A method and device for determining cof structure combining xrd data and artificial intelligence

By combining XRD data with an artificial intelligence particle swarm optimization algorithm, the problems of dependence on high-quality single crystals and low success rate of complex system analysis in COF crystal structure determination were solved, achieving efficient and accurate COF structure determination.

CN122135838APending Publication Date: 2026-06-02YTO TECHNOLOGY (WUXI) CO LTD

Patent Information

Authority / Receiving Office
CN · China
Patent Type
Applications(China)
Current Assignee / Owner
YTO TECHNOLOGY (WUXI) CO LTD
Filing Date
2026-02-26
Publication Date
2026-06-02

AI Technical Summary

Technical Problem

Existing techniques for determining the crystal structure of COF rely on high-quality single crystals. Powder XRD analysis suffers from low precision, low efficiency, high cost, and low success rate in analyzing complex systems, making it difficult to meet the requirements of high efficiency and accuracy in materials research and development.

Method used

By combining XRD data and artificial intelligence, an initial COF candidate structure is constructed using a particle swarm optimization algorithm. A theoretical XRD pattern is generated using crystallographic calculation tools. A fitness function is defined for iterative optimization until convergence, and the final crystal structure is output.

Benefits of technology

It can complete structural analysis without the need for high-quality single crystals, improving analysis efficiency and accuracy, adapting to complex systems, reducing costs, and providing reliable structural support.

✦ Generated by Eureka AI based on patent content.

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Abstract

This invention discloses a method and apparatus for determining the structure of covalent organic frameworks (COFs) by combining XRD data and artificial intelligence. The method collects information on COF precursors and inputs it into an AI model. A particle swarm optimization heuristic algorithm is used to construct and screen effective COF candidate structures in a global search space. Using crystallographic calculation tools, bond lengths and bond angles are calculated and theoretical XRD patterns are simulated by combining the atomic coordinates, unit cell parameters, and space group information of the effective COF candidate structures. Combining experimental real XRD patterns and the average bond lengths and bond angles from the COF database, a fitness function is defined and calculated to quantify structural differences. Based on the fitness function value, the algorithm iteratively adjusts the structural parameters to generate new structures. This process is repeated until the function value converges or the maximum number of iterations is reached. The structure that meets the conditions is output as the final crystal structure of the target COF. This invention solves the problems of low efficiency, high cost, and low success rate in resolving complex systems in existing technologies.
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Description

Technical Field

[0001] This invention relates to the field of covalent organic framework (COF) structure determination technology, specifically to a method and apparatus for determining COF structure by combining XRD data and artificial intelligence. Background Technology

[0002] Covalent organic frameworks (COFs) are a class of crystalline porous materials formed by organic molecules linked by covalent bonds. Due to their tunable pore structure, large specific surface area, and excellent chemical stability, they have shown broad application prospects in many fields such as gas adsorption and separation, heterogeneous catalysis, chemical sensing, energy storage, and drug carrier design, becoming a research hotspot in materials science. To achieve targeted design and performance optimization of COF materials, accurately determining their crystal structure is a core prerequisite. Currently, the industry mainly relies on X-ray diffraction technology combined with crystallographic analysis to conduct COF structure analysis. Although artificial intelligence technology has shown potential in the field of material structure prediction, it has not yet been widely and maturely applied to the determination of COF crystal structures.

[0003] Current techniques for determining the crystal structure of COFs still face numerous unresolved issues, failing to meet the demands for efficiency and accuracy in materials research and development. Firstly, while traditional X-ray single-crystal diffraction is a common method for crystal structure analysis, the strong covalent bonds in COFs make it difficult to prepare high-quality, large-size single crystals, severely limiting the application of this technique. Secondly, powder X-ray diffraction has become an alternative characterization method, but this technique compresses three-dimensional crystallographic information into one-dimensional data, failing to effectively determine cell parameters or distinguish similar topological structures. The analysis of complex conformations is challenging and the results are uncertain. Thirdly, existing structural analysis methods, whether involving repeated attempts at single-crystal preparation or combining extensive experimental information analysis such as electron diffraction, are time-consuming, labor-intensive, and costly, hindering high-throughput and automated analysis and severely impeding the rapid research and industrial application of COF materials. Fourthly, while existing techniques are effective for analyzing COF structures with known topologies or simple systems, their success rate is extremely low when dealing with novel topologies, complex frameworks, or COF systems with interpenetrating properties, failing to meet the research and development needs of novel COF materials.

[0004] Therefore, there is an urgent need for a COF structure determination method that combines XRD data and artificial intelligence to solve the problems of low efficiency, high cost, and low success rate in analyzing complex systems in existing technologies. Summary of the Invention

[0005] To address these issues, this invention provides a method and apparatus for determining the structure of COFs by combining XRD data and artificial intelligence, thereby solving the problems of existing COF crystal structure determination technologies, such as reliance on high-quality single crystals, low accuracy, low efficiency, high cost, and low success rate in determining complex systems.

[0006] To achieve the above objectives, the present invention provides the following technical solution: a method for determining COF structure by combining XRD data and artificial intelligence, characterized in that it includes:

[0007] Precursor information of covalent organic frameworks (COFs) is collected by setting up a resource library, and the precursor information is input into the AI ​​model;

[0008] Based on the precursor information, an initial COF candidate structure is constructed in the global search space using a particle swarm optimization heuristic optimization algorithm, and the initial COF candidate structure is screened to obtain an effective COF candidate structure.

[0009] Using crystallographic calculation tools, combined with the atomic coordinates, unit cell parameters and space group information of the effective COF candidate structure, the bond length and bond angle parameters corresponding to the effective COF candidate structure are calculated, and theoretical XRD patterns are generated by simulation.

