Robust optimization method and system for a paraxylene adsorptive separation device

Abstract

The application discloses a robust optimization method and system for a paraxylene adsorption separation device, and solves the problem of poor robustness of operation variables in a deterministic optimization method in a PX adsorption separation process.The technical scheme is as follows: a mathematical model of a paraxylene adsorption separation process is established by referring to operation variables and inlet and outlet material compositions of the paraxylene adsorption separation device; input variables of the mathematical model are quantified by using a polynomial chaos expansion method based on a sparse grid; Sobol indexes are used for global sensitivity analysis, influence of feed flow and component concentration of the paraxylene adsorption separation device on the paraxylene adsorption separation device is evaluated, and key input variables of the mathematical model are screened; and the mathematical model is called by using an NSGA-II multi-objective optimization algorithm, and operation variables are optimized by taking the mean value and standard deviation obtained after uncertainty quantification of performance indexes of the paraxylene adsorption separation device as optimization objectives, so that optimal operation variables are obtained.

Description

Technical Field

[0001] This invention relates to the field of xylene separation technology, and in particular to an optimized method and system for separating para-xylene. Background Technology

[0002] C8 aromatics mainly include p-xylene (PX), m-xylene (MX), o-xylene (OX), and ethylbenzene (EB). PX is the main product of aromatics production and an important raw material for the production of purified terephthalic acid, which plays a crucial role in the production of polyester fibers, resins, and films. In addition, PX can also be used as a solvent and raw material in the production of pharmaceuticals, fragrances, and other chemical products. Because these compounds have similar boiling points, separating them by distillation is not practical. Early industrial technologies used cryogenic crystallization, utilizing their melting point differences to separate PX from other C8 isomers, but this method suffers from low PX recovery rates and high energy consumption. In the early 1960s, simulated moving bed adsorption separation technology emerged, gradually replacing the crystallization process. Simulated moving bed technology utilizes the different affinities of C8 aromatics for adsorbents, improving separation efficiency and significantly reducing energy consumption. Therefore, simulated moving bed technology has become an important research direction and a widely used mainstream technology in this industry.

[0003] With increasing emphasis on product quality and cost control in industrial production, various studies aimed at reducing costs and improving production efficiency have been extensively explored in recent years. In the optimization of simulated moving bed chromatography, a key issue is determining the optimal values ​​of operating variables, i.e., optimizing under the assumption that column configuration, packing parameters, and adsorption equilibrium characteristics of each component are already determined. However, uncertainties inevitably exist in engineering problems. These uncertainties can cause the optimal performance obtained through deterministic optimization to drop sharply under non-design conditions. Therefore, robust optimization studies of the PX adsorption and separation process in simulated moving beds have the potential for practical application.

[0004] In summary, although simulated moving bed technology has achieved significant results in the adsorption and separation of C8 aromatics, uncertainties such as the complexity of system operation and feed fluctuations still pose challenges to adsorption and separation efficiency and production benefits in practical industrial applications. Therefore, it is particularly important to research and develop a robust optimization method that can adapt to feed uncertainties. Summary of the Invention

[0005] The following provides a brief overview of one or more aspects to offer a basic understanding of them. This overview is not an exhaustive summary of all conceived aspects, nor is it intended to identify key or decisive elements of all aspects, nor to define the scope of any or all aspects. Its sole purpose is to present some concepts of one or more aspects in a simplified form to prepare for the more detailed descriptions that follow.

[0006] The purpose of this invention is to solve the above-mentioned problems by providing a robust optimization method and system for a paraxylene adsorption separation device. This addresses the issue of poor robustness of operating variables obtained by deterministic optimization methods in the PX adsorption separation process. By maintaining the high efficiency and stability of the system under different operating conditions, the invention further improves the separation efficiency of PX, reduces energy consumption, and enhances the economic benefits and competitiveness of industrial production.

[0007] The technical solution of this invention is as follows: This invention discloses a robust optimization method for a xylene adsorption and separation device, the method comprising:

[0008] Step S1: Establish a mathematical model for the p-xylene adsorption separation process by referring to the operating variables of the p-xylene adsorption separation unit and the composition of the inlet and outlet materials of the p-xylene adsorption separation unit.

[0009] Step S2: Using the mathematical model established in step S1, the uncertainty of the input variables of the mathematical model is quantified by the polynomial chaotic expansion method based on sparse grid, that is, the uncertainty of the input variables is propagated.

[0010] Step S3: Use the Sobol index to perform global sensitivity analysis, evaluate the impact of feed flow rate and component concentration of the p-xylene adsorption separation unit on the p-xylene adsorption separation unit, and screen key mathematical model input variables to improve robust optimization efficiency.

[0011] Step S4: Using the NSGA-II multi-objective optimization algorithm, the mathematical model established in step S1 is called. The mean and standard deviation obtained after quantifying the uncertainty of the performance indicators of the xylene adsorption separation device are used as optimization objectives to optimize the operating variables and obtain the optimal operating variables, thereby achieving robust optimization of the xylene adsorption separation device.

[0012] According to an embodiment of the robust optimization method for the p-xylene adsorption separation device of the present invention, the main operating variables of the p-xylene adsorption separation device include: temperature, pressure, feed flow rate, desorbent flow rate, extractant flow rate, residual liquid flow rate, circulation flow rate, switching time, feed intermediate xylene concentration, feed p-xylene concentration, feed o-xylene concentration, feed ethylbenzene concentration, and adsorbent specific capacity; the composition of the feed and discharge materials of the p-xylene adsorption separation device includes: p-xylene (PX), ethylbenzene (EB), m-xylene (MX), o-xylene (OX), p-diethylbenzene (PDEB), C9A (C9A), C10A (C10A), and other non-aromatic substances.

[0013] According to an embodiment of the robust optimization method for the p-xylene adsorption separation device of the present invention, step S1 further includes:

[0014] Step S11: Based on the structural parameters of the simulated moving bed and the operating parameters of the p-xylene adsorption separation process, construct a mathematical model of the simulated moving bed, including but not limited to the mechanistic model, polynomial empirical model and data-driven model of the p-xylene simulated moving bed. The mathematical model of the simulated moving bed is used to describe key data of the adsorption separation process, including the component concentration of each bed layer of the simulated moving bed, the composition of the feed and discharge substances of the simulated moving bed, the purity of p-xylene in the simulated moving bed, and the yield of p-xylene in the simulated moving bed.

[0015] Step S12: Compare the mathematical model simulation experiment with the axial concentration distribution data collected under actual working conditions to verify the mathematical model parameters and ensure that the calculation error of the mathematical model for xylene purity and yield is within the industrial allowable range.

