Automatic optimization and simulation system of triperiodic minimal surface chromatographic structure parameters

Abstract

The application discloses a three-period minimal surface chromatographic structure parameter automatic optimization and simulation system and belongs to the technical field of three-dimensional image processing.The system comprises a three-dimensional structure image generation module, a visual simulation and image analysis module, an adaptive optimization module and a closed-loop feedback control module.The three-dimensional structure image generation module generates a three-dimensional grid image based on a hidden function equation.The visual simulation and image analysis module performs visual simulation on a flow field and a concentration field.The adaptive optimization module searches for optimal parameters based on Riemann geometry.The closed-loop feedback control module realizes automatic iteration.The four modules are deeply coupled to form a complete closed loop, and the development cycle is shortened by more than 60%.

Description

Technical Field

[0001] This invention belongs to the field of three-dimensional image processing and computer-aided design technology, and relates to an automatic optimization and simulation system for three-period minimal surface chromatographic structure parameters. Background Technology

[0002] Chromatography is one of the most important techniques in chemical analysis and separation / purification, widely used in pharmaceuticals, food, environmental monitoring, and biotechnology. The microstructure of the chromatographic stationary phase directly determines the separation performance of the chromatographic column, including key indicators such as column efficiency, resolution, back pressure, and sample throughput. Traditional chromatographic stationary phases are mainly composed of spherical or irregularly shaped porous particles. This packed bed structure has inherent defects such as uneven particle spacing, numerous dead zones, and limited mass transfer efficiency.

[0003] In recent years, with the development of additive manufacturing technology, researchers have begun to explore the use of 3D printing technology to fabricate chromatographic stationary phases with regular microstructures. Triply Periodic Minimal Surfaces (TPMS) are a class of mathematical surfaces with zero mean curvature and periodic repetition characteristics. Their unique topology makes them exhibit excellent performance in multiple engineering fields. TPMS structures have advantages such as high specific surface area, low flow resistance, continuous pore network, and tunable porosity, making them theoretically very suitable as the microstructure framework of chromatographic stationary phases. However, the parameter space of TPMS structures is extremely broad. Different combinations of surface types, periodic parameters, phase parameters, and amplitude parameters will produce drastically different flow and mass transfer characteristics. How to quickly determine the optimal TPMS structure parameters for a specific separation task has become a key bottleneck restricting the practical application of this technology.

[0004] Chinese invention CN107204002A discloses a method for automatic surface recognition and intelligent extraction of surface structure parameters based on three-dimensional digital images. This method divides the spatial points of a data volume containing surfaces into central surface skeleton points, curve skeleton points, and simple points. It characterizes the topological features of the three-dimensional structure by extracting the central skeleton and measures surface structure parameters such as surface contour, surface angle, and surface thickness. However, this technology has the following shortcomings: This method can only passively extract surface parameters from existing three-dimensional scanned images and cannot actively generate and optimize new surface structures; it lacks performance simulation capabilities for chromatographic separation applications and cannot predict the impact of different surface structures on chromatographic performance; it does not establish a quantitative relationship between surface structure parameters and chromatographic performance indicators, and cannot achieve structure optimization for specific separation targets; and it uses a fixed algorithm flow and lacks a closed-loop feedback mechanism to dynamically adjust structural parameters based on simulation results.

[0005] Currently, the structural design of chromatographic stationary phases mainly relies on experimental trial and error, i.e., preparing a large number of samples with different parameters and evaluating performance through actual separation experiments. This method is time-consuming, costly, and inefficient. Although computational fluid dynamics simulation technology can predict the flow characteristics of stationary phase structures to some extent, existing simulation methods are usually single-point analyses of a given structure, lacking organic integration with structural optimization algorithms. In addition, traditional optimization algorithms such as genetic algorithms and particle swarm optimization often require a large number of iterations and simulation calculations when dealing with multi-objective optimization problems with complex constraints, resulting in low optimization efficiency.

[0006] Therefore, there is an urgent need to develop an integrated system that can automatically generate three-dimensional structural images of three-period minimal surfaces, efficiently perform visualization simulation, intelligently optimize structural parameters, and form a closed-loop feedback, so as to shorten the research and development cycle of chromatographic stationary phases and improve the accuracy and pertinence of structural design. Summary of the Invention

[0007] The purpose of this invention is to overcome the shortcomings of existing technologies and provide an automatic optimization and simulation system for three-period minimal surface chromatography structural parameters. This system establishes a deep coupling relationship between a 3D structural image generation module, a visualization simulation and image analysis module, an adaptive optimization module, and a closed-loop feedback control module. This achieves a complete closed loop from 3D image generation, visualization simulation, intelligent optimization to parameter feedback, significantly shortening the development cycle of three-period minimal surface chromatography stationary phases and improving the accuracy and efficiency of column design.

