention.

[0044] Figure 10 This is the prediction result of the model at the SSMB product collection location in the experiment of this invention. Detailed Implementation

[0045] The hybrid modeling method for sequential simulation of moving bed separation performance optimization described in this invention includes:

[0046] Design multiple sets of dual-column experiments to collect effluent concentration data at different times during chromatographic separation to form a dataset;

[0047] A dual-branch neural network model was constructed, and the two branches of the dual-branch neural network model were used to replace the adsorption kinetic equations of the strongly adsorbed component and the weakly adsorbed component in the mass conservation equation of the traditional mechanism model, respectively, to obtain a hybrid model embedded in the dual-branch neural network.

[0048] In the dataset, the successful history adaptive differential evolution algorithm with linear population size reduction combined with a grid search strategy is used to jointly optimize the structure of the two-branch neural network model and the parameters of the hybrid model, with the goal of minimizing the weighted sum of squares error, to obtain the optimal hybrid model.

[0049] The mass conservation equation of the optimal mixing model is solved discretely to obtain the outlet concentration at different times; based on the obtained outlet concentrations at different times, the performance of the optimal mixing model is evaluated.

[0050] The evaluation indexes for the sequential simulated moving bed are determined, and the optimal hybrid model is used for process optimization to solve for the Pareto optimal solution of the evaluation indexes for the sequential simulated moving bed.

[0051] In this embodiment,

[0052] The operation diagram of the sequential simulated moving bed SSMB is as follows: Figure 1 As shown, one operating cycle of SSMB consists of three sub-steps: feeding, circulation, and elution, involving a total of seven operating parameters, including the time variables (t1, t2, t3) of the three sub-steps and the flow rate variables (t4, t5, t6). , , and The relationship between columns at different stages within a cycle is determined by the column connection conditions.

[0053] Feeding stage:

[0054] , (1);

[0055] , (2);

[0056] Cycle phase:

[0057] (3);

[0058] , , , (4);

[0059] Washout phase:

[0060] (5);

[0061] , , (6);

[0062] In the formula, This refers to the eluent flow rate during the feeding stage; The feed liquid flow rate during the feeding stage The feed concentration of component i; This refers to the circulating flow rate during the cyclic phase. The eluent flow rate during the elution phase; This represents the flow rate in region j. This represents the inlet concentration of component i in region j. This represents the inlet concentration of component i in region j.

[0063] To construct the data needed for training and validating the hybrid model, this invention designs a two-column experiment, the operation of which is illustrated below. Figure 2 As shown. The dual-column experiment consists of two chromatographic columns identical to those in the SSMB, connected in series. The experimental process includes two stages: feed and elution. In the feed stage, feed solution is continuously injected into the first column (column I) at a constant flow rate, and the effluent concentration data of the feed stage are collected simultaneously until a complete breakthrough curve is obtained at the effluent of the first column. In the elution stage, eluent is injected into the first column at a constant elution flow rate, and the effluent concentration data of the second column (column II) are collected simultaneously until a complete elution curve is obtained at the effluent of the second column. Multiple sets of dual-column experimental data were collected, with some sets used as the training set and the remainder as the test set. There are four variables that need to be controlled in the dual-column experiment: feed time (… ), feed flow rate ( ), washout time ( ) and elution flow rate ( ).

[0064] Dual-column experiments can simulate the typical conditions of each column during SSMB cycle operation, especially the combination of column inlet concentration and column flow rate. The specific correspondences are as follows:

[0065] (1) Column I in the feeding stage: Column I in the feeding zone 3 of SSMB, with the inlet being the feed liquid concentration and the flow rate being the feed flow rate;

[0066] (2) Column II in the feed stage: It corresponds to the chromatographic column other than column I in the feed zone. The inlet concentration is the outlet concentration of the previous column, and the flow rate is the same as the feed flow rate.

[0067] (3) Column I in the elution stage: Column I in the feed or elution zone of SSMB, with zero inlet concentration and elution flow rate;

[0068] (4) Column II in the elution stage: corresponds to other chromatographic columns in the SSMB operation cycle. The inlet is the outlet concentration of the previous column, and the flow rate is the elution flow rate or the circulation flow rate.

[0069] Therefore, by setting the experimental parameters appropriately, the dual-column experiment can cover various states of the chromatographic column during SSMB operation, thus providing representative data for model training.

[0070] In contrast, directly collecting data through complete SSMB cycle experiments presents challenges such as blind selection of process parameters, long experimental cycles, and high costs. While single-column experiments offer advantages in terms of short cycles and low cost, they cover limited operating conditions in each experiment, failing to reflect the diverse states of each column during cycle operation and resulting in insufficient data representativeness. Dual-column experiments provide an effective compromise between these two approaches: reducing experimental costs while improving data coverage and representativeness, thus providing reliable support for the training and validation of hybrid models.