[0016] According to an embodiment of the robust optimization method for the p-xylene adsorption separation device of the present invention, the mathematical model in step S11 further includes a polynomial empirical model:

[0017]

[0018] Among them, purity PX and yield PX R1, R2, R3, and R4 represent the purity and yield of p-xylene, respectively, and R1, R2, R3, and R4 represent the reflux ratios of the four zones of the xylene adsorption separation unit. i b j c k and d l These are R1, R2, R3, and R4, representing the purity. PX The coefficients, i, j, k and l, are R1, R2, R3 and R4 in purity, respectively. PX In the different powers, n, m, p, and q represent R1, R2, R3, and R4 respectively in purity PX The highest power in It is purity PX The constant term, e r f s g t and h x These are R1, R2, R3, and R4, representing yield. PX The coefficients, r, s, t, and x, are R1, R2, R3, and R4 respectively in yield. PX In the different powers, u, v, w, and y represent R1, R2, R3, and R4 respectively in yield. PX The highest power in It is yield PX The constant term is calculated using methods including least squares, gradient descent, polynomial kernel method, genetic algorithm, and Newton's method to calculate polynomial coefficients, the highest power, and the constant term, in order to help optimize model parameters in polynomial empirical models to obtain the best fit and prediction capabilities.

[0019] According to an embodiment of the robust optimization method for the p-xylene adsorption separation device of the present invention, the mathematical model in step S11 includes a neural network data-driven model. Based on the operating data of the p-xylene adsorption separation device, a regression model is established using a feedforward neural network model, a feedback neural network, and a graph neural network, thereby realizing the data-driven model.

[0020] The feedforward neural network model consists of one input layer, two hidden layers, and one output layer. The input layer represents the operating variables of the p-xylene adsorption separation device, and the output layer represents the purity and yield of p-xylene or the concentration of components in the extract and raffinate.

[0021] The feedback neural network model consists of an input layer, two recurrent neural network layers, and an output layer. The input layer contains the manipulated variables and historical component concentrations. The two recurrent neural network layers are long short-term memory neural networks or gated recurrent units. The output layer is a fully connected layer used to predict the purity and yield of paraxylene or the concentration of components in the extract and raffinate.

[0022] Graph neural networks are deep learning models that learn the feature representations of nodes through graph convolution operations, capturing the topological structure and relationships between nodes in the graph. The graph data construction module converts the operational variables into the adjacency matrix and feature matrix required by the graph convolution layer module. The fully connected layer predicts the purity and yield of paraxylene or the concentration of components in the extract and raffinate.

[0023] According to an embodiment of the robust optimization method for the p-xylene adsorption separation device of the present invention, step S2 further includes the following steps:

[0024] Step S21: Perform Latin hypercube sampling on the operating variables of the simulated moving bed. Each variable is uniformly sampled within a large range of values ​​and then combined to form a sample set.

[0025] Step S22: Perform simulation calculations for each sample, record the axial concentration distribution data of p-xylene, ethylbenzene, m-xylene, o-xylene and p-xylene under each set of operating variables, and establish a sample set;

[0026] Step S23: Use non-embedded polynomial chaotic expansion to quantify the uncertainty of the operational variables with uncertainty, and construct a polynomial chaotic expansion proxy model to realize the propagation of uncertainty;

[0027] Step S24: Solve for the coefficients of the chaotic polynomial using the Galerkin projection method;

[0028] Step S25: Use sparse grid integrals instead of full tensor integrals to solve for the coefficients of the chaotic polynomial.

[0029] According to an embodiment of the robust optimization method for the p-xylene adsorption separation device of the present invention, step S3 further includes the following steps:

[0030] Step S31: The sample set established in step 2 was randomly divided into ten subsets of equal size, and tenfold cross-validation was used to evaluate the predictive performance of the mathematical model.

[0031] Step S32: Quantify the uncertainty of the input variables of the stochastic model based on the mathematical model in order to study and characterize the uncertainty of the model input;

[0032] Step S33: Perform global sensitivity analysis using the Sobol index to evaluate the impact of feed flow rate and component concentration on PX purity and yield;

[0033] Step S34: Determine the key input variables for the stochastic model to improve robust optimization efficiency.

[0034] According to an embodiment of the robust optimization method for the p-xylene adsorption separation device of the present invention, step S4 further includes the following steps:

[0035] Step S41: Encode and initialize the population required for the NSGA-II algorithm by generating Latin hypercube sampling to ensure that the population has diversity;

[0036] Step S42: Call the mathematical model obtained in step S3 to predict the axial concentration distribution of each individual, calculate the corresponding PX purity and yield, and provide basic data for subsequent uncertainty quantification.

[0037] Step S43: Apply the SGPCE method to quantify uncertainty and determine the mean and standard deviation of PX purity yield;

[0038] Step S44: Calculate the fitness of each individual based on the constraints and objective function set in the NSGA-II algorithm, and determine whether the design requirements are met.

[0039] Step S45: If the design requirements are not met, proceed with the crossover, mutation, and selection process, and return to step S2 until the maximum number of iterations is reached, at which point the iteration ends.

[0040] This invention also discloses a robust optimization system for a p-xylene adsorption separation device, the system comprising:

[0041] The model building module establishes a mathematical model of the p-xylene adsorption separation process by referring to the operating variables of the p-xylene adsorption separation unit and the composition of the inlet and outlet materials of the p-xylene adsorption separation unit.

[0042] The uncertainty quantification module utilizes the mathematical model established by the model building module to quantify the uncertainty of the input variables of the mathematical model through a polynomial chaotic expansion method based on sparse grids, that is, to propagate the uncertainty of the input variables.

[0043] The variable screening module uses the Sobol index to perform global sensitivity analysis, evaluate the impact of feed flow rate and component concentration of the p-xylene adsorption separation unit on the p-xylene adsorption separation unit, and screen key mathematical model input variables to improve robust optimization efficiency.

[0044] The variable optimization module calls the mathematical model established by the model building module through the NSGA-II multi-objective optimization algorithm. It optimizes the operating variables with the mean and standard deviation obtained after quantifying the uncertainty of the performance indicators of the xylene adsorption separation device as the optimization objectives, and obtains the optimal operating variables, thereby achieving robust optimization of the xylene adsorption separation device.

[0045] The present invention also discloses a computer-readable storage medium storing program instructions executable by a processor to implement the steps of the robust optimization method for the p-xylene adsorption separation apparatus as described above.

[0046] The present invention also discloses a computer device comprising a memory, a processor, and program instructions stored in the memory that are executable by the processor, wherein the processor executes the program instructions to implement the steps of the robust optimization method for the p-xylene adsorption separation apparatus as described above.