[0008] To achieve the above objectives, the technical solution adopted in this invention is: an automatic optimization and simulation system for three-period minimal surface chromatographic structure parameters. This system achieves intelligent design of three-dimensional structure images of the chromatographic stationary phase through deep coupling and closed-loop collaboration of four core modules. The three-dimensional structure image generation module generates three-dimensional candidate structure images based on the mathematical essence of the three-period minimal surface; the visualization simulation and image analysis module evaluates the chromatographic performance of the structure and generates a visualization image; the adaptive optimization module searches for optimal parameters using Riemannian geometry theory; and the closed-loop feedback control module realizes automatic iteration of the optimization process. A complete closed loop is formed between the four modules: image generation → visualization simulation → optimization → feedback → regeneration, ensuring that the system can quickly converge to the optimal three-dimensional structure image configuration for a specific separation task.

[0009] The 3D structure image generation module automatically generates 3D mesh image models with different topological features by storing and calling implicit function equations for various three-period minimal surface types and adjusting the equation parameters according to the target chromatographic performance requirements. The output of this module is directly used as the input to the visualization simulation and image analysis modules, establishing a deep parameter-level coupling relationship.

[0010] The visualization simulation and image analysis module receives three-dimensional candidate structure images, comprehensively solves the fluid dynamics and mass transfer kinetics equations, generates flow field distribution images and concentration distribution images, and predicts key performance indicators such as column efficiency, resolution, and back pressure of the structure under actual chromatographic operating conditions. The simulation results of this module are not only used for performance evaluation of the current structure, but also serve as input data for the adaptive optimization module, forming a state-level coupling.

[0011] The adaptive optimization module maps the multi-objective optimization problem to a Riemannian manifold space, leveraging the geometry on the manifold to accelerate optimization convergence. The optimized 3D structure parameters output by this module are fed back to the 3D structure image generation module via a closed-loop feedback control module, achieving logical-level coupling and back-feedback.

[0012] The closed-loop feedback control module monitors the optimization process, determines the convergence status, triggers a new round of iteration if convergence fails, and outputs the optimal 3D structural image model upon convergence. This module ensures the automated operation of the system and the reliability of the optimization effect.

[0013] Through the synergistic effect of the four modules mentioned above, the system achieves the following synergistic effects: In terms of mutual promotion, the flexibility of 3D structural image generation provides a broad search space for the optimization algorithm, while the intelligence of the optimization algorithm, in turn, enhances the targeting of image generation; in terms of synergistic effect, the visualization simulation and image analysis modules simultaneously consider both flow and mass transfer physical processes, resulting in prediction accuracy far exceeding that of single-physics field simulations; in terms of adaptive adjustment, the closed-loop feedback mechanism enables the system to dynamically adjust the optimization strategy based on simulation results, avoiding getting trapped in local optima. The entire system exhibits a nonlinear synergistic effect characteristic of 1+1>2.

[0014] Compared with the prior art, the present invention has the following beneficial effects:

[0015] This invention establishes a deep coupling relationship between four modules: three-dimensional structural image generation, visualization simulation, intelligent optimization, and closed-loop feedback, forming a complete structural design closed loop. This changes the traditional chromatographic stationary phase design, which relies on experimental trial and error, shortens the development cycle by more than 60%, and significantly reduces R&D costs.

[0016] This invention is the first to apply Riemannian geometry theory to the problem of chromatographic structure optimization. By performing optimization search in the manifold space, it makes full use of the geometric structure information of the parameter space. The optimization convergence speed is 3 to 5 times faster than that of traditional genetic algorithms. Under the same computing resource conditions, it can explore a wider parameter space and obtain a better structure configuration.

[0017] The visualization simulation and image analysis module of this invention simultaneously considers the interaction between fluid dynamics and mass transfer dynamics, and the simulation accuracy is significantly higher than that of existing single-physics field simulation methods. The prediction error of chromatographic performance indicators is controlled within 10%, providing a reliable evaluation benchmark for structural optimization.

[0018] The closed-loop feedback control mechanism of this invention realizes an automated process of forward transmission → performance evaluation → reverse feedback → parameter adjustment. The system can autonomously adjust the optimization strategy based on simulation results without manual intervention, thereby improving the intelligence level and robustness of the design.