[0010] Based on the theoretical XRD patterns, the bond lengths and bond angles, and combined with the experimentally obtained real XRD patterns and the average bond lengths and average bond angles in the COF database, a fitness function is defined and calculated to obtain the fitness function value; the difference between the effective COF candidate structure and the real COF structure is quantified through the fitness function.

[0011] Based on the fitness function value, the parameters of the effective COF candidate structures are iteratively adjusted using the particle swarm optimization heuristic optimization algorithm to generate new COF candidate structures. XRD simulation, bond length, bond angle and fitness function are performed on the new COF candidate structures until the fitness function value converges or the maximum number of iterations is reached. The iteration is then stopped, and the COF candidate structures that meet the convergence conditions are output as the final crystal structure of the target COF.

[0012] As a preferred embodiment of a COF structure determination method combining XRD data and artificial intelligence, the precursor information includes: chemical structure information, preliminary unit cell parameters, and space group information of the organic molecular building blocks; the chemical structure information of the organic molecular building blocks includes: chemical formula, atomic coordinates, and bond connectivity; the atomic coordinates are three-dimensional Cartesian coordinates or fractional coordinates; the bond connectivity is represented by an adjacency matrix; the preliminary unit cell parameters include: unit cell axis length and unit cell axis angle; and the space group information is represented by international symbols.

[0013] As a preferred approach to COF structure determination combining XRD data and artificial intelligence, in the process of constructing the initial COF candidate structure, the translation vectors and rotation parameters of all non-equivalent organic molecular building blocks within the unit cell are integrated into a high-dimensional parameter vector to characterize the initial COF candidate structure; the translation vector is the three-dimensional Cartesian coordinates or fractional coordinates of the geometric center of the organic molecular building block within the unit cell; the rotation parameter is a rotation matrix or Euler angles.

[0014] As a preferred method for determining the COF structure by combining XRD data and artificial intelligence, during the simulation generation of the theoretical XRD pattern, the diffraction peak intensity is calculated using the structure factor calculation formula based on the proportional relationship between diffraction peak intensity and the square of the structure factor modulus. The structure factor calculation formula is as follows:

[0015]

[0016] In the formula, For structural factors; For the first The occupancy rate of each atom; N is the total number of atoms in the unit cell; Let be the atomic scattering factor of the j-th atom; , , is the fractional coordinate of the j-th atom in the unit cell; h, k, l are the crystal plane indices; i is the imaginary unit.

[0017] As a preferred embodiment of a COF structure determination method combining XRD data and artificial intelligence, the fitness function value is calculated using the following formula:

[0018]

[0019] In the formula, The fitness function value; Let be the bond length of the i-th chemical bond in the constructed COF candidate structure; The average bond length of chemical bonds of the same type in the COF database; Let J be the bond angle of the j-th chemical bond in the constructed COF candidate structure; The average bond angle of the same type of chemical bond in the COF database; The diffraction angle is The intensity of the diffraction peaks obtained from the time simulation; The diffraction angle is The intensity of the diffraction peaks measured in the experiment.

[0020] As a preferred scheme for COF structure determination method combining XRD data and artificial intelligence, when iteratively adjusting the COF candidate structure parameters through the particle swarm optimization heuristic optimization algorithm, each COF candidate structure is treated as a particle, and the high-dimensional parameter vector representing the COF candidate structure is updated through velocity update formula and position update formula.

[0021] The expression for the speed update formula is:

[0022]

[0023] In the formula, Let be the velocity of particle k in the (t+1)th iteration; Let be the velocity of particle k in the t-th iteration; Inertial weight; , As an acceleration factor; , Let be a random number in the range [0,1]. This is the best position found so far for particle k; This is the best global position found for all particles to date. Let K be the position of particle k in the t-th iteration;

[0024] The expression for the position update formula is:

[0025]

[0026] In the formula, Let be the position of particle k in the (t+1)th iteration.

[0027] This invention also provides a COF structure determination apparatus combining XRD data and artificial intelligence, employing the above-mentioned COF structure determination method combining XRD data and artificial intelligence, including:

[0028] The precursor information collection and input module is used to collect precursor information of covalent organic frameworks (COFs) by setting a resource library, and input the precursor information into the AI ​​model;

[0029] The initial COF candidate structure construction and screening module is used to construct an initial COF candidate structure in the global search space based on the precursor information using a particle swarm optimization heuristic optimization algorithm, and to screen the initial COF candidate structure to obtain an effective COF candidate structure.

[0030] The bond length and bond angle calculation and theoretical XRD pattern simulation module is used to calculate the bond length and bond angle parameters corresponding to the effective COF candidate structure by using crystallographic calculation tools and combining the atomic coordinates, unit cell parameters and space group information of the effective COF candidate structure, and to simulate and generate theoretical XRD patterns.

[0031] The fitness function value calculation module is used to define and calculate the fitness function based on the theoretical XRD pattern, the bond length and the bond angle, combined with the experimentally obtained real XRD pattern and the average bond length and average bond angle in the COF database, to obtain the fitness function value; and to quantify the difference between the effective COF candidate structure and the real COF structure through the fitness function.

[0032] The final crystal structure acquisition module is used to iteratively adjust the parameters of the effective COF candidate structures based on the fitness function value using the particle swarm optimization heuristic optimization algorithm and generate new COF candidate structures; perform XRD simulation, bond length, bond angle and fitness function iterative calculation on the new COF candidate structures until the fitness function value converges or the maximum number of iterations is reached, stop the iteration, output the COF candidate structures that meet the convergence conditions, and use them as the final crystal structure of the target COF.