[0071] Mechanistic models characterize the mass transfer and kinetics of the chromatographic process. Among common chromatographic kinetic models, the transport-diffusion model is widely used because it better suits the characteristics of SSMB. Compared with the equilibrium diffusion model, the transport-diffusion model introduces a finite-rate adsorption term, which can more accurately reflect the adsorption kinetics process; at the same time, compared with the general rate model, it has higher modeling simplicity while maintaining a reasonable physical explanation.

[0072] For a two-component separation process, the partial differential equations for mass conservation and adsorption kinetics in the transport-diffusion model (TDM) are as follows:

[0073] (7)

[0074] (8)

[0075] In the formula, c and q represent the concentrations of the components in the mobile phase and stationary phase, respectively; the subscript i indicates different components (i = A or B, where A is a strongly adsorbed component and B is a weakly adsorbed component); It is a comparison; The column porosity; The velocity of the interstitial flow phase; The axial diffusion coefficient is denoted as . The theoretical number of plates; is the mass transfer coefficient of component i; Q is the volumetric flow rate; L is the column length; r is the column radius; z and t represent the spatial and temporal coordinates, respectively.

[0076] At high concentrations, different components will interact due to competition for adsorption sites. To characterize this property, the competitive Langmuir adsorption isotherm model can be used as the adsorption kinetic model for the transport-diffusion model, and its mathematical form is as follows:

[0077] (9)

[0078] In the formula, Let i be the Henry's constant for component i. Let i be the adsorption constant of component i. In the competitive Langmuir adsorption isotherm model, the equilibrium adsorption amount of component i on the solid phase is the amount of component that the solid phase can ultimately adsorb at a given temperature and liquid phase concentration (or gas phase pressure).

[0079] Chromatographic column separation processes typically begin with an empty column, with the following initial conditions:

[0080] t = 0, = = 0 (10)

[0081] The Danckwerts boundary conditions at the inlet and outlet of the chromatographic column are as follows:

[0082] , (11)

[0083] , (12)

[0084] in, This represents the concentration of component i at the column inlet.

[0085] To effectively integrate physical knowledge with data-driven approaches and address the shortcomings of traditional modeling methods in complex chromatographic systems, such as insufficient accuracy, difficulty in obtaining parameters, and poor generalization ability, this invention constructs a hybrid model embedded with a neural network. Using a transport-diffusion model as the mechanistic framework, it establishes a mass conservation partial differential equation describing the mass transfer process between the mobile and stationary phases within the chromatographic column. A two-branch neural network structure is constructed, taking the mobile phase concentration and stationary phase concentration as inputs and outputting the adsorption rates of strongly and weakly adsorbed components. Nonlinear mapping relationships are established between the adsorption rate of the strongly adsorbed component and the concentrations of the mobile and stationary phases, respectively, and between the adsorption rate of the weakly adsorbed component and the concentrations of the mobile and stationary phases. These nonlinear mapping relationships replace the adsorption kinetic equations of the strongly and weakly adsorbed components in the transport-diffusion model, forming a hybrid model embedded with a neural network.

[0086] Specifically, this invention retains the mass conservation equation (7) in the transfer-diffusion model to maintain the physical basis of the model; at the same time, it replaces the adsorption kinetic equation (8) in the traditional mechanistic model with a two-branch neural network, in the following form:

[0087] (13)

[0088] in, Let x be the concentration of component A in the mobile phase at axial position x and time t. Let x be the concentration of component B in the mobile phase at position x and time t. Let be the solid phase concentration of component i at position x and time t. The adsorption kinetics at each time point are considered to be determined by the liquid phase concentration. and solid concentration A nonlinear mapping to the adsorption rate is established, and a neural network branch is constructed for each component (i=A or B). Let's learn this mapping (the network parameters of the two components are denoted as θ). A , θ B Therefore, the partial differential equation for mass conservation in the chromatographic separation process can be rewritten as:

[0089] (14)

[0090] The above equations constitute a hybrid model with a mechanistic model as the backbone and a neural network replacing the adsorption kinetics terms. In this model, the neural network is directly embedded into the right-hand side of the differential equation of the mechanistic model using a forward computation method, allowing it to replace the adsorption kinetics terms in real time at each integration step.

[0091] Because the bibranch neural network model uses intermediate states (mobile phase concentration and stationary phase concentration) generated by the ODE solver during the hybrid model solution process as input, this input varies with time and location and cannot be predetermined. Furthermore, since the bibranch neural network is embedded within the partial differential equations, its parameters cannot be updated through traditional backpropagation.

[0092] Therefore, training the parameters of a hybrid model can be viewed as a single-objective, multi-parameter optimization problem. The parameters to be optimized include the parameter sets of the two neural networks (θ). A , θ B ) and two column model parameters (ε, N) L ), where ε is the porosity, and N L The theoretical plate number is used to optimize the concentration prediction at the effluent by minimizing the weighted sum of squares error between the mixture model and the training set. This optimization problem can be expressed as:

[0093] , (15)

[0094] The weighted sum of squares error on the training set is defined as follows:

[0095] (16)

[0096] In the formula, K train n is the number of experimental groups in the training set. k ω represents the number of data points in the k-th experiment; k For the corresponding weights; λ A , λ B These are the error weights for component A and component B, respectively. , These are the experimental values ​​of the outlet concentrations of component A and component B at the i-th data point in the k-th experiment, respectively. , These are the corresponding mixed model predictions.