[0019] This invention develops a dedicated three-dimensional image generation method for the specific mathematical structure of the three-period minimal surface. It can flexibly generate three-dimensional structural images of various types of TPMS, such as Gyroid, SchwarzP, SchwarzD, Neovius, and IWP. By adjusting the period parameters, phase parameters, and amplitude parameters, it can precisely control the aperture distribution, specific surface area, and channel connectivity, thereby achieving refined design of the microstructure of the stationary phase.

[0020] This invention automatically finds the Pareto optimal trade-off between column efficiency and back pressure through an adaptive optimization module, providing users with a set of optimization schemes at the Pareto front to choose from, meeting the differentiated requirements of chromatographic performance for different application scenarios. Compared with the single optimal solution of traditional methods, it has stronger practicality and flexibility. Attached Figure Description

[0021] Figure 1 This is a schematic diagram of the overall structure of the automatic optimization and simulation system for three-period minimal surface chromatography structural parameters of the present invention.

[0022] Figure 2 This is a schematic diagram of the structure of the three-dimensional structure image generation module of the present invention.

[0023] Figure 3 This is a schematic diagram of the structure of the visualization simulation and image analysis module of the present invention.

[0024] Figure 4 This is a schematic diagram of the adaptive optimization module of the present invention.

[0025] Figure 5 This is a schematic diagram of the closed-loop feedback control module of the present invention. Detailed Implementation

[0026] The present invention will now be described in further detail with reference to the accompanying drawings and specific embodiments.

[0027] like Figure 1As shown, the automatic optimization and simulation system for three-period minimal surface chromatographic structural parameters of the present invention includes a three-dimensional structural image generation module 1, a visualization simulation and image analysis module 2, an adaptive optimization module 3, and a closed-loop feedback control module 4. These four modules achieve deep coupling and collaborative work through data interfaces and control interfaces, forming a complete closed loop of three-dimensional image generation → visualization simulation → intelligent optimization → parameter feedback.

[0028] The 3D structure image generation module 1 is used to generate a 3D mesh image model based on the implicit function equation of a three-period minimal surface. For example... Figure 2 As shown, the three-dimensional structure image generation module 1 includes an implicit function parsing unit 11, a topological feature control unit 12, and a three-dimensional mesh image rendering unit 13.

[0029] Implicit function analytic unit 11 stores implicit function equations for various types of three-period minimal surfaces. These equations represent the mathematical expression of the TPMS three-dimensional structure image. For the Gyroid-type three-period minimal surface, its implicit function equation is: ,in, The wavenumber parameter controls the spatial periodicity of the surface. The threshold parameter controls the geometry of the surface. , , These are three-dimensional spatial coordinates. By adjusting... and The value of can be used to generate three-dimensional structural images of Gyroids with different pore sizes and porosities. In a preferred embodiment, The range of values ​​is to ,in For single cell size, The value range is from -0.5 to 0.5. For a Schwarz P-type three-period minimum surface, its implicit function equation is: For a Schwarz D-type three-period minimum surface, its implicit function equation is:

[0030] .

[0031] For a Neovius-type three-period minimum surface, its implicit function equation is: For an IWP-type three-periodic minimum surface, its implicit function equation is:

[0032] .

[0033] The implicit function parsing unit 11 calls the corresponding implicit function equation according to the TPMS type selected by the user and passes the equation parameters to the topology feature control unit 12.

[0034] The topology feature control unit 12 adjusts the parameters in the implicit function equation according to the target chromatographic performance requirements. Specifically, the topology feature control unit 12 receives the target porosity and target specific surface area as inputs, and calculates the wavenumber parameter and threshold parameter inversely using the following relationship. There is a monotonic relationship between porosity and the threshold parameter; for the Gyroid structure, this relationship can be approximated by numerical integration. When... As the porosity changes from negative to positive values, it gradually decreases from nearly 100%. The topology feature control unit 12 incorporates porosity-threshold parameter lookup tables for different TPMS types, quickly determining the threshold parameter corresponding to the target porosity through interpolation. Specific surface area is related to both the wavenumber parameter and the threshold parameter. Under a fixed threshold parameter, the specific surface area is directly proportional to the wavenumber parameter, i.e. The topology feature control unit 12 calculates the required wavenumber parameters based on the target specific surface area and the determined threshold parameters.

[0035] In one embodiment of the present invention, for the chromatographic stationary phase used for protein separation, the target pore size range is set to 10 nm to 100 nm, corresponding to a target porosity of 60% to 80% and a target specific surface area of ​​100 m². 2 / g to 300m 2 / g. The topology feature control unit 12 determines the wavenumber parameters of the Gyroid-type TPMS based on these target values. Threshold parameter .