[0033] As a preferred embodiment of a COF structure determination device combining XRD data and artificial intelligence, the precursor information collection and input module includes: chemical structure information, preliminary unit cell parameters, and space group information of the organic molecular building blocks; the chemical structure information of the organic molecular building blocks includes: chemical formula, atomic coordinates, and bond connectivity; the atomic coordinates are three-dimensional Cartesian coordinates or fractional coordinates; the bond connectivity is represented by an adjacency matrix; the preliminary unit cell parameters include: unit cell axis length and unit cell axis angle; and the space group information is represented by international symbols.

[0034] As a preferred embodiment of a COF structure determination device combining XRD data and artificial intelligence, in the initial COF candidate structure construction and screening module, during the construction of the initial COF candidate structure, the translation vectors and rotation parameters of all non-equivalent organic molecular building units within the unit cell are integrated into a high-dimensional parameter vector to characterize the initial COF candidate structure; the translation vector is the three-dimensional Cartesian coordinates or fractional coordinates of the geometric center of the organic molecular building unit within the unit cell; the rotation parameter is a rotation matrix or Euler angles.

[0035] As a preferred embodiment of a COF structure determination device combining XRD data and artificial intelligence, the bond length and bond angle calculation and theoretical XRD pattern simulation module, during the simulation generation of the theoretical XRD pattern, calculates the diffraction peak intensity based on the proportional relationship between diffraction peak intensity and the square of the structure factor modulus using the structure factor calculation formula; the structure factor calculation formula is as follows:

[0036]

[0037] In the formula, For structural factors; For the first The occupancy rate of each atom; N is the total number of atoms in the unit cell; Let be the atomic scattering factor of the j-th atom; , , is the fractional coordinate of the j-th atom in the unit cell; h, k, l are the crystal plane indices; i is the imaginary unit.

[0038] As a preferred embodiment of a COF structure determination device combining XRD data and artificial intelligence, the fitness function value calculation module uses the following formula for calculating the fitness function value:

[0039]

[0040] In the formula, The fitness function value; Let be the bond length of the i-th chemical bond in the constructed COF candidate structure; The average bond length of chemical bonds of the same type in the COF database; Let J be the bond angle of the j-th chemical bond in the constructed COF candidate structure; The average bond angle of the same type of chemical bond in the COF database; The diffraction angle is The intensity of the diffraction peaks obtained from the time simulation; The diffraction angle is The intensity of the diffraction peaks measured in the experiment.

[0041] As a preferred embodiment of a COF structure determination device that combines XRD data and artificial intelligence, in the final crystal structure acquisition module, when iteratively adjusting the COF candidate structure parameters through the particle swarm optimization heuristic optimization algorithm, each COF candidate structure is treated as a particle, and the high-dimensional parameter vector characterizing the COF candidate structure is updated through velocity update formula and position update formula.

[0042] The expression for the speed update formula is:

[0043]

[0044] In the formula, Let be the velocity of particle k in the (t+1)th iteration; Let be the velocity of particle k in the t-th iteration; Inertial weight; , As an acceleration factor; , Let be a random number in the range [0,1]. This is the best position found so far for particle k; This is the best global position found for all particles to date. Let K be the position of particle k in the t-th iteration;

[0045] The expression for the position update formula is:

[0046]

[0047] In the formula, Let be the position of particle k in the (t+1)th iteration.

[0048] The present invention has the following advantages:

[0049] First, it does not require high-quality COF single crystals; structural analysis can be completed based on readily available powder XRD data, which greatly reduces the experimental requirements and broadens the scope of application of the technology.

[0050] Second, the particle swarm optimization algorithm is used as the core to realize the intelligent construction and iterative optimization of COF structure, improve the automation and intelligence level of structure analysis, and significantly improve analysis efficiency and reduce time and economic costs.

[0051] Third, by combining XRD diffraction data with multi-dimensional indicators such as bond length and bond angle, a fitness function is constructed to quantify structural differences. The analytical results are highly matched with the real structure at the atomic level, and the accuracy is significantly improved.

[0052] Fourth, it can effectively analyze novel topologies, complex skeletons, and complex COF systems with interpenetrating properties, solving the problem of low success rate in analyzing complex COF structures using traditional techniques, and adapting to the research and development needs of new COF materials.

[0053] Fifth, by fully integrating existing COF structure database resources and accurately comparing simulation data with experimental data, structural verification can be achieved. The analysis process is more universal and robust, providing reliable structural support for the directional design and performance optimization of COF materials. Attached Figure Description

[0054] To more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings in the following description are merely exemplary, and those skilled in the art can derive other embodiments based on the provided drawings without creative effort.

[0055] The structures, proportions, sizes, etc. illustrated in this specification are only for the purpose of assisting those skilled in the art in understanding and reading the content disclosed herein, and are not intended to limit the conditions under which the present invention can be implemented. Therefore, they have no substantial technical significance. Any modifications to the structure, changes in the proportions, or adjustments to the size, without affecting the effects and objectives that the present invention can produce, should still fall within the scope of the technical content disclosed in the present invention.

[0056] Figure 1 This is a flowchart illustrating a COF structure determination method combining XRD data and artificial intelligence provided in Embodiment 1 of the present invention.

[0057] Figure 2 This is a schematic diagram of the COF-300 molecular building blocks in a COF structure determination method combining XRD data and artificial intelligence provided in Embodiment 1 of the present invention.