[0097] To solve the optimization problem defined in equation (15), the successful history-based adaptive differential evolution with linear population size reduction (L-SHADE) algorithm is used for parameter optimization. L-SHADE is an advanced variant of differential evolution (DE). By introducing an adaptive parameter update mechanism based on the success history and a linear population size reduction strategy, it achieves stronger global search capabilities and higher optimization efficiency, making it an effective tool for solving high-dimensional continuous optimization problems.

[0098] In this study, to balance convergence and optimization efficiency, the iteration stopping condition of L-SHADE considers both the maximum number of iterations G. max The relative change of the objective function RI(g). Specifically, when the relative change of the optimal objective value over several consecutive generations is less than a preset threshold ϵ rel If the objective function shows no significant improvement, the algorithm terminates early; otherwise, it terminates after reaching the maximum number of iterations. On the other hand, since L-SHADE is a stochastic optimization algorithm, to verify the stability of the results, it is run independently multiple times under the same conditions, and the solution that performs best across multiple experiments is taken as the final optimization result. The relative change is defined as follows:

[0099] (17)

[0100] In the formula, Let Δg be the optimal objective function value for the g-th generation, and Δg be the width of the calculation window for the improvement amount.

[0101] For dual-branch neural networks, it is necessary to further determine their optimal structure, including the number of hidden layers, the number of neurons in each layer, and the type of activation function. This invention employs a grid search method to screen structures within a preset range: first, L-SHADE is used to optimize the parameters of each candidate structure, and then the prediction accuracy of the models under different structures is compared. The overall training process of the hybrid model is as follows: Figure 4 As shown. It should be noted that since the training and test sets obtained from different bi-column experiments do not satisfy the independent and identically distributed assumption, the weighted sum of squared errors of all experiments is used as a unified evaluation metric when comparing the performance of different structural models. Its definition is as follows:

[0102] (18)

[0103] In the formula, K totalThe number of all experimental groups, including the training and test sets, is given; the meanings of the other symbols are the same as in equation (16).

[0104] After determining the optimal network structure and model parameters, the optimal hybrid model was obtained. Further evaluation of the performance of the optimal hybrid model in the two-column experiment and in predicting the SSMB product outlet concentration is needed. Specifically, the coefficient of determination (R²) was selected. 2 The normalized root mean square error (NRMSE) and the normalized root mean square error (NRMSE) are used as performance evaluation metrics for the optimal mixture model, and their definitions in the k-th group of experiments are as follows:

[0105] (19)

[0106] (20)

[0107] In the formula, n k This represents the number of outlet concentration values ​​collected in the k-th experiment; This represents the experimental value of the i-th outlet concentration in the k-th experiment group; This represents the average outlet concentration of the k-th experimental group. This is the mixed model prediction value for the i-th outlet concentration in the k-th experiment.

[0108] The mathematical model of the chromatographic separation process is represented by equations from a mixed model. These equations are partial differential equations and require numerical methods to solve. The overall solution process is as follows: Figure 3 As shown, by first discretizing the partial differential equation along the chromatographic column axis in the spatial domain, transforming it into a set of differential algebraic equations, and then integrating the component concentration over time in the time domain, the liquid and solid phase concentrations of each component at different times are obtained.

[0109] This invention employs orthogonal collocation on finite elements (OCFE) to discretize the spatial term: the chromatographic column is divided into I finite elements, and N orthogonal collocation points are arranged within each finite element, so that the entire axial space is discretized into I(N+1)+1 nodes. According to OCFE, the discretized form of equation (7) at the nth collocation point within the i-th finite element can be expressed as:

[0110] (twenty one)

[0111] in, Let be the concentration of the component in the mobile phase at the nth configuration point within the i-th finite element. Let be the concentration of the component in the mobile phase at the j-th configuration point within the i-th finite element. Let h be the concentration of the component in the stationary phase at the nth placement point within the i-th finite element, h be the length of a single finite element, and A(n,j) and B(n,j) represent the coefficient matrices calculated by the orthogonal placement method at the j-th node at the n-th placement point.

[0112] Discretizing equations (11) and (12) yields the corresponding discrete forms of the boundary conditions:

[0113] (twenty two)

[0114] (twenty three)

[0115] In the formula, i=1,2,…,I, n=2,3,…,N; denoted as , where is the concentration at the column inlet; A(1,j) is the coefficient matrix generated by the orthogonal configuration method at the j-th node of the first configuration point, and A(N+2,j) is the coefficient matrix generated by the orthogonal configuration method at the j-th node of the (N+2)-th configuration point.