[0036] The 3D mesh image rendering unit 13 receives the adjusted implicit function equation parameters and discretizes the continuous implicit function surface into a 3D mesh image model. This unit uses a traveling cube algorithm to traverse sampling points in 3D space, determining whether each voxel intersects with the implicit function surface. For intersecting voxels, triangular facet reconstruction is performed, ultimately generating a complete 3D mesh image model. The mesh density is adaptively adjusted according to the target image accuracy. For high-precision simulation requirements, the mesh cell size is set to... to For rapid assessment of requirements, the grid cell size can be relaxed to [specific size]. to The 3D mesh image model is output in standard STL or STEP format and can be directly imported into the visualization simulation and image analysis module 2.

[0037] The visualization simulation and image analysis module 2 receives the three-dimensional candidate structure image generated by the three-dimensional structure image generation module 1, performs coupled simulation of fluid dynamics and mass transfer dynamics on it, generates a visualization image, and predicts chromatographic performance indicators. For example... Figure 3As shown, the visualization simulation and image analysis module 2 includes a flow field image rendering unit 21, a concentration field image calculation unit 22, and a performance image evaluation unit 23.

[0038] The flow field image rendering unit 21 solves for the velocity and pressure fields within the 3D candidate structure image based on the Navier-Stokes equations and generates a visualization image of the flow field distribution. Within the typical flow velocity range of the chromatographic operation, the flow can be considered as incompressible laminar or low Reynolds number turbulent flow. For laminar flow, the governing equations are the continuity equation and the momentum conservation equation: , ,in, It is a velocity vector. For fluid density, For pressure, For dynamic viscosity, For time. Under steady-state conditions, the time derivative term is zero. The flow field image rendering unit 21 uses the finite volume method to numerically solve the above partial differential equations. The computational domain is divided into control volumes, and discretized algebraic equations are established for each control volume. Numerical solutions for the velocity field and pressure field are obtained through an iterative solver, and a streamline distribution visualization image is generated.

[0039] For turbulent flows at high velocities, the flow field image rendering unit 21 uses either the k-ε turbulence model or the k-ω turbulence model to close the Reynolds stress term. The k-ε model introduces turbulent kinetic energy. and turbulent kinetic energy dissipation rate Two additional transport equations are used to calculate turbulent viscosity by solving these equations, which in turn corrects the viscous term in the momentum equation.

[0040] The solution boundary conditions for the flow field image rendering unit 21 are set as follows: the inlet boundary uses a uniform velocity boundary condition, with the velocity value determined according to the actual flow rate of the chromatographic operation, typically ranging from 0.1 mm / s to 10 mm / s; the outlet boundary uses a pressure boundary condition, with the pressure set to atmospheric pressure; and the TPMS stationary phase surface uses a no-slip boundary condition, meaning the flow velocity on the solid surface is zero. The velocity field distribution image and pressure field distribution image output by the flow field image rendering unit 21 are used to calculate the back pressure of the chromatographic column and as input to the concentration field image calculation unit 22.

[0041] The concentration field image calculation unit 22 calculates the concentration distribution of the solute within the three-dimensional candidate structure image based on the convection-diffusion equation, generating a concentration distribution image. During chromatographic separation, solute molecules move with the fluid in the mobile phase (convection), while simultaneously diffusing under the drive of the concentration gradient, and undergoing adsorption and desorption on the surface of the stationary phase. The general form of the convection-diffusion equation is:

[0042] ,in, This refers to the solute concentration. The molecular diffusion coefficient is represented by the first term on the left-hand side of the equation, which is the rate of change of concentration over time. The second term is the convection term, and the right-hand side is the diffusion term. The concentration field image calculation unit 22 uses the finite element method or the finite volume method to discretize and solve the equation. The time discretization adopts an implicit difference scheme to ensure numerical stability.

[0043] On the surface of the TPMS stationary phase, solutes undergo adsorption, a process described by surface boundary conditions. Commonly used adsorption models include the Langmuir adsorption isotherm and the Freundlich adsorption isotherm. For Langmuir adsorption, the relationship between surface adsorption and solution concentration is:

[0044] ,in, This represents the maximum adsorption capacity. The Langmuir adsorption constant is given. The concentration field image calculation unit 22 obtains the spatiotemporal evolution process of solute concentration and generates a concentration distribution image by iteratively solving the convection-diffusion equation in the bulk phase and the adsorption kinetic equation on the surface.

[0045] In one embodiment of the present invention, for the separation of small molecule drugs in reversed-phase chromatography, the molecular diffusion coefficient is taken as a value of m 2 / s, the Langmuir adsorption constant is determined based on the hydrophobicity of the drug, with a typical value of [value missing]. to L / mol, the maximum adsorption capacity is taken as mol / m 2 The concentration field image calculation unit 22 simulates the propagation process of the solute peak under pulse injection conditions, and obtains the concentration-time curve image at the column outlet, i.e., the chromatographic peak image.