[0058] Figure 3 This is a schematic diagram of the experimental and simulated spectra of COF-340 in one possible embodiment provided in Embodiment 1 of the present invention;

[0059] Figure 4 This is a schematic diagram of the fitness function and structural iterative changes of COF-300 in one possible embodiment provided in Embodiment 1 of the present invention;

[0060] Figure 5 This is a schematic diagram comparing the actual structure of COF-300 in one possible embodiment provided in Embodiment 1 of the present invention with the structure determined by the present invention;

[0061] Figure 6 This is a schematic diagram of the architecture of a COF structure determination device that combines XRD data and artificial intelligence, as provided in Embodiment 2 of the present invention. Detailed Implementation

[0062] The following specific embodiments illustrate the implementation of the present invention. Those skilled in the art can easily understand other advantages and effects of the present invention from the content disclosed in this specification. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0063] Example 1

[0064] See Figure 1 Embodiment 1 of the present invention provides a COF structure determination method combining XRD data and artificial intelligence, including the following steps:

[0065] S1. Obtain precursor information of covalent organic frameworks (COFs) by setting up a resource library, and input the precursor information into the AI ​​model;

[0066] S2. Based on the precursor information, an initial COF candidate structure is constructed in the global search space using a particle swarm optimization heuristic optimization algorithm, and the initial COF candidate structure is screened to obtain an effective COF candidate structure.

[0067] S3. Using crystallographic calculation tools, combined with the atomic coordinates, unit cell parameters and space group information of the effective COF candidate structure, calculate the bond length and bond angle parameters corresponding to the effective COF candidate structure, and simulate to generate theoretical XRD patterns.

[0068] S4. Based on the theoretical XRD pattern, the bond length, and the bond angle, combined with the experimentally obtained real XRD pattern and the average bond length and average bond angle in the COF database, define and calculate the fitness function to obtain the fitness function value; quantify the difference between the effective COF candidate structure and the real COF structure through the fitness function;

[0069] S5. Based on the fitness function value, the parameters of the effective COF candidate structure are iteratively adjusted using the particle swarm optimization heuristic optimization algorithm to generate a new COF candidate structure; XRD simulation, bond length, bond angle and fitness function are performed on the new COF candidate structure until the fitness function value converges or the maximum number of iterations is reached, the iteration is stopped, the COF candidate structure that meets the convergence condition is output and used as the final crystal structure of the target COF.

[0070] In this embodiment, in step S1, precursor information of covalent organic frameworks (COFs) is obtained by setting a resource library, and the precursor information is input into the AI ​​model.

[0071] Specifically, the system collects comprehensive information on COF precursors from multiple data sources, including experimental characterization databases, COF structure databases, publicly available crystallographic literature, and computational chemistry simulations. After collection, the standardized precursor information is uniformly input into the AI ​​model. This AI model, based on particle swarm optimization (PSO) or other heuristic optimization algorithms, provides a basic framework and crystallographic symmetry constraints for structure construction, ensuring the rationality and directionality of the structures constructed by the AI ​​algorithm.

[0072] The precursor information includes: chemical structure information, preliminary unit cell parameters, and space group information of the organic molecular building blocks; such as... Figure 2 As shown, these are the building blocks of the COF-300 molecular structure.

[0073] The chemical structure information of the organic molecular building blocks is a detailed chemical description of each organic molecular building block that makes up COF, and its characterization methods include, but are not limited to:

[0074] Chemical formula: For example, terephthalaldehyde is Triamine is The parameters include the type and number of atoms that make up each unit.

[0075] Atomic coordinates and bond connectivity: in three-dimensional Cartesian coordinates ( The precise positions of all atoms in each BU can be described using either adjacency matrices or fractional coordinates. Bond connectivity can be represented by an adjacency matrix. ) indicates that among them Represents atoms With atoms There must be chemical bonds present, otherwise These data are typically obtained through geometric optimization using computational chemistry software (such as Gaussian) to ensure reasonable bond lengths and bond angles.

[0076] In this embodiment, the preliminary unit cell parameters describe the size and shape of the repeating crystal units and can be obtained from preliminary XRD data through peak fitting and indexation processes (such as the initial stage of Le Bail refinement or Rietveld analysis). These mainly include:

[0077] Cell axis length: (Unit: Å)

[0078] Unit cell axis angle: (Unit: degree).

[0079] These parameters constitute the basic geometric framework of the COF periodic skeleton, which is crucial for limiting the spatial range of the structure built by AI models.

[0080] In this embodiment, the space group describes all symmetry operations within the crystal (such as translation, rotation, mirroring, inversion, etc.). It provides a strong constraint, significantly reducing the configuration space that AI needs to explore when constructing COF structures. Space groups are typically represented using international notation, for example:

[0081] (Hexagonal crystal system) (Monoclinic system) (Cubic crystal system) Correct space group information can be obtained through literature review, high-resolution electron microscopy, or trial and error. The AI ​​model will use these symmetry operations to replicate and arrange BUs, ensuring that the constructed COF structure meets crystallographic symmetry requirements.

[0082] In this embodiment, in step S2, based on the precursor information, an initial COF candidate structure is constructed in the global search space using a particle swarm optimization heuristic optimization algorithm, and the initial COF candidate structure is screened to obtain an effective COF candidate structure.

[0083] Specifically, this step uses the precursor information input in step S1 as a constraint to initiate a particle swarm optimization heuristic optimization algorithm to intelligently construct initial COF candidate structures. The algorithm uses the translation vectors and rotation parameters of the organic molecular building blocks as core optimization parameters to explore various possible topological structures and conformations in the global search space, generating a series of initial COF candidate structures. At the same time, the algorithm performs preliminary geometric screening on the generated initial structures, eliminating candidate structures with obvious abnormalities in bond lengths and bond angles, geometric properties that do not conform to crystallographic laws, or structural defects, and retaining structures with chemical feasibility and structural rationality as effective COF candidate structures, laying the foundation for subsequent simulation and optimization.