[0116] This invention uses OCFE to discretize the partial differential equations of the optimal mixing model, selecting 5 finite element methods, each with 4 orthogonal collocation points, for a total of 20 discretization points. Since it is necessary to simultaneously solve for the liquid and solid phase concentrations of both strongly and weakly adsorbed components, this invention ultimately yields 104 differential-algebraic equations, forming a system of differential-algebraic equations. The system of differential-algebraic equations is then integrated over time using the ODE solver (ode15s) in MATLAB R2023a to obtain the outlet concentrations of each component at different times.

[0117] Based on the outlet concentrations of each component at different times, the coefficient of determination (R²) was calculated. 2 The performance of the optimal mixture model is evaluated using the normalized root mean square error (NRMSE) and the normalized root mean square error (NRMSE).

[0118] To simplify the process variables that need to be optimized during SSMB process optimization, it is assumed that the flow rate in zone I remains constant at each stage, and the value is the maximum allowable flow rate of the column limited by column pressure. , that is to say = = = and will As a scaling factor, the remaining process variables (operating parameters) to be optimized can be simplified to four: t1, t2 and t3.

[0119] Based on the remaining process variables to be optimized, the purity and recovery rate of the target product were selected as performance indicators for SSMB. On the one hand, the definitions of these two indicators directly depend on the product effluent concentration and can be used to evaluate the model's predictive accuracy for column effluent behavior; on the other hand, they have clear engineering significance and decision-making value, and are the key indicators most frequently focused on and optimized in separation processes.

[0120] According to the separation principle of SSMB, the weakly adsorbed component B is mainly collected through the raffinate from the feed and elution stages. Therefore, the definitions of purity and recovery rate are as follows:

[0121] (twenty four);

[0122] (25);

[0123] In the formula, Let i be the concentration of component i in the raffinate; To increase the collection flow rate of the residual liquid, corresponding to the feed and elution stages respectively. and , This is the switching cycle.

[0124] Product purity and recovery rate are simultaneously set as objective functions, and the range of values ​​for operational variables such as switching time and feed flow rate are constrained to establish a multi-objective optimization problem. The non-dominated sorting genetic algorithm NSGA-II is used to iteratively solve the multi-objective optimization problem. In each iteration, the hybrid model is called to calculate product purity and recovery rate until a non-dominated frontier covering the entire objective space is generated. From the non-dominated frontier, the product purity-recovery rate combination that meets the production requirements is selected as the Pareto optimal operation scheme for purity and recovery rate.

[0125] The hybrid modeling system for sequential simulation of moving bed separation performance optimization described in this invention includes:

[0126] The data acquisition module is used to design multiple sets of dual-column experiments and collect effluent concentration data at different times during the chromatographic separation process to form a dataset.

[0127] The hybrid model building module is used to construct a dual-branch neural network model. The two branches of the dual-branch neural network model are used to replace the adsorption kinetic equations of the strongly adsorbed component and the weakly adsorbed component in the mass conservation equation of the traditional mechanism model, respectively, to obtain a hybrid model embedded with the dual-branch neural network.

[0128] The parameter structure tuning module is used to jointly optimize the structure of the dual-branch neural network model and the parameters of the hybrid model in the dataset by combining the success history adaptive differential evolution algorithm with linear population size reduction and grid search strategy, with the goal of minimizing the weighted sum of squares error, to obtain the optimal hybrid model.

[0129] The evaluation module is used to discretize and solve the mass conservation partial differential equation of the optimal mixing model to obtain the outlet concentrations predicted by the optimal mixing model at different times; based on the predicted outlet concentrations at different times, the performance of the optimal mixing model is evaluated.

[0130] The process optimization module is used to determine the evaluation index of the sequential simulated moving bed and to optimize the process using the optimal hybrid model to find the Pareto optimal solution of the evaluation index of the sequential simulated moving bed.

[0131] The computer device of the present invention includes a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the steps of the above method.

[0132] The computer-readable storage medium of the present invention stores a computer program thereon, which, when executed by a processor, implements the steps of the above-described method.

[0133] Regarding the above technical solution in this embodiment, the following is a detailed explanation. Figures 5 to 10 This will detail the experimental process of applying the technical solution to a specific xylooligosaccharide purification process and the technical effects of the solution.

[0134] This invention focuses on the purification process of xylo-oligosaccharides (XOS) to verify the effectiveness of the proposed hybrid model in SSMB process simulation and optimization. The target product (XOS) is used as a weakly adsorbed component, while impurities (xylose and arabinose) are used as strong adsorbed components. Typical estimation methods were employed to set the corresponding SSMB system parameters, and the results are shown in Table 1.