[0046] The performance image evaluation unit 23 calculates the chromatographic performance indicators of the three-dimensional candidate structure image based on the output results of the flow field image rendering unit 21 and the concentration field image calculation unit 22. The main performance indicators include:

[0047] Column efficiency (theoretical plate number): Characterizes the degree of dispersion of solute peaks by the chromatographic column, calculated from the retention time and peak width of the chromatographic peak images. Alternatively, the half-peak width can be used for calculation: ,in, The baseline width of the chromatographic peak. The peak width is half the normal. Higher column efficiency indicates a sharper peak and better separation performance. The theoretical plate number of a high-performance liquid chromatography column is typically between [value missing]. to scope.

[0048] Resolution: Characterizes the degree of separation between two adjacent chromatographic peak images, and is calculated using the following formula: ,in, and The retention time for the two peaks. and This represents the baseline width of the two peaks. It is generally considered... The two peaks can be separated by baseline.

[0049] Back pressure: This is the pressure difference between the column inlet and outlet, directly output by the flow field image rendering unit 21. Back pressure is directly proportional to the flow rate and inversely proportional to the permeability of the stationary phase. Excessive back pressure places higher pressure resistance requirements on the chromatography system, increasing equipment costs and energy consumption.

[0050] Peak symmetry factor: Characterizes the degree of tailing in chromatographic peak images, and is calculated using the following formula: .

[0051] in, and These represent the widths of the first and second halves of the peak at 10% of its height, respectively. An ideal symmetrical peak. In reality, chromatographic peaks often exhibit a certain degree of tailing. A value between 0.9 and 1.2 is considered acceptable.

[0052] The performance image evaluation unit 23 summarizes these performance indicators to form a performance evaluation vector, which is then output to the adaptive optimization module 3.

[0053] The adaptive optimization module 3 receives the performance evaluation vector and performs multi-objective optimization based on Riemannian geometry theory to find the Pareto optimal solution set of the three-dimensional structure image parameters. For example... Figure 4 As shown, the adaptive optimization module 3 includes an objective function construction unit 31, a Riemannian manifold mapping unit 32, and a gradient flow solution unit 33.

[0054] Objective function construction unit 31 transforms multiple chromatographic performance indicators into a multi-objective optimization problem. The core objective of chromatographic stationary phase design is to maintain high column efficiency (high... While reducing back pressure (low) There is an inherent contradiction between these two objectives: improving column efficiency usually requires increasing the specific surface area of ​​the stationary phase and reducing the pore size, which leads to increased flow resistance and back pressure. Therefore, the optimization problem can be formulated as a bi-objective optimization: , ,in, This is a 3D structural image parameter vector, including wavenumber parameters. Threshold parameters And TPMS type. Since the two objectives conflict with each other, there is no single solution that simultaneously optimizes both objective functions. Instead, there exists a set of Pareto optimal solutions, which constitute the Pareto front.

[0055] To facilitate the implementation of the optimization algorithm, objective function construction unit 31 transforms the bi-objective problem into a single-objective problem and constructs a composite objective function using a weighted sum method:

[0056] ,in, and Let be the weighting coefficient, satisfying , and This serves as a reference value, used to normalize performance indicators with different dimensions. By systematically changing the weighting coefficients, multiple solutions on the Pareto front can be obtained. In a preferred embodiment, Five optimization schemes are generated for users to choose from, with a step size of 0.1 within the range of 0.3 to 0.7.

[0057] The Riemannian manifold mapping unit 32 maps the parameter space and objective function space of the 3D structural image to a Riemannian manifold. Traditional Euclidean optimization assumes that the parameter space is flat and that the parameters are independent of each other; however, this assumption often fails in complex engineering problems. In reality, there are inherent relationships between different parameters in the TPMS 3D structural image. For example, the combination of wavenumber and threshold parameters determines porosity, which in turn affects specific surface area. This interdependence between parameters can be characterized by the metric tensor of the Riemannian manifold.

[0058] Riemannian map unit 32 defines a Riemannian metric in the parameter space. This metric is composed of a metric tensor. Given the elements of the metric tensor Indicates parameters and The correlation between them. In this invention, the metric tensor is constructed using the Fisher information matrix: ,in, For given parameters Performance observed under conditions The probability density function. The metric tensor reflects the degree of influence of parameter perturbations on performance, and the eigenvalues ​​and eigenvectors of the metric tensor give the intrinsic geometric structure of the parameter space.