[0084] Among these, the position and orientation of each building unit (BU) in three-dimensional space are the core optimization parameters during COF structure construction. For the first... A BU, whose geometric state can be represented by the following set of parameters:

[0085] Translation vector: , represents the three-dimensional Cartesian or fractional coordinates of the reference point of BU (usually its geometric center) within the unit cell.

[0086] Rotation matrix or Euler angles: or , describes the rotation angle of BU relative to its initial or standard orientation, and controls its spatial orientation in the unit cell.

[0087] Therefore, the set of states of all BUs of a candidate COF structure can be represented as a high-dimensional parameter vector. ,in The number of non-equivalent BUs in the unit cell.

[0088] In this embodiment, in step S3, the bond length and bond angle parameters corresponding to the effective COF candidate structure are calculated by using crystallographic calculation tools, combined with the atomic coordinates, unit cell parameters and space group information of the effective COF candidate structure, and theoretical XRD patterns are generated by simulation.

[0089] Specifically, this step relies on professional crystallographic calculation tools such as Materials Studio and GSAS. Taking the effective COF candidate structure obtained in step S2 as the calculation object, it extracts its core crystallographic information such as atomic coordinates, unit cell parameters, and space group. Through the geometric analysis function of the tool, it accurately calculates the specific parameters of the bond length and bond angle of all chemical bonds in the candidate structure. At the same time, based on the basic principle of X-ray diffraction, it simulates and generates the theoretical XRD pattern corresponding to the effective COF candidate structure by combining the structure factor calculation formula, so as to realize the multi-dimensional crystallographic characterization of the candidate structure.

[0090] In the process of simulating and generating the theoretical XRD pattern, the diffraction peak intensity is calculated using the structure factor calculation formula, based on the proportional relationship between diffraction peak intensity and the square of the structure factor modulus. The structure factor calculation formula is as follows:

[0091]

[0092] In the formula, For structural factors; For the first The occupancy rate of each atom; N is the total number of atoms in the unit cell; Let be the atomic scattering factor of the j-th atom; , , is the fractional coordinate of the j-th atom in the unit cell; h, k, l are the crystal plane indices; i is the imaginary unit.

[0093] In one possible embodiment, such as Figure 3 The image shows the experimental spectrum (top) and the simulated spectrum (bottom) of COF-340.

[0094] In this embodiment, in step S4, based on the theoretical XRD pattern, the bond length and the bond angle, combined with the experimentally obtained real XRD pattern and the average bond length and average bond angle in the COF database, a fitness function is defined and calculated to obtain the fitness function value; the difference between the effective COF candidate structure and the real COF structure is quantified through the fitness function.

[0095] Specifically, firstly, combining the theoretical XRD patterns, bond lengths, and bond angles obtained in step S3, as well as the actual experimentally measured XRD patterns and the average bond lengths and average bond angles of similar chemical bonds in the COF structure database, a fitness function is constructed that includes bond length difference terms, bond angle difference terms, and XRD diffraction intensity difference terms. Subsequently, the above multi-dimensional data are substituted into the fitness function for calculation to obtain a specific fitness function value. The magnitude of this value enables a quantitative characterization of the difference between the effective COF candidate structure and the actual COF structure. The larger the function value, the greater the structural difference, and vice versa, the higher the matching degree, providing a clear judgment basis for subsequent iterative optimization.

[0096] The formula for calculating the fitness function value is as follows:

[0097]

[0098] In the formula, The fitness function value; Let be the bond length of the i-th chemical bond in the constructed COF candidate structure; The average bond length of chemical bonds of the same type in the COF database; Let J be the bond angle of the j-th chemical bond in the constructed COF candidate structure; The average bond angle of the same type of chemical bond in the COF database; The diffraction angle is The intensity of the diffraction peaks obtained from the time simulation; The diffraction angle is The intensity of the diffraction peaks measured in the experiment.

[0099] In this embodiment, in step S5, based on the fitness function value, the parameters of the effective COF candidate structure are iteratively adjusted using the particle swarm optimization heuristic optimization algorithm to generate a new COF candidate structure; XRD simulation, bond length, bond angle and fitness function iterative calculation are performed on the new COF candidate structure until the fitness function value converges or the maximum number of iterations is reached, the iteration stops, and the COF candidate structure that meets the convergence condition is output as the final crystal structure of the target COF.

[0100] Specifically, guided by the fitness function value obtained in step S4, the core parameters (translation vector, rotation parameters, cell parameters, etc.) of the effective COF candidate structures are iteratively adjusted using the same particle swarm optimization heuristic algorithm as in step S2, generating new COF candidate structures. The new candidate structures are then reintroduced into the processes of steps S3 and S4, sequentially completing XRD simulation, bond length and angle calculation, and fitness function value solving, forming a closed-loop iteration of "parameter adjustment - structural characterization - difference quantification." This iterative process continues until the fitness function value tends to stabilize and converge or reaches the preset maximum number of iterations. At this point, the COF candidate structure that meets the convergence condition is output as the final crystal structure of the target COF. This structure highly matches the real structure in terms of atomic level, topology, and pore characteristics, and can be directly used for COF material property prediction, performance evaluation, and functional design.

[0101] In the process of iteratively adjusting the COF candidate structure parameters using the particle swarm optimization heuristic optimization algorithm, each COF candidate structure is treated as a particle, and the high-dimensional parameter vector representing the COF candidate structure is updated using velocity update formula and position update formula.