[0135] Table 1 System parameters of SSMB

[0136]

[0137] In the SSMB system, the flow rate within the column is constrained by pressure drop and system safety, and its operating range is strictly limited to 0~Q. maxThis invention divides the process design of the two-column experiment into two categories: a training set and a test set. The training set is used to learn the parameters of the hybrid model, and the test set is used to evaluate the model's generalization ability under unseen operating conditions. The test set is further divided into interpolation tests and extrapolation tests, used to evaluate the model's generalization ability within the training flow range (operating conditions not encountered within the operating domain) and outside the training range (operating conditions at the boundary of the operating domain), respectively. By jointly validating these two types of cases, the applicability and robustness of the model throughout the entire operating domain can be comprehensively verified.

[0138] In the dual-column experiment, each experiment started from an empty column, and the outlet concentration data of column I and column II were collected at a frequency of 1 minute per cycle. The feed flow rate of the dual-column experiment was... Expected working range (0~ The selection is within the range, while the elution flow rate is fixed. This invention sets up a total of 6 sets of experiments to generate training set data, and additionally sets up 5 sets of interpolation tests and 4 sets of extrapolation tests to evaluate the generalization performance of the model within the operating domain and outside the boundary, respectively. The experimental parameters for each set are shown in Table 2.

[0139] Table 2. Process conditions for the two-column experiment

[0140]

[0141] To facilitate a unified evaluation of the performance of the hybrid model under different experimental conditions, WSSE is used during the training of the hybrid model. train and WSSE total The sum of squared errors and weighting parameters for each group of experiments ( Set the error weights to the same value (e.g., 1). Meanwhile, to ensure the prediction accuracy of target component B, set the error weights to λ. A : λ B = 1 : 2. Furthermore, a consistent topology is used for the two-branch neural network to simplify the structure selection process. The main parameter settings of the L-SHADE algorithm are shown in Table 3.

[0142] Table 3. Results of the main parameters of the L-SHADE algorithm

[0143]

[0144] Since the neural network is only used to replace the adsorption kinetics module in the model, the computational structure of this part is relatively independent and has low complexity. Therefore, a simpler network topology is sufficient to meet the fitting requirements. Furthermore, the training method of the neural network in this study differs from the traditional backpropagation-based training process. To improve computational efficiency, the forward computation of the network is explicitly expressed as a directly callable mathematical expression, and each round of optimization is executed in parallel on multiple computers. To determine the most suitable network structure for the hybrid model, a grid search method is used to screen network structures. The search range and screening results are shown in Table 4.

[0145] Table 4. Selection Results of Neural Network Structures

[0146]

[0147] In this invention, the network structures shown in Table 4 can all be optimized within the maximum number of iterations, and their execution time is affected by the size of the training set and the network complexity. On the Intel i7-13700 platform and in the MATLAB R2023a environment, the time taken for a single optimization varies with increasing network complexity, ranging from 3.6 to 6.2 hours. Based on the structure selection results, the optimal neural network structure is a single hidden layer, 3 neurons, and a tanh activation function (e.g., ...). Figure 5 (As shown). This structure can ensure the ability to express the complex dynamic characteristics of the system while avoiding overfitting, thereby improving the model's generalization performance on the test set.

[0148] To evaluate the fitting ability and predictive performance of the constructed hybrid model, it is necessary to validate it in real-world scenarios using a two-column experimental training and test set. The quantitative metrics for model validation are shown in Table 5.

[0149] Table 5. Fitting and prediction accuracy of the model on the training and test sets in the two-column experiment.

[0150]

[0151] The training set contains six sets of dual-column experimental data under different feed flow rates, covering the main operating range of the SSMB process. The concentration fitting curve for one set of experiments (Experiment 4) is shown below. Figure 6As shown in the figure. The results indicate that the model can stably reproduce the concentration dynamics of column I and column II during the training phase, accurately capturing key features such as the leading edge, steepness, and plateau segment of the elution curve. A small number of errors are mainly concentrated in the concentration transition region, manifested as underestimation in the low-concentration stage and overestimation in the high-concentration stage. Due to the larger error weight applied to component B in the objective function, component B performs better than component A in concentration fitting, although the fitting accuracy of component A is still acceptable. According to the quantitative indicators, the R² of all training experiments exceeds 0.994, and the NRMSE is controlled within 3.1%. Particularly for component B, the lowest R² is 0.9992, and the highest NRMSE is only 1.05%, showing high fitting accuracy.

[0152] The interpolation test included 5 intermediate flow rate experiments that were within the training interval but had not yet occurred. The concentration prediction curve for one of these experiments (Experiment 8) is shown below. Figure 7 As shown, despite the input flow being a new value unseen by the model, its prediction curve still closely matches the reference result, accurately reproducing key dynamic features. Similarly, component B shows better prediction performance than component A. In terms of quantification metrics, the accuracy of the interpolation test is slightly lower than that of the training set, but the R² of all experiments is higher than 0.993, and the NRMSE does not exceed 3.2%, indicating that the model has good generalization ability within the operational domain.