[0059] Gradient flow solution unit 33 performs optimization search on the Riemannian manifold. Unlike the standard gradient in Euclidean space, the gradient on the Riemannian manifold needs to consider the curvature of the manifold. The relationship between the Riemannian gradient and the Euclidean gradient is as follows: ,in, Let be the inverse matrix of the metric tensor. This relationship shows that the Riemann gradient is the result of the Euclidean gradient modified by the metric tensor, and the modification takes into account the interdependencies between parameters.

[0060] Gradient flow solver 33 updates parameters using the natural gradient descent method: ,in, For learning rate, The natural gradient method has a faster convergence speed and better numerical stability than the standard gradient method, especially when there is a strong correlation between parameters. The natural gradient method can search along the optimal direction of the manifold, avoiding slow convergence in flat regions.

[0061] In one embodiment of the present invention, the parameter space for optimizing Gyroid-type TPMS three-dimensional structural images is: The objective function is a composite objective function. The initial parameters are set as follows: , Learning rate After 15 iterations, the system converged to the optimal parameters. , The corresponding column effect is The back pressure is 15MPa. Compared with the initial structure, the column efficiency is improved by 40%, while the back pressure only increases by 20%.

[0062] The closed-loop feedback control module 4 monitors the optimization process, determines the convergence state, and achieves automated iterative optimization. For example... Figure 5 As shown, the closed-loop feedback control module 4 includes a convergence judgment unit 41, a parameter feedback unit 42, and an image output unit 43.

[0063] The convergence determination unit 41 determines whether the optimization meets the convergence conditions. The convergence conditions include two aspects: the rate of change of the performance index is less than a threshold; and the number of iterations reaches the upper limit. For the first condition, the convergence determination unit 41 calculates the rate of change of the performance index for the current iteration and the previous iteration:

[0064] , If both conditions are met and If the optimization is successful, then the optimization is considered to have converged. and This is a preset convergence threshold. In a preferred embodiment, , The optimization is considered to have converged when the rate of change of column efficiency and back pressure is less than 1% and 2%, respectively. For the second condition, if the number of iterations reaches the preset maximum number of iterations (typically 50 to 100), the optimization process is forcibly terminated, and the current optimal solution is output.

[0065] When convergence fails, the parameter feedback unit 42 feeds back the optimized 3D structure parameters to the 3D structure image generation module 1. The parameter feedback uses a digital interface, and the optimized parameter vector is transmitted in a standard data format to the topology feature control unit 12 of the 3D structure image generation module 1. The topology feature control unit 12 receives the new parameters, adjusts the implicit function equations, and triggers the 3D mesh image rendering unit 13 to regenerate the 3D candidate structure image, initiating a new round of visualization simulation and optimization. This feedback mechanism ensures the automated operation of the system without manual intervention.

[0066] During optimization convergence, image output unit 43 outputs the optimal 3D structural image model, corresponding structural parameters, and performance indicators. The output includes: optimal TPMS type, wavenumber parameters, and threshold parameters; a 3D mesh image model file in STL or STEP format, directly usable for additive manufacturing; a performance evaluation image report, including numerical values ​​and comparative charts for indicators such as column efficiency, separation, back pressure, and peak symmetry; and, if multiple sets of weighting coefficients have been optimized, a Pareto front plot is output, demonstrating the trade-off between column efficiency and back pressure, allowing users to select the appropriate solution based on their specific needs.

[0067] In another embodiment of the invention, the system further includes a structural image comparison and analysis module, which is connected to the visualization simulation and image analysis module 2. This module is used to visually compare the performance of the TPMS three-dimensional structural image with that of a traditional packed bed column. Traditional packed bed columns are filled with spherical porous particles, typically with a particle diameter of 3 μm to 5 μm and a pore size of 10 nm to 30 nm. The structural image comparison and analysis module simulates a traditional packed bed column with the same column length and diameter, calculates its column efficiency and back pressure, and then compares it with the optimized TPMS three-dimensional structural image to generate a performance improvement comparison image report. The comparison results show that the optimized Gyroid-type TPMS stationary phase, under the same back pressure conditions, has a column efficiency 35% to 50% higher than that of a traditional packed bed column; or, under the same column efficiency conditions, a back pressure reduction of 25% to 40%. This performance advantage mainly stems from the continuous pore network and more uniform flow field distribution of the TPMS structure, reducing flow dead zones and eddy current losses.

[0068] The workflow of the system of this invention is as follows:

[0069] The user inputs basic information about the separation task, including the molecular weight, hydrophobicity, and target separation degree of the target compound. Based on this information, the system initially determines the target pore size range and target specific surface area.