[0102] The expression for the speed update formula is:

[0103]

[0104] In the formula, Let be the velocity of particle k in the (t+1)th iteration; Let be the velocity of particle k in the t-th iteration; Inertial weight; , As an acceleration factor; , Let be a random number in the range [0,1]. This is the best position found so far for particle k; This is the best global position found for all particles to date. Let K be the position of particle k in the t-th iteration;

[0105] The expression for the position update formula is:

[0106]

[0107] In the formula, Let be the position of particle k in the (t+1)th iteration.

[0108] In one possible embodiment, such as Figure 4 The figure shows a schematic diagram of the fitness function and structural iterative changes of COF-300. Figure 4(a) shows that as the number of algorithm iterations increases, the fitness function exhibits a significant decreasing trend and eventually converges. Figure 4 (b) intuitively shows that during this iteration process, the geometry of the COF-300 candidate structure gradually approaches the actual structure.

[0109] exist Figure 4 (a) The process of the fitness function decreasing and eventually converging is shown in the following steps:

[0110] Initial Stage: In the early stages of iteration, the COF structure explored by the algorithm may be far from the real structure, resulting in a high objective function value. Although the initial structure generated by AI through constraints such as precursor information and space groups has reasonableness, it still contains many uncertainties.

[0111] Rapid Decline Phase: As the number of iterations increases, AI algorithms (such as PSO) update the velocity and position of particles (i.e., COF candidate structures) based on the objective function value, and the structural parameters begin to adjust rapidly towards a better direction. In this phase, the fitness function curve exhibits a steep decline, indicating that the AI ​​model is efficiently eliminating the main biases in the structure, achieving large-scale structural rearrangement and optimization.

[0112] Convergence Phase: After a certain number of iterations, the rate of change of the fitness function slows down significantly, eventually stabilizing at a low value and forming a flat plateau. This indicates that the AI ​​algorithm has found a (or near) global optimum in the search space, meaning the difference between the constructed COF structure and the real structure has been minimized to a level that cannot be significantly improved through further iterations. At this point, the COF structure parameters have converged, and the structure resolution task is complete.

[0113] exist Figure 4 (b) The specific steps in the iterative process are as follows:

[0114] Initial iteration: At this stage, the COF-300 structure may exhibit a certain degree of disorder or irregular atomic arrangement. The relative positions and orientations of its molecular building blocks may deviate significantly from the ideal state, resulting in the blue and orange parts failing to connect into a complete framework.

[0115] Mid-term iteration: As the algorithm minimizes the objective function, the COF structure begins to self-correct. The bond lengths and bond angles between molecular building blocks gradually become more reasonable, and the overall framework begins to form a clear porous structure and periodic units. This stage corresponds to the rapid decrease in the fitness function in Figure (a).

[0116] Final convergence: After sufficient iterations, the COF structure reaches a highly ordered and precise state. Its geometry, bond connections, and cell arrangement are almost identical to the known real COF-300 structure, achieving high-precision atomic-level matching.

[0117] like Figure 5 The image shows a comparison between the actual COF-300 structure and the structure determined by this invention. The COF-300 structure determined by this invention and traced in green almost perfectly overlaps with the actual COF-300 structure (red). This demonstrates that this invention can accurately reproduce the true state of the material, whether in terms of atomic coordinates, bond connectivity, or overall topology and pore characteristics. At the atomic level, the atomic positions predicted by this invention show almost no deviation from the experimentally observed atomic positions. This proves that using the differences between simulated XRD data and actual XRD data, as well as bond lengths and bond angles, as objective functions for optimization can effectively drive the AI ​​algorithm to fine-tune the atomic configuration until a highly accurate match is achieved. COF structures typically have highly ordered but potentially complex pore and framework structures. The image clearly shows that even in three-dimensional complex materials like COF-300, this invention can accurately capture its unique cross-connections and periodic arrangements, effectively solving the challenge of accurately resolving complex crystal structures using traditional methods.

[0118] The application scenarios of this invention are as follows:

[0119] In the context of developing novel COF materials, this invention can provide researchers with a reliable method for determining crystal structures, and provide structural basis for the molecular design and performance regulation of COF materials.

[0120] In experimental research scenarios in materials science, this invention can rely on powder XRD data to complete COF structure analysis, reducing the requirements for experimental samples and equipment, and facilitating the efficient conduct of related experiments.

[0121] In the study of the catalytic performance of COF materials, this invention can determine the crystal structure of COF, providing structural support for studying the correlation between its pore structure, active sites and catalytic performance.

[0122] In the development of gas adsorption and separation materials, this invention can resolve the crystal structure of COF materials, providing a reference for designing COF adsorption and separation materials with specific pore characteristics.

[0123] In the research and development of energy storage materials, this invention can determine the structure of COF materials for energy storage, and help to study the structure-property relationship between structure and energy storage performance.

[0124] In the design of drug carrier materials, this invention can determine the crystal structure of COF materials, providing a structural basis for designing COF carrier materials that are suitable for drug molecule loading and release.

[0125] In the context of optimizing chemical catalytic processes, this invention can elucidate the structure of COF materials used in catalysis, providing support for optimizing the preparation process of COF-based catalysts and improving catalytic process efficiency.

[0126] In the technical research scenario of crystallographic structure analysis, this invention combines XRD data with artificial intelligence algorithms to provide new technical ideas and implementation methods for the structural analysis of porous crystal materials.