[0153] Extrapolation testing includes four sets of extreme flow experiments located at the upper and lower bounds of the operating domain. Figure 8 One set of lower bound experiments (Experiment 13) and upper bound experiments (Experiment 14) are presented. From the prediction curves, the extrapolation test also shows a tendency to underestimate at low concentrations and overestimate at high concentrations in the concentration transition region, but the error is more pronounced than that of the interpolation test. Quantization results also show a decrease in prediction accuracy, with the lowest R² at 0.9922 and the highest NRMSE at 3.72%. Nevertheless, the mixture model can still capture the overall trend of concentration changes well, and the prediction results in the stable concentration phase almost coincide with the mechanistic model, indicating that it still has good generalization performance at the operational domain boundary.

[0154] In the purification of xylooligosaccharides (XOS), the purity and recovery rate of XOS (weakly adsorbed component B) are the core indicators for evaluating the separation performance of SSMB. To evaluate the effectiveness of the hybrid model in SSMB modeling and process optimization, this invention builds an SSMB system based on the trained hybrid model and uses NSGA-II to solve the multi-objective function defined in equation (26). The decision variables in this problem are the process parameters t1, t2, t3 and Q. F The optimization objectives are the performance metrics Pur(B) and Rec(B). The main parameters of NSGA-II are set as follows: population size n. pop =30, crossover probability p c =0.7, mutation probability pm =0.2, the variability μ=0.02 and the variable length σ=0.2.

[0155] (26)

[0156] To verify the convergence and stability of the hybrid model for multi-objective optimization, the maximum number of iterations was first set to 100, and the Pareto front was recorded every 5 generations. When the number of Pareto fronts recorded in two consecutive iterations stabilized at the population size, the average Euclidean distance between them was calculated and used as the convergence metric d. avg Its mathematical expression is as follows:

[0157] (27)

[0158] In the formula, N is the number of Pareto front solutions; M is the number of objective functions; f k (x) represents the k-th objective value; This is the i-th non-dominated solution in the t-th generation.

[0159] Optimization results show that when the number of iterations exceeds 55, d avg The Pareto front decreased to below 0.01 and remained relatively stable, while exhibiting a uniform distribution in the target space, indicating that the algorithm had reached approximate convergence at this number of iterations. Subsequently, the maximum number of iterations was fixed at 55, and five independent optimization experiments were repeated to evaluate the algorithm's stability. In these five experiments, a reference point was set at (0.8, 0.8), and the hypervolume (HV) of the Pareto solution set was calculated for each. Statistical results show that the mean HV value obtained from the five repeated experiments was 0.026, the variance was 3.6 × 10⁻⁶, and the corresponding standard deviation was 0.0019. The corresponding coefficient of variation (CV) was 7.3%, which is within the acceptable range for engineering optimization problems, demonstrating the good stability of the optimization results.

[0160] To more intuitively demonstrate the algorithm's search performance in the target space, Figure 9 The Pareto front obtained from one of the optimizations is shown, revealing that the optimal solution forms a continuous and uniformly distributed non-dominated front in the target space, illustrating the typical trade-off between purity and recovery under different operating conditions. The overall trend shows that purity decreases as recovery increases, indicating a clear mutual constraint between the two, consistent with empirical conclusions from actual industrial processes.

[0161] To evaluate the generalization ability of the hybrid model under different process conditions, from Figure 9Four sets of process parameters (a, b, c, and d) were uniformly selected within the Pareto front for validation. The concentration trajectories of the mixing model and the mechanistic model at the outlet of the three zones were compared. This location was chosen as the evaluation target because the target product is mainly collected here, and the accuracy of its concentration prediction directly affects the reliability of the calculated process performance indicators. The four sets of process parameters and their quantitative evaluation indicators are shown in Table 6, and the prediction curves are shown in... Figure 10 As shown, the purple shaded area corresponds to the product collection stage within a single cycle.

[0162] Table 6. Prediction accuracy of the model at the collection location of SSMB products.

[0163]

[0164] Overall, the hybrid model maintained high consistency in predicting target component B, especially in the high-concentration region, where it closely matched the mechanistic model. However, for component A, a more significant deviation emerged during the concentration transition phase. The main reason for this is that during the training phase of the two-column experiment, component A was assigned a lower error weight, resulting in relatively weaker prediction accuracy compared to component B. While still within an acceptable range, a certain difference in accuracy was evident. When this model was further applied to SSMB simulations, the dynamic transition process of approximately 15 cycles before reaching a periodic steady state, coupled with the neural network's need to participate in the solution through rolling predictions within the mechanistic framework, caused single-cycle prediction errors to accumulate over multiple iterations. Although these errors gradually converged under the constraints of the mechanistic solution framework after the concentration stabilized, they were significantly amplified during the transition phase of drastic concentration changes. The above analysis indicates that adjusting the error weights during the training phase can prioritize improving the prediction accuracy of key components; however, it is also necessary to pay attention to the error amplification effect of non-key components during the dynamic simulation process, in order to achieve a balance between the accuracy of key components and the overall system stability in the error weight design.