[0047] Compared with the prior art, the present invention has the following advantages: The present invention establishes a sample set of axial concentration distributions of five components under different operating variables through mathematical model simulation, and achieves robust optimization of operating variables by means of mathematical model, uncertainty quantification method and multi-objective optimization algorithm, thereby solving the complex mechanism and parameter change problem of simulated moving bed adsorption separation device, and improving the operational stability and model calculation efficiency.

[0048] In detail, this invention improves the efficiency and robustness of the system and can be applied to the adsorption and separation process of xylene in the petrochemical industry.

[0049] This invention introduces the quantification of uncertainty in input variables, which helps assess the system's robustness to parameter changes, improves the model's reliability and predictive ability, and thus better guides process optimization and decision-making. Using the Sobol exponent for global sensitivity analysis helps identify and quantify the impact of input variables on output results, helps determine key influencing factors, and guides further parameter adjustments and optimizations, thereby improving the system's efficiency, reliability, and robustness.

[0050] Therefore, by using the NSGA-II multi-objective optimization algorithm, with the mean and standard deviation obtained after quantifying the performance uncertainty of the xylene adsorption separation unit as the optimization objectives, the operating variables can be optimized. This is beneficial for achieving robust optimization of the xylene adsorption separation unit, further improving the system's efficiency and robustness, thereby optimizing the xylene adsorption separation process in the petrochemical industry and achieving more efficient production and resource utilization. Attached Figure Description

[0051] The above-described features and advantages of the present invention will be better understood after reading the following detailed description of embodiments of the present disclosure in conjunction with the accompanying drawings. In the drawings, components are not necessarily drawn to scale, and components having similar related characteristics or features may have the same or similar reference numerals.

[0052] Figure 1 A flowchart of an embodiment of the robust optimization method for the p-xylene adsorption separation apparatus of the present invention is shown;

[0053] Figure 2 It shows Figure 1 The graph neural network structure diagram of the embodiment shown is shown.

[0054] Figure 3 It shows Figure 1 The NSGA-II algorithm optimization logic diagram of the embodiment shown is illustrated below.

[0055] Figure 4 It shows Figure 1 The comparison chart shows the optimization results of PX axial concentration distribution.

[0056] Figure 5 A schematic diagram of an embodiment of the robust optimization system of the p-xylene adsorption separation apparatus of the present invention is shown. Detailed Implementation

[0057] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments. It should be noted that the aspects described below with reference to the accompanying drawings and specific embodiments are merely exemplary and should not be construed as limiting the scope of protection of the present invention in any way.

[0058] Figure 1 The flowchart illustrates an embodiment of the robust optimization method for the p-xylene adsorption separation apparatus of the present invention. Please refer to... Figure 1 The implementation process of the method in this embodiment is described in detail below.

[0059] Step S1: Based on the operating variables of the p-xylene adsorption separation unit and the composition of the inlet and outlet materials of the p-xylene adsorption separation unit, establish a mathematical model of the p-xylene adsorption separation process.

[0060] The mathematical models for the p-xylene adsorption and separation process include, but are not limited to, mechanistic models, polynomial models, and data-driven models.

[0061] The main operating variables of the p-xylene adsorption separation unit are as follows: temperature, pressure, feed flow rate, desorbent flow rate, evaporator flow rate, residual liquid flow rate, circulation flow rate, switching time, MX concentration in feed, PX concentration in feed, OX concentration in feed, EB concentration in feed, and specific capacity of adsorbent.

[0062] The main components of the materials entering and leaving the p-xylene adsorption separation unit include: p-xylene, ethylbenzene, m-xylene, o-xylene, p-diethylbenzene, C9 aromatics, C10 aromatics, and other non-aromatic substances.

[0063] Step S1, establishing a mathematical model for the p-xylene adsorption separation process, further includes:

[0064] Step S11: Based on the structural parameters of the simulated moving bed and the operating parameters of the p-xylene adsorption separation process, a mathematical model of the simulated moving bed is constructed. In this embodiment, the mathematical model is an adsorption separation simulated moving bed mechanism model, a polynomial empirical model, and a data-driven model based on a graph convolutional neural network. The simulated moving bed mathematical model is used to describe key data of the adsorption separation process, including the component concentration of each bed layer of the simulated moving bed, the composition of the feed and discharge substances of the simulated moving bed, the purity of p-xylene in the simulated moving bed, and the yield of p-xylene in the simulated moving bed.

[0065] The mathematical model in step S11 further includes a polynomial empirical model:

[0066]

[0067] Among them, purity PX and yield PX R1, R2, R3, and R4 represent the purity and yield of p-xylene, respectively, and R1, R2, R3, and R4 represent the reflux ratios of the four zones of the xylene adsorption separation unit. i b j c k and d l These are R1, R2, R3, and R4, representing the purity. PX The coefficients, n, m, p, and q, are R1, R2, R3, and R4 in purity, respectively. PX The highest power in It is purity PX The constant term, e r f s g t and h x These are R1, R2, R3, and R4, representing yield. PX The coefficients, u, v, w, and y, are R1, R2, R3, and R4 respectively in yield. PX The highest power in It is yield PX The constant term is calculated using methods such as least squares, gradient descent, polynomial kernel methods, genetic algorithms, and Newton's method. These methods play important roles in polynomial empirical models, helping to optimize model parameters to achieve the best fit and predictive ability.

[0068] The mathematical model in step S11 includes an artificial neural network data-driven model. Based on the operating data of the p-xylene adsorption separation unit, a regression model can be established using a feedforward neural network model, a feedback neural network model, and a graph neural network, thereby realizing a data-driven model.

[0069] The feedforward neural network model consists of an input layer, two hidden layers, and an output layer. The input layer contains the operating variables of the p-xylene adsorption separation device, and the output layer can contain the purity and yield of p-xylene or the concentration of components in the extract and raffinate.

[0070] The feedback neural network model consists of an input layer, two RNN (Recurrent Neural Network) layers, and an output layer. The input layer contains the manipulated variables and historical component concentrations. The two RNN layers can be LSTM (Long Short-Term Memory) or GRU (Gated Recurrent Unit). The output layer is a fully connected layer used to predict the purity and yield of paraxylene or the concentrations of components in the extract and raffinate.

[0071] Graph Neural Networks (GNNs) are deep learning models that learn feature representations of nodes through graph convolution operations, capturing the topological structure and relationships between nodes in a graph. Specifically, the graph data construction module transforms the operational variables into the adjacency matrix and feature matrix required by the graph convolutional layer module, and then uses fully connected layers to predict the purity and yield of paraxylene or the concentration of components in the extract and raffinate.