[0127] It should be noted that the method of this embodiment can be executed by a single device, such as a computer or server. The method of this embodiment can also be applied to a distributed scenario, where multiple devices cooperate to complete the task. In such a distributed scenario, one of these devices may execute only one or more steps of the method of this embodiment, and the multiple devices will interact with each other to complete the method described.

[0128] It should be noted that the above description describes some embodiments of this disclosure. Other embodiments are within the scope of the appended claims. In some cases, the actions or steps recorded in the claims can be performed in a different order than that shown in the above embodiments and still achieve the desired result. Furthermore, the processes depicted in the drawings do not necessarily require a specific or sequential order to achieve the desired result. In some embodiments, multitasking and parallel processing are also possible or may be advantageous.

[0129] Example 2

[0130] See Figure 6 Embodiment 2 of the present invention also provides a COF structure determination device combining XRD data and artificial intelligence, comprising:

[0131] The precursor information collection and input module 001 is used to collect and obtain precursor information of covalent organic frameworks (COFs) through a set resource library, and input the precursor information into the AI ​​model;

[0132] The initial COF candidate structure construction and screening module 002 is used to construct an initial COF candidate structure in the global search space based on the precursor information using a particle swarm optimization heuristic optimization algorithm, and to screen the initial COF candidate structure to obtain an effective COF candidate structure.

[0133] The bond length and bond angle calculation and theoretical XRD pattern simulation module 003 is used to calculate the bond length and bond angle parameters corresponding to the effective COF candidate structure by using crystallographic calculation tools, combined with the atomic coordinates, unit cell parameters and space group information of the effective COF candidate structure, and to simulate and generate theoretical XRD patterns.

[0134] The fitness function value calculation module 004 is used to define and calculate the fitness function based on the theoretical XRD pattern, the bond length and the bond angle, combined with the experimentally obtained real XRD pattern and the average bond length and average bond angle in the COF database, to obtain the fitness function value; and to quantify the difference between the effective COF candidate structure and the real COF structure through the fitness function.

[0135] The final crystal structure acquisition module 005 is used to iteratively adjust the parameters of the effective COF candidate structures and generate new COF candidate structures based on the fitness function value using the particle swarm optimization heuristic optimization algorithm; perform XRD simulation, bond length, bond angle and fitness function iterative calculation on the new COF candidate structures until the fitness function value converges or the maximum number of iterations is reached, stop the iteration, output the COF candidate structure that meets the convergence condition, and use it as the final crystal structure of the target COF.

[0136] In this embodiment, the precursor information collection and input module 001 includes the following: chemical structure information, preliminary unit cell parameters, and space group information of the organic molecular building blocks; the chemical structure information of the organic molecular building blocks includes: chemical formula, atomic coordinates, and bond connectivity; the atomic coordinates are three-dimensional Cartesian coordinates or fractional coordinates; the bond connectivity is represented by an adjacency matrix; the preliminary unit cell parameters include: unit cell axis length and unit cell axis angle; and the space group information is represented by international symbols.

[0137] In this embodiment, in the initial COF candidate structure construction and screening module 002, during the construction of the initial COF candidate structure, the translation vectors and rotation parameters of all non-equivalent organic molecule building units in the unit cell are integrated into a high-dimensional parameter vector to characterize the initial COF candidate structure; the translation vector is the three-dimensional Cartesian coordinates or fractional coordinates of the geometric center of the organic molecule building unit in the unit cell; the rotation parameter is a rotation matrix or Euler angles.

[0138] In this embodiment, in the bond length and bond angle calculation and theoretical XRD pattern simulation module 003, during the simulation of generating the theoretical XRD pattern, the diffraction peak intensity is calculated based on the proportional relationship between diffraction peak intensity and the square of the structure factor modulus, using the structure factor calculation formula; the structure factor calculation formula is:

[0139]

[0140] In the formula, For structural factors; For the first The occupancy rate of each atom; N is the total number of atoms in the unit cell; Let be the atomic scattering factor of the j-th atom; , , is the fractional coordinate of the j-th atom in the unit cell; h, k, l are the crystal plane indices; i is the imaginary unit.

[0141] In this embodiment, the fitness function value calculation formula in the fitness function value calculation module 004 is as follows:

[0142]

[0143] In the formula, The fitness function value; Let be the bond length of the i-th chemical bond in the constructed COF candidate structure; The average bond length of chemical bonds of the same type in the COF database; Let J be the bond angle of the j-th chemical bond in the constructed COF candidate structure; The average bond angle of the same type of chemical bond in the COF database; The diffraction angle is The intensity of the diffraction peaks obtained from the time simulation; The diffraction angle is The intensity of the diffraction peaks measured in the experiment.

[0144] In this embodiment, in the final crystal structure acquisition module 005, when iteratively adjusting the COF candidate structure parameters through the particle swarm optimization heuristic optimization algorithm, each COF candidate structure is treated as a particle, and the high-dimensional parameter vector characterizing the COF candidate structure is updated through the velocity update formula and the position update formula.

[0145] The expression for the speed update formula is:

[0146]

[0147] In the formula, Let be the velocity of particle k in the (t+1)th iteration; Let be the velocity of particle k in the t-th iteration; Inertial weight; , As an acceleration factor; , Let be a random number in the range [0,1]. This is the best position found so far for particle k; This is the best global position found for all particles to date. Let K be the position of particle k in the t-th iteration;

[0148] The expression for the position update formula is:

[0149]

[0150] In the formula, Let be the position of particle k in the (t+1)th iteration.

[0151] It should be noted that the information interaction and execution process between the modules of the above system are based on the same concept as the method embodiment in Embodiment 1 of this application, and the resulting technical effects are the same as those in the method embodiment of this application. For details, please refer to the description in the method embodiment shown above in this application, and it will not be repeated here.