[0165] From a quantitative perspective, although the four sets of process parameters are distributed in different regions of the Pareto front, their predicted outlet concentrations show good consistency. The R² of component B is consistently higher than 0.994, and the NRMSE does not exceed 2.32%, indicating that the hybrid model has good generalization ability for the SSMB process under different operating conditions. Regarding time cost: in an Intel i7-13700 environment and MATLAB R2023a, the mechanistic model takes an average of approximately 37 seconds per simulation of SSMB, while the hybrid model, by replacing adsorption kinetic calculations with neural network inference, increases the simulation time to approximately 60 seconds per simulation. Although the computation time is increased, this is acceptable in offline full-process simulations. Furthermore, the hybrid model avoids theoretical derivation and parameter measurement experiments of the adsorption kinetic process, significantly reducing the workload of modeling and parameter acquisition, and still has significant advantages in engineering practice.

[0166] It is worth noting that under the optimized process conditions, product collection mainly occurs during the concentration stabilization phase, at which point the mixing model demonstrates high prediction accuracy for both components. Based on the mixing model's prediction of the outlet concentration during the product collection phase, the system performance indicators were further calculated under four sets of process parameters (a, b, c, and d), and compared with the results of the mechanistic model, as shown in Table 7. The results show that the calculated values ​​of the mixing model and the mechanistic model exhibit good consistency under different operating conditions, with a maximum relative error not exceeding 2%, and prediction errors for most process parameters below 1.5%. This indicates that despite differences in local concentration details, the mixing model can still accurately estimate purity and recovery rate in the overall prediction of the critical product collection zone, demonstrating high reliability in process performance prediction.

[0167] Table 7. Predictions of performance indicators by the hybrid model

[0168]

[0169] This invention proposes a hybrid modeling and optimization strategy for sequential simulated moving bed processes. Its core objective is to construct a model that combines predictive accuracy with engineering practicality, achieving accurate simulation and optimization of the process while avoiding complex adsorption kinetics modeling and parameter experimental determination. Training data is obtained through dual-column experiments, reducing data acquisition costs while ensuring representativeness and providing reliable support for model training. During model validation, the hybrid model exhibits high accuracy on both the training and test sets of the dual-column experiments, with R² not less than 0.9922 and NRMSE not exceeding 3.72%, demonstrating good fitting and generalization capabilities. In the optimization of the sequential simulated moving bed process, the multi-objective optimization results based on the hybrid model show a continuous and uniformly distributed Pareto front, clearly revealing the trade-off between product purity and recovery rate. Under different process conditions, the hybrid model can accurately predict the outlet concentration of key column segments; especially in the product collection stage, the prediction error is smaller, reliably characterizing process performance indicators. Compared with the mechanistic model, the relative error in performance indicator calculation is less than 2%, indicating that the hybrid model has high reliability and application potential in process optimization. In summary, the hybrid modeling strategy proposed in this invention significantly reduces modeling complexity and parameter acquisition costs while maintaining the ability to accurately predict and optimize the dynamic characteristics and performance indicators of sequential simulated moving bed processes. This provides a feasible and promising technical path for intelligent modeling and efficient process design of such complex chromatographic systems.

Claims

1. A hybrid modeling method for sequential simulation of moving bed separation performance optimization, characterized in that, include: Design multiple sets of dual-column experiments to collect effluent concentration data at different times during chromatographic separation to form a dataset; A dual-branch neural network model was constructed, and the two branches of the dual-branch neural network model were used to replace the adsorption kinetic equations of the strongly adsorbed component and the weakly adsorbed component in the mass conservation equation of the traditional mechanism model, respectively, to obtain a hybrid model embedded in the dual-branch neural network. In the dataset, the successful history adaptive differential evolution algorithm with linear population size reduction combined with a grid search strategy is used to jointly optimize the structure of the two-branch neural network model and the parameters of the hybrid model, with the goal of minimizing the weighted sum of squares error, to obtain the optimal hybrid model. Discretely solve the mass conservation partial differential equation of the optimal mixing model to obtain the outlet concentrations predicted by the optimal mixing model at different times; evaluate the performance of the optimal mixing model based on the predicted outlet concentrations at different times. The evaluation indexes for the sequential simulated moving bed are determined, and the optimal hybrid model is used for process optimization to solve for the Pareto optimal solution of the evaluation indexes for the sequential simulated moving bed.

2. The hybrid modeling method for sequential simulation of moving bed separation performance optimization according to claim 1, characterized in that, The hybrid model embedding a dual-branch neural network includes: Using a transport-diffusion model as the mechanistic framework, a mass conservation partial differential equation describing the mass transfer process between the mobile phase and the stationary phase within the chromatographic column is established. A two-branch neural network structure is employed, with the outlet concentration as input and the adsorption rates of strongly and weakly adsorbed components as output. Nonlinear mapping relationships between the adsorption rates of strongly and weakly adsorbed components and the outlet concentration are established, respectively. These nonlinear mapping relationships are then used to replace the adsorption kinetic equations of strongly and weakly adsorbed components in the transport-diffusion model, forming a hybrid model embedded in the neural network.