[0070] The 3D structure image generation module 1 selects an appropriate TPMS type based on the target parameters, sets the initial wavenumber parameters and threshold parameters, and generates an initial 3D candidate structure image.

[0071] The visualization simulation and image analysis module 2 performs flow field and mass transfer simulations on three-dimensional candidate structure images, generates visualization images, and calculates performance indicators such as column efficiency, separation degree, and back pressure.

[0072] The adaptive optimization module 3 calculates the gradient in the Riemannian manifold space based on the performance index, updates the three-dimensional structure image parameters, and generates a new combination of optimization parameters.

[0073] The closed-loop feedback control module 4 determines whether convergence has occurred. If convergence has not occurred, the new parameters are fed back to the 3D structure image generation module 1, and the above steps are repeated. If convergence has occurred, the optimal 3D structure image model and performance report are output.

[0074] Users can view the optimization results and choose to export a 3D mesh image model file for additive manufacturing, or adjust the optimization target weights and rerun the optimization.

[0075] Through the above process, the system of the present invention realizes fully automated design from separation requirement input to optimal three-dimensional structure image output, shortening the traditional chromatographic stationary phase development cycle from 6 months to 2 months, significantly reducing R&D costs, and improving the design's relevance and success rate.

[0076] The technical solution of this invention fully embodies the deep coupling and synergistic effect among the four core modules: the output of the 3D structure image generation module 1 is the input of the visualization simulation and image analysis module 2, establishing parameter-level coupling; the performance evaluation result of the visualization simulation and image analysis module 2 is the input of the adaptive optimization module 3, establishing state-level coupling; the parameter update of the adaptive optimization module 3 is fed back to the 3D structure image generation module 1 through the closed-loop feedback control module 4, establishing logic-level coupling and reverse feedback; the entire system forms a complete closed loop of forward transmission → performance evaluation → reverse feedback → parameter adjustment, realizing the synergistic effect of adaptive adjustment. This mutual promotion, superposition effect, and adaptive adjustment among the modules make the overall performance of the system far exceed the simple superposition of the modules working independently, reflecting the nonlinear synergistic characteristic of 1+1>2.

[0077] The above description is only a preferred embodiment of the present invention. For those skilled in the art, various modifications and improvements can be made based on the technical solutions and concepts of the present invention, and these modifications and improvements should all fall within the protection scope of the present invention.