[0072] Step S12: Compare the mathematical model simulation experiment with the axial concentration distribution data collected under actual working conditions to verify the mathematical model parameters and ensure that the calculation error of the mathematical model for xylene purity and yield is within the industrial allowable range.

[0073] The remaining process parameters of the mechanistic model include: adsorption isotherm parameters, mass transfer coefficient, axial diffusion coefficient, chromatographic column geometry parameters, and adsorbent characteristic parameters. These parameters remain unchanged in subsequent optimizations. Specifically, the sample set of the mechanistic model was randomly divided into ten equal subsets, and tenfold cross-validation was used to evaluate the predictive performance of the mechanistic model. The evaluation metrics were mean absolute error (MAE), root mean square error (RMSE), and coefficient of determination (R²).

[0074] Figure 2 It shows Figure 1 The diagram shown illustrates the architecture of the graph convolutional neural network used in the robust optimization method for the p-xylene adsorption separation unit, where Q... E Q R Q F Q D Q ref These represent the effluent flow rate, residual effluent flow rate, feed flow rate, eluent flow rate, and circulation flow rate, respectively. T represents the bed switching time, and C represents the bed switching time. PX C MX C OX and C EB These represent the concentrations of PX, MX, OX, and EB in the extract, respectively. Figure 2 As shown, the architecture consists of four modules: a graph data construction module for the manipulated variables, a graph convolutional layer module, a flattening layer module, and a fully connected layer module. The graph data construction module transforms the manipulated variables into the adjacency matrix and feature matrix required by the graph convolutional layer module. The graph convolutional layer module includes two graph convolutional layers. The purpose of the flattening layer module is to flatten the multidimensional input data into a one-dimensional vector to accommodate the subsequent fully connected layer. The input to the fully connected layer contains the values ​​of ten manipulated variables; the output of the fully connected layer contains the concentration values ​​of five components in 24 chromatographic columns (the axial concentration distribution of the five components). Each neuron in the hidden or output layer is determined by the weighted sum of all neurons in the previous layer.

[0075] Step S2: Using the mathematical model established in step S1, the uncertainty of the input variables of the mathematical model is quantified by the polynomial chaotic expansion method based on sparse grid, that is, the uncertainty of the input variables is propagated.

[0076] Step S2 further includes the following steps:

[0077] Step S21: Perform Latin hypercube sampling on the operating variables of the simulated moving bed. Each variable is uniformly sampled within a large range of values ​​and then combined to form a sample set.

[0078] Step S22: Perform simulation calculations for each sample, record the axial concentration distribution data of PDEB, EB, MX, OX and PX under each set of operational variables, and establish a sample set;

[0079] Step S23: Use non-embedded polynomial chaotic expansion to quantify the uncertainty of the operational variables with uncertainty, and construct a polynomial chaotic expansion proxy model to realize the propagation of uncertainty;

[0080] Step S24: Solve for the coefficients of the chaotic polynomial using the Galerkin projection method;

[0081] Step S25: Use sparse grid integrals instead of full tensor integrals to solve for the coefficients of the chaotic polynomial.

[0082] In this embodiment, the input variables are delineated in a four-dimensional sample space using Latin hypercube sampling.

[0083] In this embodiment, uncertainty quantification is divided into the following four important steps: identification of uncertainty sources, characterization of uncertainty sources, uncertainty propagation, and analysis of uncertainty.

[0084] The specific steps are as follows:

[0085] Uncertainty source identification: Identify all input variables that may introduce uncertainty;

[0086] Characterization of uncertainty sources: Choose an appropriate statistical representation for each uncertain input variable, and characterize each random variable as a probability distribution. The parameters of these distributions can be determined based on experimental data or literature data.

[0087] Uncertainty propagation: For a given probability distribution, an appropriate orthogonal polynomial is selected to construct the polynomial chaotic expansion expression of the model output. The sparse grid method can calculate the coefficients in the polynomial chaotic expansion by selecting appropriate weighting and node combinations.

[0088] Analyze uncertainty: Calculate the mean and standard deviation of the output based on the expansion coefficients.

[0089] Uncertain variables include the feed flow rate of the p-xylene adsorption separator, the concentration of p-xylene in the feed, the concentration of intermediate xylene in the feed, the concentration of o-xylene in the feed, the concentration of ethylbenzene in the feed, temperature, and pressure.

[0090] Polynomial chaotic expansion can be divided into two types: embedded and non-embedded.

[0091] Embedded Polynomial Chaos Expansion (IPCE) addresses the propagation of uncertainties in dynamical systems by embedding a polynomial chaotic expansion model into the system's differential equations. However, this introduces numerical errors, limiting its application.

[0092] Non-intrusive Polynomial Chaos Expansion (NIPCE) takes a more flexible approach, treating the system response function as a black box. It achieves the propagation of uncertainty by constructing a polynomial chaotic expansion surrogate model, avoiding the modification of the system equations. It is suitable for complex engineering analysis involving black-box response functions and reduces the introduction of numerical errors.

[0093] Step S3: Use the Sobol index to perform global sensitivity analysis, evaluate the impact of feed flow rate and component concentration of the p-xylene adsorption separation unit on the p-xylene adsorption separation unit, screen key mathematical model input variables, and improve robust optimization efficiency.

[0094] The Sobol index is a statistical tool used for sensitivity analysis. Based on full factorial ANOVA, it is mainly used to determine which parts of the input variables the model output is most sensitive to.

[0095] The Sobol exponent can be directly calculated using polynomial chaotic expansion coefficients based on a sparse grid. Specifically, for each random variable, the first-order Sobol exponent is the proportion of the sum of the variances of all polynomial expansion terms related to that variable to the total variance, while the second-order Sobol exponent is the proportion of the sum of the variances of the polynomial expansion terms related to the interaction of that variable with other variables to the total variance. Through these steps, the uncertainty contribution of random variables and their interactions to the model output can be quantified, thereby gaining a deeper understanding of the impact of each variable and their interactions in the system.

[0096] Step S3 further includes the following steps:

[0097] Step S31: The sample set established in step 2 was randomly divided into ten equal-sized subsets, and tenfold cross-validation was used to evaluate the predictive performance of the mathematical model; the dataset contains 6000 samples, each of which includes 10 operational variables and their corresponding axial concentration distributions.

[0098] Step S32: Based on the mathematical model, the uncertainty of the input variables of the stochastic model is quantified to study and characterize the uncertainty of the model input. All uncertain variables follow a Gaussian distribution, and the range of variation is approximately set at ±0.9% of the initial value. When all uncertain variables follow a Gaussian distribution, the overall values ​​of the second-order Sobol exponents of PX yield and purity are very small and can be ignored.