3. The hybrid modeling method for sequential simulation of moving bed separation performance optimization according to claim 2, characterized in that, The discrete solution of the mass conservation equation of the optimal mixing model includes: using the orthogonal collocation finite element method (OCFE) to spatially discretize the partial differential equation of mass conservation of the optimal mixing model, transforming it into a system of differential algebraic equations, and calling the ODE solver to perform time integration to obtain the outlet concentration predicted by the optimal mixing model at different times.

4. The hybrid modeling method for sequential simulation of moving bed separation performance optimization according to claim 1, characterized in that, The collected outlet concentration data under the feed and elution conditions include: A dual-column experimental system was constructed, consisting of two chromatographic columns connected in series, to simulate the state of the columns in the feeding and elution stages of a sequential moving bed. During the feeding stage, feed solution was continuously injected into the first column at a constant flow rate, and the outlet concentration data of the feeding stage were collected simultaneously until a complete breakthrough curve was obtained at the outlet of the first column. During the elution stage, eluent was injected into the first column at a constant elution flow rate, and the concentration data of the outlet of the second column were collected simultaneously until a complete elution curve was obtained at the outlet of the second column.

5. The hybrid modeling method for sequential simulation of moving bed separation performance optimization according to claim 1, characterized in that, The joint optimization includes: The dataset is divided into training and testing sets. The structure of the dual-branch neural network model is enumerated using a grid search strategy. For each candidate structure, the first objective function is to minimize the weighted sum of squares error of the training set exit concentration. The L-SHADE success history adaptive differential evolution algorithm with linear population size reduction is used to iteratively optimize the parameters of the hybrid model. If the number of iterations is reached or the optimization condition is met, the iterative optimization of the candidate structure is stopped, and the optimal parameters of each candidate structure are obtained. The second objective function is to minimize the weighted sum of squares error of the export concentration on the dataset. Candidate structures that satisfy the second objective function are selected from the candidate structures with optimal parameters and taken as the optimal candidate structures. The hybrid model that uses the optimal candidate structures and the optimal parameters of the optimal candidate structures is taken as the optimal hybrid model.

6. The hybrid modeling method for sequential simulation of moving bed separation performance optimization according to claim 5, characterized in that, The evaluation of the performance of the optimal mixing model includes: using the coefficient of determination R² and the normalized root mean square error NRMSE as performance evaluation indicators of the optimal mixing model, and evaluating the outlet concentrations obtained by the optimal mixing model at different times on the test set.

7. The hybrid modeling method for sequential simulation of moving bed separation performance optimization according to claim 1, characterized in that, The process of determining the evaluation index of the sequential simulated moving bed and using an optimal hybrid model for process optimization to solve for the Pareto optimal solution of the evaluation index of the sequential simulated moving bed includes: Product purity and recovery rate are used as evaluation indicators for sequential simulated moving bed; By setting both product purity and recovery rate as objective functions, a multi-objective optimization problem is established. The non-dominated sorting genetic algorithm NSGA-II is used to iteratively solve the multi-objective optimization problem. In each iteration, a hybrid model is called to indirectly calculate the product purity and recovery rate until a non-dominated front covering the entire target space is generated. From the non-dominated frontier, select the product purity-recovery combination that meets production requirements as the Pareto optimal operating scheme for product purity and recovery.

8. A hybrid modeling system for sequential simulation of moving bed separation performance optimization, characterized in that, include: The data acquisition module is used to design multiple sets of dual-column experiments and collect effluent concentration data at different times during the chromatographic separation process to form a dataset. The hybrid model building module is used to construct a dual-branch neural network model. The two branches of the dual-branch neural network model are used to replace the adsorption kinetic equations of the strongly adsorbed component and the weakly adsorbed component in the mass conservation equation of the traditional mechanism model, respectively, to obtain a hybrid model embedded with the dual-branch neural network. The parameter structure tuning module is used to jointly optimize the structure of the dual-branch neural network model and the parameters of the hybrid model in the dataset by combining the success history adaptive differential evolution algorithm with linear population size reduction and grid search strategy, with the goal of minimizing the weighted sum of squares error, to obtain the optimal hybrid model. The evaluation module is used to discretize and solve the mass conservation partial differential equation of the optimal mixing model to obtain the outlet concentrations predicted by the optimal mixing model at different times; based on the predicted outlet concentrations at different times, the performance of the optimal mixing model is evaluated. The process optimization module is used to determine the evaluation index of the sequential simulated moving bed and to optimize the process using the optimal hybrid model to find the Pareto optimal solution of the evaluation index of the sequential simulated moving bed.

9. A computer device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the computer program, it implements the steps of the method according to any one of claims 1 to 7.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by a processor, it implements the steps of the method according to any one of claims 1 to 7.

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