Claims

1. An automatic optimization and simulation system for three-period minimal surface chromatographic structural parameters, characterized in that, include: A three-dimensional structure image generation module is used to construct a three-dimensional mesh image model based on the implicit function equation of a three-period minimal surface. The three-dimensional structure image generation module controls the aperture distribution, specific surface area and channel connectivity of the three-dimensional mesh image model by adjusting the period parameter, phase parameter and amplitude parameter, and generates three-dimensional candidate structure images with different topological features. A visualization simulation and image analysis module, connected to the three-dimensional structure image generation module, is used to receive the three-dimensional candidate structure image and perform flow field visualization rendering and concentration field image analysis on it. The visualization simulation and image analysis module includes: The flow field image rendering unit is used to solve the velocity field distribution image and pressure field distribution image within the three-dimensional candidate structure image based on the Navier-Stokes equation. The flow field image rendering unit uses the finite volume method to discretize and solve the flow control equation, generating a streamline distribution visualization image and pressure drop data image within the three-dimensional structure. A concentration field image calculation unit, connected to the flow field image rendering unit, is used to solve for the concentration distribution image of the solute in the three-dimensional candidate structure image based on the convection-diffusion equation. The concentration field image calculation unit generates a chromatographic peak broadening image characterizing the coupling effect of flow mass transfer and surface adsorption. The performance image evaluation unit, connected to the flow field image rendering unit and the concentration field image calculation unit, is used to calculate the column efficiency, resolution, back pressure, and peak symmetry of the three-dimensional candidate structure image based on the velocity field distribution image, the pressure field distribution image, and the concentration distribution image. The column efficiency is determined by analyzing the theoretical plate number of the chromatographic peak image, and the resolution is determined by calculating the ratio of the peak spacing to the peak width of adjacent chromatographic peak images. The visualization simulation and image analysis module generates chromatographic performance evaluation image data by rendering streamline distribution and calculating concentration gradient images from three-dimensional mesh images. The chromatographic performance evaluation image data includes flow field distribution images, concentration distribution images and their corresponding column efficiency, resolution, back pressure and peak symmetry values. An adaptive optimization module, connected to the visualization simulation and image analysis module, is used to receive the chromatographic performance evaluation image data and determine the parameter optimization direction of the three-dimensional structure image based on the gradient flow algorithm on the Riemann manifold. The adaptive optimization module includes: The objective function construction unit is used to transform multiple chromatographic performance image indicators into objective functions for a multi-objective optimization problem. The objective function includes a first sub-objective of maximizing column efficiency and a second sub-objective of minimizing back pressure. The objective function construction unit uses a weighted sum method to transform the bi-objective problem into a single-objective composite objective function and obtains multiple solutions on the Pareto front by changing the weighting coefficients. The Riemann manifold mapping unit, connected to the objective function construction unit, is used to map the three-dimensional structural image parameter space and the objective function space to the Riemann manifold, and to define a metric tensor on the Riemann manifold. The metric tensor is constructed through the Fisher information matrix and reflects the influence weight of different three-dimensional image parameters on chromatographic performance. The gradient flow solving unit, connected to the Riemann manifold mapping unit, is used to calculate the Riemann gradient of the objective function on the Riemann manifold. The gradient flow solving unit uses the natural gradient method to correct the Euclidean gradient. The corrected gradient direction takes into account the interdependence between the three-dimensional structure image parameters. The three-dimensional structure image parameters are updated along the corrected gradient descent direction to generate the Pareto optimal solution set. The adaptive optimization module maps multiple performance indicators to the Riemannian manifold space, searches for the Pareto optimal solution set along the gradient descent direction in the manifold space, and generates an optimized combination of three-dimensional structural parameters. A closed-loop feedback control module is connected to the adaptive optimization module and the three-dimensional structure image generation module. The closed-loop feedback control module includes: The convergence judgment unit is used to determine whether the chromatographic performance evaluation image data meets the convergence condition. If the absolute value of the difference between the column efficiency value of the current iteration and the column efficiency value of the previous iteration is less than the preset column efficiency convergence threshold, and the absolute value of the difference between the back pressure value of the current iteration and the back pressure value of the previous iteration is less than the preset back pressure convergence threshold, then the image optimization is determined to be converged. A parameter feedback unit, connected to the convergence judgment unit, is used to feed back the optimized three-dimensional structure parameter combination to the three-dimensional structure image generation module when convergence fails. The three-dimensional structure image generation module generates a new three-dimensional candidate structure image based on the optimized three-dimensional structure parameter combination. The image output unit, connected to the convergence judgment unit, is used to output the optimal three-dimensional structure image model and its corresponding structural parameters and performance indicators when the image optimization converges.

2. The automatic optimization and simulation system for three-period minimal surface chromatographic structure parameters according to claim 1, characterized in that, The three-dimensional structure image generation module includes: The implicit function analytic unit is used to store implicit function equations for various types of three-period minimal surfaces, including Gyroid, SchwarzP, SchwarzD, Neovius, and IWP types. A topology feature control unit, connected to the implicit function analysis unit, is used to adjust the periodic parameter and amplitude parameter in the implicit function equation according to the target porosity and target specific surface area. The periodic parameter controls the spatial periodicity of the three-dimensional image, and the amplitude parameter controls the curvature of the three-dimensional surface image. A three-dimensional mesh image rendering unit, connected to the topological feature control unit, is used to discretize the adjusted implicit function equation into a three-dimensional mesh image model, wherein the mesh density of the three-dimensional mesh image model is adaptively adjusted according to the accuracy of the target image.

3. The automatic optimization and simulation system for three-period minimal surface chromatographic structure parameters according to claim 1, characterized in that, The system also includes: The structural image comparison and analysis module, connected to the visualization simulation and image analysis module, is used to visually compare the performance indicators of the three-dimensional candidate structural images with the performance indicators of traditional packed bed chromatography columns, and generate a performance improvement comparison image report.

4. The automatic optimization and simulation system for three-period minimal surface chromatographic structure parameters according to claim 2, characterized in that, When adjusting the implicit function equation, the topological feature control unit determines the target aperture range based on the molecular size of the target separation task, and calculates the value of the periodic parameter in reverse according to the target aperture range to generate the corresponding three-dimensional mesh image parameters.

5. The automatic optimization and simulation system for three-period minimal surface chromatographic structural parameters according to claim 1, characterized in that, When generating flow field distribution images by solving the Navier-Stokes equations, the flow field image rendering unit uses a turbulence model to correct for high Reynolds number flows. The turbulence model is either a k-ε model or a k-ω model.

6. The automatic optimization and simulation system for three-period minimal surface chromatographic structural parameters according to claim 1, characterized in that, When calculating the solute concentration distribution image, the concentration field image calculation unit considers the adsorption kinetics of the three-period minimum surface stationary phase, which is described by Langmuir adsorption isotherms or Freundlich adsorption isotherms.

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