[0099] Step S33: Perform global sensitivity analysis using the Sobol index to evaluate the impact of feed flow rate and component concentration on PX purity and yield; the Sobol index includes the first-order and second-order Sobol indices for PX purity and yield.

[0100] Among them, the SGPCE method (Sparse Grid based Polynomial Chaos Expansion), that is, the Sobol exponential analysis of the finite element model based on the polynomial chaotic expansion of sparse grids, is used.

[0101] The total variance of the objective includes the variances of each parameter and their interactions; that is, the variances of individual parameters and their interactions are both taken into account. The specific calculation is as follows:

[0102]

[0103] Where Var(Y) represents the total variance of the objective, and D i (Y) represents the first-order variance of each input parameter, D ij (Y) and D 12…n (Y) represents the second-order variance and the higher-order variance, respectively.

[0104] The Sobol index is evaluated based on its percentage contribution to the total variance:

[0105] First-order Sobol index:

[0106]

[0107] Second-order Sobol index:

[0108] Calculate the first and second Sobol exponents of PX purity and yield based on the SGPCE method.

[0109] Step S34: Determine the key input variables for the stochastic model to improve robust optimization efficiency.

[0110] Step S4: Using the NSGA-II multi-objective optimization algorithm, the mathematical model established in step S1 is called. The mean and standard deviation obtained after quantifying the uncertainty of the performance indicators of the xylene adsorption separation device are used as optimization objectives to optimize the operating variables and obtain the optimal operating variables, thereby achieving robust optimization of the xylene adsorption separation device.

[0111] Step S4 further includes the following steps:

[0112] Step S41: Encode and initialize the population required for the NSGA-II algorithm by generating Latin hypercube sampling to ensure that the population has diversity;

[0113] The NSGA-II algorithm is used to solve optimization problems with multiple objective functions. Based on a genetic algorithm, it aims to find a Pareto-optimal set of solutions to the problem. NSGA-II maintains population diversity through non-dominated sorting and crowding sorting to find a set of near-optimal solutions in the solution space, such that there is no significant room for improvement across different objectives.

[0114] Step S42: Call the mathematical model obtained in step S2 to predict the axial concentration distribution of each individual, calculate the corresponding PX purity and yield, and provide basic data for subsequent uncertainty quantification.

[0115] Step S43: Using the SGPCE method from step S23, uncertainty is quantified to determine the mean and standard deviation of the PX purity yield.

[0116] Step S44: Calculate the fitness of each individual based on the constraints and objective function set in the NSGA-II algorithm, and determine whether the design requirements are met.

[0117] Step S45: If the design requirements are not met, proceed with the crossover, mutation, and selection process, and return to step S2 until the maximum number of iterations is reached, at which point the iteration ends.

[0118] The following example illustrates a robust optimization method for a xylene adsorption separation unit.

[0119] In this example, a domestic petrochemical adsorption separation unit is used as the test object to provide a detailed explanation of the robust optimization method for the p-xylene adsorption separation unit.

[0120] Step S1: Obtain the process parameters and operating data of a petrochemical adsorption separation unit, and establish a mechanism model. The specific process is as follows:

[0121] Obtain the physical parameters of the device, such as length, width, and diameter, of the device described in step S1;

[0122] Fixed parameters such as adsorption isotherm parameters, mass transfer coefficient, axial diffusion coefficient, chromatographic column geometric parameters, and adsorbent characteristic parameters of the device described in step S1 are calculated.

[0123] Obtain the production and operation parameters of the device described in step S1 within one year, including but not limited to the inlet and outlet flow rates and composition, the flow rates and composition of each area, the reflux ratio of each area, and other production parameters, and build a mechanism model of the adsorption separation device based on these parameters.

[0124] Furthermore, Latin hypercube sampling was used to uniformly sample the manipulated variables and combine them to form a sample set. The simulation results under each set of manipulated variables were obtained through mechanistic model simulation calculation. The axial concentration distribution data of 5 components (PDEB, EB, MX, OX, PX) in 24 bed layers were recorded, which included a total of 6000 samples.

[0125] For the task of predicting axial concentration distribution, a data-driven model based on a graph convolutional neural network was built using this sample set. The performance of four other classic machine learning models was compared, mainly considering four indicators: mean absolute error, root mean square error, coefficient of determination, and prediction time per sample for each model. The specific results are shown in Table 1.

[0126] Table 1. Prediction results of the data-driven model

[0127]

[0128] Compared with mechanistic models, data-driven models have shown unique computational advantages. Graph Convolutional Neural Network (OV-GCN) has shown the best prediction performance, with the lowest mean absolute error and root mean square error among all models, and the coefficient of determination has reached 0.9984.

[0129] The results show that the graph convolutional neural network has the best prediction performance for the axial concentration distribution of the five components.

[0130] Step S2: Using the mathematical model established in step S1, the uncertainty of the input variables of the mathematical model is quantified by the polynomial chaotic expansion method based on sparse grid, that is, the uncertainty of the input variables is propagated.

[0131] In this embodiment, the specific process is as follows:

[0132] The uncertainty of operational variables is quantified using NIPCE. X(θ) is a function representing a stochastic process of random events. Based on the probability distribution of the input parameters, an optimal orthogonal basis can be selected. To reduce computational cost, a truncation strategy is often considered to remove some higher-order cross polynomial terms, which can be expressed in the following form:

[0133]

[0134] Where, ψ j (ξ) has a one-to-one correspondence with the orthogonal basis of the polynomial chaotic expansion under multidimensional random parameters, where ξ is a multidimensional random variable and k j Here are the corresponding coefficients, M represents the order of the highest-order term retained, n is a positive integer, and d is a positive integer less than n;

[0135] The method for solving PCE coefficients in this invention is the Galerkin projection method, which utilizes the orthogonality of basis functions and decouples the coefficients through inner product transformation.

[0136] The main idea of ​​the Sparse Mesh-based Polynomial Chaotic Expansion (SGPCE) method is to reduce computational cost and solve for PCE coefficients by replacing the full tensor (FTP) integral with the sparse mesh (SG) integral.

[0137] Specifically, the formulas for calculating PX purity and yield are as follows:

[0138] PX purity in the extract:

[0139]

[0140] PX yield in extract:

[0141]

[0142] in, and Q represents the concentrations of PX, MX, OX, and EB in the extract (i.e., the 6th bed). E Q F and represent the extract flow rate and feed flow rate, respectively, both of which can be calculated using the graph convolutional neural network model.

[0143] Step S3: Use the Sobol index to perform global sensitivity analysis to evaluate the impact of feed flow rate and component concentration of the p-xylene adsorption separation unit on the p-xylene adsorption separation unit, and screen key mathematical model input variables.

[0144] This invention performs global sensitivity analysis of the Sobol exponent based on a data-driven model. Using SGPCE for Sobol exponent analysis not only improves the efficiency of sensitivity analysis but also takes into account the impact of the uncertainty of input random variables on the output. The specific calculation process is as follows:

[0145] The total variance of the objective, Var(Y), includes the variances of the individual parameters and their interactions; that is, the variances of individual parameters and their interactions are taken into account, and can be calculated by the following formula:

[0146]

[0147] Among them, D i (Y) represents each input parameter X. i The first variance, D ij (Y) and D 12…n (Y) represent the second-order variance and higher-order variance, respectively. The Sobol index is evaluated based on the percentage contribution to the total variance:

[0148] First-order Sobol index:

[0149]

[0150] Second-order Sobol index:

[0151]

[0152] In this embodiment, all uncertain variables follow a Gaussian distribution and the range of variation is set to ±0.9% of the initial value. The results show that the PX concentration, MX concentration, and feed flow rate in the feed are the key uncertain variables to be considered in robust optimization, thereby improving optimization efficiency and avoiding the curse of dimensionality.

[0153] Step S4: Using the NSGA-II multi-objective optimization algorithm, the mathematical model established in step S1 is called. The mean and standard deviation obtained after quantifying the uncertainty of the performance indicators of the xylene adsorption separation device are used as optimization objectives to optimize the operating variables and obtain the optimal operating variables, thereby achieving robust optimization of the xylene adsorption separation device.

[0154] Figure 3 It shows Figure 1 The axial concentration fractionation Brussels brane optimization process of the robust optimization method embodiment for the p-xylene adsorption separation device shown is as follows: Figure 3 As shown, the axial concentration distribution optimization process of the present invention includes the following steps:

[0155] Latin hypercube sampling is used to generate the population required for the NSGA-II algorithm, and the population is encoded and initialized to ensure that the population has diversity;

[0156] The data-driven model is invoked to predict the axial concentration distribution of each individual and to calculate the corresponding PX purity and yield, providing basic data for subsequent uncertainty quantification.

[0157] The SGPCE method was applied to quantify uncertainty and determine the mean and standard deviation of PX yield.

[0158] Based on the constraints and objective function set in the NSGA-II algorithm, calculate the fitness of each individual and determine whether the design requirements are met.

[0159] If the design requirements are not met, a crossover, mutation, and selection process is performed, and the process returns to step S2 until the maximum number of iterations is reached, at which point the iteration ends.

[0160] To meet the requirements of this implementation case, the optimization objective is defined as: robust optimization of the axial concentration distribution under a certain working condition.

[0161] This problem is a constrained multi-objective optimization problem, and its mathematical description is as follows:

[0162] F(x) = [maxμ(yield)] PX ), minσ(yield PX )]

[0163] st99.70%≤purity PX ≤99.90%

[0164] 96.00% ≤ yield PX ≤99.00%

[0165] 310.000m 3 ·h -1 ≤Q E ≤410.000m 3 ·h -1

[0166] 1410.000m 3 ·h -1 ≤Q R ≤1470.000m 3 ·h -1

[0167] 2165.000m 3 ·h -1 ≤Q ref ≤2195.000m 3 ·h -1

[0168] Q D =Q E +Q R -Q F

[0169] 58.00s≤T≤65.00s

[0170] σ(yield PX )≤0.03

[0171] Among them, purity PX with yield PXμ represents the purity and yield of PX, respectively. PX ) and σ(yield PX Q represents the mean and standard deviation of the PX yield, respectively. E Q R Q F Q D Q ref These represent the effluent flow rate, residual effluent flow rate, feed flow rate, eluent flow rate, and circulation flow rate, respectively, while T represents the bed switching time.

[0172] An increase in the mean and standard deviation of PX yield indicates that maximizing μ(yield) is beneficial. PX and minimizing σ(yield) PX This is a multi-objective optimization problem. The experimental results for deterministic optimization are as follows: Figure 4 As shown in Table 2, the results of the comparison of optimized operational variables are presented.

[0173] Table 2 Comparison of optimized operational variables

[0174]

[0175]

[0176] Simulation results show that, compared with deterministic optimization results, the robust optimization framework exhibits characteristics that make the optimized axial concentration distribution robust, thus enhancing the robustness and reliability of the system or optimization scheme against external changes or internal disturbances. By considering uncertainties or the range of parameter variations, the robust optimization framework seeks solutions that not only perform well under deterministic conditions but also maintain good performance under uncertain conditions during the optimization process, thereby increasing the stability of the system and making the final optimization results more reliable.

[0177] In the optimization of axial concentration distribution, improved robustness means that the optimized axial concentration distribution remains relatively stable and reliable even in the face of changes in the external environment, fluctuations in operating conditions, or uncertainties in model parameters. This robustness is crucial for practical engineering applications because real-world systems are often affected by various uncertainties, and robust optimization can better adapt to these changes and provide reliable solutions.

[0178] Figure 5 The principle of an embodiment of the robust optimization system for the p-xylene adsorption separation apparatus of the present invention is shown. Please refer to... Figure 5 The system in this embodiment includes: a model building module, an uncertainty quantification module, a variable selection module, and a variable optimization module.

[0179] The model building module, referencing the operating variables and the composition of the inlet and outlet materials of the p-xylene adsorption separation unit, establishes a mathematical model of the p-xylene adsorption separation process. Specific processing details for this module are provided below. Figure 1 Step S1 of the illustrated embodiment.

[0180] The uncertainty quantification module utilizes the mathematical model established by the model building module and employs a sparse grid-based polynomial chaotic expansion method to quantify the uncertainty of the input variables, essentially propagating uncertainty from the input variables. For details on this module's processing, please refer to [link / reference needed]. Figure 1 Step S2 of the illustrated embodiment.

[0181] The variable selection module utilizes the Sobol index for global sensitivity analysis to evaluate the impact of feed flow rate and component concentration on the p-xylene adsorption separation unit, thus selecting key mathematical model input variables to improve robust optimization efficiency. For detailed processing of this module, please refer to [link / reference needed]. Figure 1 Step S3 of the illustrated embodiment.

[0182] The variable optimization module uses the NSGA-II multi-objective optimization algorithm to call the mathematical model established by the uncertainty quantification module. It optimizes the operating variables using the mean and standard deviation obtained after quantifying the uncertainty of the performance indicators of the xylene adsorption separation unit as the optimization objectives, thereby achieving robust optimization of the xylene adsorption separation unit. Figure 1 Step S4 of the illustrated embodiment.

[0183] The present invention also discloses a computer-readable storage medium storing program instructions executable by a processor to achieve, for example... Figure 1 The steps of the robust optimization method embodiment for the p-xylene adsorption separation device shown are illustrated.

[0184] The present invention also discloses a computer device comprising a memory, a processor, and program instructions stored in the memory and executable by the processor, wherein the processor executes the program instructions to perform, as Figure 1 The steps of the robust optimization method embodiment for the p-xylene adsorption separation device shown are illustrated.

[0185] Although the methods described above are illustrated and depicted as a series of actions for the sake of simplicity, it should be understood and appreciated that these methods are not limited by the order of the actions, as some actions may occur in a different order and / or concurrently with other actions from the illustrations and descriptions herein or not illustrated and described herein but which may be understood by those skilled in the art, according to one or more embodiments.

[0186] Those skilled in the art will further appreciate that the various illustrative logic blocks, modules, circuits, and algorithm steps described in conjunction with the embodiments disclosed herein can be implemented as electronic hardware, computer software, or a combination of both. To clearly illustrate this interchangeability between hardware and software, the various illustrative components, blocks, modules, circuits, and steps are described above in a generalized manner in terms of their functionality. Whether such functionality is implemented as hardware or software depends on the specific application and the design constraints imposed on the overall system. Those skilled in the art may implement the described functionality in different ways for each specific application, but such implementation decisions should not be construed as departing from the scope of the invention.

[0187] The various illustrative logic blocks, modules, and circuits described in conjunction with the embodiments disclosed herein can be implemented or performed using a general-purpose processor, a digital signal processor (DSP), an application-specific integrated circuit (ASIC), a field-programmable gate array (FPGA) or other programmable logic device, discrete gate or transistor logic, discrete hardware components, or any combination thereof designed to perform the functions described herein. The general-purpose processor may be a microprocessor, but in alternatives, it may be any conventional processor, controller, microcontroller, or state machine. The processor may also be implemented as a combination of computing devices, such as a combination of a DSP and a microprocessor, multiple microprocessors, one or more microprocessors cooperating with a DSP core, or any other such configuration.

[0188] The steps of the methods or algorithms described in conjunction with the embodiments disclosed herein may be embodied directly in hardware, in a software module executed by a processor, or in a combination of both. The software module may reside in RAM memory, flash memory, ROM memory, EPROM memory, EEPROM memory, registers, hard disk, removable disk, CD-ROM, or any other form of storage medium known in the art. An exemplary storage medium is coupled to a processor such that the processor can read and write information to / from the storage medium. In an alternative, the storage medium may be integrated into the processor. The processor and storage medium may reside in an ASIC. The ASIC may reside in a user terminal. In an alternative, the processor and storage medium may reside as discrete components in the user terminal.

[0189] In one or more exemplary embodiments, the described functionality may be implemented in hardware, software, firmware, or any combination thereof. If implemented in software as a computer program product, the functionality may be stored or transmitted as one or more instructions or code on or through a computer-readable medium. A computer-readable medium includes both computer storage media and communication media, encompassing any medium that facilitates the transfer of a computer program from one location to another. A storage medium may be any available medium accessible to a computer. By way of example and not limitation, such a computer-readable medium may include RAM, ROM, EEPROM, CD-ROM or other optical disc storage, disk storage or other magnetic storage devices, or any other medium that can be used to carry or store desired program code in the form of instructions or data structures and is accessible to a computer. Any connection is also legitimately referred to as a computer-readable medium. For example, if the software is transmitted from a website, server, or other remote source using coaxial cable, fiber optic cable, twisted pair, digital subscriber line (DSL), or wireless technologies such as infrared, radio, and microwave, then the coaxial cable, fiber optic cable, twisted pair, DSL, or wireless technologies such as infrared, radio, and microwave are included in the definition of a medium. As used in this article, disk and disc include compact discs (CDs), laser discs, optical discs, digital multi-purpose discs (DVDs), floppy disks, and Blu-ray discs. Disks typically reproduce data magnetically, while discs reproduce data optically using lasers. Combinations of these should also be included within the scope of computer-readable media.

[0190] The prior description of this disclosure is provided to enable any person skilled in the art to make or use this disclosure. Various modifications to this disclosure will be apparent to those skilled in the art, and the general principles defined herein may be applied to other variations without departing from the spirit or scope of this disclosure. Therefore, this disclosure is not intended to be limited to the examples and designs described herein, but should be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A robust optimization method for a xylene adsorption separation device, characterized in that, The methods include: Step S1: Establish a mathematical model for the p-xylene adsorption separation process by referring to the operating variables of the p-xylene adsorption separation unit and the composition of the inlet and outlet materials of the p-xylene adsorption separation unit. Step S2: Using the mathematical model established in step S1, the uncertainty of the input variables of the mathematical model is quantified by the polynomial chaotic expansion method based on sparse grid, that is, the uncertainty of the input variables is propagated. Step S3: Use the Sobol index to perform global sensitivity analysis, evaluate the impact of feed flow rate and component concentration of the p-xylene adsorption separation unit on the p-xylene adsorption separation unit, and screen key mathematical model input variables to improve robust optimization efficiency. Step S4: Using the NSGA-II multi-objective optimization algorithm, the mathematical model established in step S1 is called. The mean and standard deviation obtained after quantifying the uncertainty of the performance index of the xylene adsorption separation device are used as optimization objectives to optimize the operating variables and obtain the optimal operating variables, thereby achieving robust optimization of the xylene adsorption separation device. Step S2 further includes the following steps: Step S21: Perform Latin hypercube sampling on the operating variables of the simulated moving bed. Each variable is uniformly sampled within a range of values ​​and then combined to form a sample set. Step S22: Perform simulation calculations for each sample, record the axial concentration distribution data of p-xylene, ethylbenzene, m-xylene, o-xylene and p-xylene under each set of operating variables, and establish a sample set; Step S23: Use non-embedded polynomial chaotic expansion to quantify the uncertainty of the operational variables with uncertainty, and construct a polynomial chaotic expansion proxy model to realize the propagation of uncertainty; Step S24: Solve for the coefficients of the chaotic polynomial using the Galerkin projection method; Step S25: Use sparse grid integrals instead of full tensor integrals to solve for the coefficients of the chaotic polynomials; In step S2, the input variables are delineated using Latin hypercube sampling to define the four-dimensional sample space of the input variables; Uncertainty quantification in step S2 is divided into: identification of uncertainty sources, characterization of uncertainty sources, uncertainty propagation and analysis of uncertainty. Polynomial chaos expansion is divided into embedded polynomial chaos expansion and non-embedded polynomial chaos expansion.

2. The robust optimization method for the p-xylene adsorption separation device according to claim 1, characterized in that, The main operating variables of the p-xylene adsorption separation unit include: temperature, pressure, feed flow rate, desorbent flow rate, evaporator flow rate, residual liquid flow rate, circulation flow rate, switching time, feed intermediate xylene concentration, feed p-xylene concentration, feed o-xylene concentration, feed ethylbenzene concentration, and adsorbent specific capacity. The composition of the feed and effluent of the p-xylene adsorption separation unit includes: p-xylene (PX), ethylbenzene (EB), m-xylene (MX), o-xylene (OX), p-diethylbenzene (PDEB), C9A (C9A), C10A (C10A), and other non-aromatic substances.

3. The robust optimization method for the p-xylene adsorption separation device according to claim 1, characterized in that, Step S1 further includes: Step S11: Based on the structural parameters of the simulated moving bed and the operating parameters of the p-xylene adsorption separation process, construct a mathematical model of the simulated moving bed, including a mechanistic model, a polynomial empirical model, and a data-driven model of the p-xylene simulated moving bed. The mathematical model of the simulated moving bed is used to describe key data of the adsorption separation process, including the component concentration of each bed layer of the simulated moving bed, the composition of the feed and discharge substances of the simulated moving bed, the purity of p-xylene in the simulated moving bed, and the yield of p-xylene in the simulated moving bed. Step S12: Compare the mathematical model simulation experiment with the axial concentration distribution data collected under actual working conditions to verify the mathematical model parameters and ensure that the calculation error of the mathematical model for xylene purity and yield is within the industrial allowable range.

4. The robust optimization method for the p-xylene adsorption separation device according to claim 1, characterized in that, The mathematical model in step S11 further includes a polynomial empirical model: in, and The values ​​represent the purity and yield of p-xylene, respectively. , , and These represent the reflux ratios of the four zones in the xylene adsorption separation unit. , , and They are , , and right coefficient, , , and They are , , and exist Different powers in , , and They are , , and exist The highest power in yes The constant term, , , and They are , , and right coefficient, , , and They are , , and exist Different powers in , , and They are , , and exist The highest power in yes The constant term is calculated using methods including least squares, gradient descent, polynomial kernel method, genetic algorithm, and Newton's method to calculate polynomial coefficients, the highest power, and the constant term, in order to help optimize model parameters in polynomial empirical models to obtain the best fit and prediction capabilities.

5. The robust optimization method for the p-xylene adsorption separation device according to claim 1, characterized in that, The mathematical model in step S11 includes a neural network data-driven model. Based on the operating data of the p-xylene adsorption and separation unit, a regression model is established using a feedforward neural network model, a feedback neural network model, and a graph neural network, thereby realizing the data-driven model. The feedforward neural network model consists of an input layer, two hidden layers, and an output layer. The input layer contains the operating variables of the p-xylene adsorption separation device, and the output layer contains the purity and yield of p-xylene or the concentration of components in the extract and raffinate. The feedback neural network model consists of an input layer, two recurrent neural network layers, and an output layer. The input layer contains the manipulated variables and historical component concentrations. The two recurrent neural network layers are long short-term memory neural networks or gated recurrent units. The output layer is a fully connected layer used to predict the purity and yield of paraxylene or the concentration of components in the extract and raffinate. Graph neural networks are deep learning models that learn the feature representations of nodes through graph convolution operations, capturing the topological structure and relationships between nodes in the graph. The graph data construction module converts the operational variables into the adjacency matrix and feature matrix required by the graph convolution layer module. The fully connected layer predicts the purity and yield of paraxylene or the concentration of components in the extract and raffinate.

6. The robust optimization method for the p-xylene adsorption separation device according to claim 1, characterized in that, Step S3 further includes the following steps: Step S31: The sample set established in step 2 was randomly divided into ten subsets of equal size, and tenfold cross-validation was used to evaluate the predictive performance of the mathematical model. Step S32: Quantify the uncertainty of the input variables of the stochastic model based on the mathematical model in order to study and characterize the uncertainty of the model input; Step S33: Perform global sensitivity analysis using the Sobol index to evaluate the impact of feed flow rate and component concentration on PX purity and yield; Step S34: Determine the key input variables for the stochastic model to improve robust optimization efficiency.

7. The robust optimization method for the p-xylene adsorption separation device according to claim 1, characterized in that, Step S4 further includes the following steps: Step S41: Encode and initialize the population required for the NSGA-II algorithm by generating Latin hypercube sampling to ensure that the population has diversity; Step S42: Call the mathematical model obtained in step S3 to predict the axial concentration distribution of each individual, calculate the corresponding PX purity and yield, and provide basic data for subsequent uncertainty quantification. Step S43: Apply the SGPCE method to quantify uncertainty and determine the mean and standard deviation of PX purity yield; Step S44: Calculate the fitness of each individual based on the constraints and objective function set in the NSGA-II algorithm, and determine whether the design requirements are met. Step S45: If the design requirements are not met, proceed with the crossover, mutation, and selection process, and return to step S2 until the maximum number of iterations is reached, at which point the iteration ends.

8. A robust optimization system for a p-xylene adsorption separation device, characterized in that, The system includes: The model building module establishes a mathematical model of the p-xylene adsorption separation process by referring to the operating variables of the p-xylene adsorption separation unit and the composition of the inlet and outlet materials of the p-xylene adsorption separation unit. The uncertainty quantification module utilizes the mathematical model established by the model building module to quantify the uncertainty of the input variables of the mathematical model through a polynomial chaotic expansion method based on sparse grids, that is, to propagate the uncertainty of the input variables. The variable screening module uses the Sobol index to perform global sensitivity analysis, evaluate the impact of feed flow rate and component concentration of the p-xylene adsorption separation unit on the p-xylene adsorption separation unit, and screen key mathematical model input variables to improve robust optimization efficiency. The variable optimization module calls the mathematical model established by the model building module through the NSGA-II multi-objective optimization algorithm. It optimizes the operating variables with the mean and standard deviation obtained after quantifying the uncertainty of the performance indicators of the xylene adsorption separation device as the optimization objectives, and obtains the optimal operating variables, thereby achieving robust optimization of the xylene adsorption separation device.

9. A computer-readable storage medium storing program instructions executable by a processor to implement the steps of the robust optimization method for the p-xylene adsorption separation apparatus as described in any one of claims 1 to 7.

10. A computer device comprising a memory, a processor, and program instructions stored in the memory and executable by the processor, wherein the processor executes the program instructions to implement the steps of the robust optimization method for the p-xylene adsorption separation apparatus as claimed in any one of claims 1 to 7.

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