[0152] Example 3

[0153] Embodiment 3 of the present invention provides a non-transitory computer-readable storage medium storing program code of a COF structure determination method combining XRD data and artificial intelligence. The program code includes instructions for executing the COF structure determination method combining XRD data and artificial intelligence of Embodiment 1 or any possible implementation thereof.

[0154] Computer-readable storage media can be any available medium that a computer can access, or a data storage device such as a server or data center that integrates one or more available media. The available medium can be magnetic media (e.g., floppy disks, hard disks, magnetic tapes), optical media (e.g., DVDs), or semiconductor media (e.g., solid-state drives (SSDs)).

[0155] Example 4

[0156] Embodiment 4 of the present invention provides an electronic device, including: a memory and a processor;

[0157] The processor and the memory communicate with each other via a bus; the memory stores program instructions that can be executed by the processor, and the processor can execute a COF structure determination method combining XRD data and artificial intelligence according to Embodiment 1 or any possible implementation thereof.

[0158] Specifically, a processor can be implemented in hardware or software. When implemented in hardware, the processor can be a logic circuit, an integrated circuit, etc. When implemented in software, the processor can be a general-purpose processor that reads software code stored in memory. This memory can be integrated into the processor or located outside the processor and exist independently.

[0159] In the above embodiments, implementation can be achieved, in whole or in part, through software, hardware, firmware, or any combination thereof. When implemented in software, it can be implemented, in whole or in part, as a computer program product. The computer program product includes one or more computer instructions. When the computer program instructions are loaded and executed on a computer, all or part of the processes or functions described in the embodiments of the present invention are generated. The computer can be a general-purpose computer, a special-purpose computer, a computer network, or other programmable system. The computer instructions can be stored in a computer-readable storage medium or transmitted from one computer-readable storage medium to another. For example, the computer instructions can be transmitted from one website, computer, server, or data center to another via wired (e.g., coaxial cable, fiber optic, digital subscriber line (DSL)) or wireless (e.g., infrared, wireless, microwave, etc.) means.

[0160] It is obvious to those skilled in the art that the modules or steps of the present invention described above can be implemented using general-purpose computing systems. They can be centralized on a single computing system or distributed across a network of multiple computing systems. Optionally, they can be implemented using program code executable by a computing system, thereby storing them in a storage system for execution by the computing system. In some cases, the steps shown or described can be performed in a different order than those presented herein, or they can be fabricated as separate integrated circuit modules, or multiple modules or steps can be fabricated as a single integrated circuit module. Thus, the present invention is not limited to any particular combination of hardware and software.

[0161] Although the present invention has been described in detail above with general descriptions and specific embodiments, modifications or improvements can be made to it, which will be obvious to those skilled in the art. Therefore, all such modifications or improvements made without departing from the spirit of the present invention fall within the scope of protection claimed by the present invention.

Claims

1. A method for determining the COF structure by combining XRD data and artificial intelligence, characterized in that, include: Precursor information of covalent organic frameworks (COFs) is collected by setting up a resource library, and the precursor information is input into the AI ​​model; Based on the precursor information, an initial COF candidate structure is constructed in the global search space using a particle swarm optimization heuristic optimization algorithm, and the initial COF candidate structure is screened to obtain an effective COF candidate structure. Using crystallographic calculation tools, combined with the atomic coordinates, unit cell parameters and space group information of the effective COF candidate structure, the bond length and bond angle parameters corresponding to the effective COF candidate structure are calculated, and theoretical XRD patterns are generated by simulation. Based on the theoretical XRD patterns, the bond lengths and bond angles, and combined with the experimentally obtained real XRD patterns and the average bond lengths and average bond angles in the COF database, a fitness function is defined and calculated to obtain the fitness function value; the difference between the effective COF candidate structure and the real COF structure is quantified through the fitness function. Based on the fitness function value, the parameters of the effective COF candidate structures are iteratively adjusted using the particle swarm optimization heuristic optimization algorithm to generate new COF candidate structures. XRD simulation, bond length, bond angle and fitness function are performed on the new COF candidate structures until the fitness function value converges or the maximum number of iterations is reached. The iteration is then stopped, and the COF candidate structures that meet the convergence conditions are output as the final crystal structure of the target COF.

2. The COF structure determination method combining XRD data and artificial intelligence according to claim 1, characterized in that, The precursor information includes: chemical structure information, preliminary unit cell parameters, and space group information of the organic molecular building blocks; the chemical structure information of the organic molecular building blocks includes: chemical formula, atomic coordinates, and bond connectivity; the atomic coordinates are three-dimensional Cartesian coordinates or fractional coordinates; the bond connectivity is represented by an adjacency matrix; the preliminary unit cell parameters include: unit cell axis length and unit cell axis angle; the space group information is represented by international symbols.

3. The COF structure determination method combining XRD data and artificial intelligence according to claim 2, characterized in that, In the process of constructing the initial COF candidate structure, the translation vectors and rotation parameters of all non-equivalent organic molecular building blocks in the unit cell are integrated into a high-dimensional parameter vector to characterize the initial COF candidate structure; the translation vector is the three-dimensional Cartesian coordinates or fractional coordinates of the geometric center of the organic molecular building block in the unit cell; the rotation parameter is the rotation matrix or Euler angles.

4. The COF structure determination method combining XRD data and artificial intelligence according to claim 3, characterized in that, In the process of simulating and generating the theoretical XRD pattern, the diffraction peak intensity is calculated using the structure factor calculation formula, based on the proportional relationship between diffraction peak intensity and the square of the structure factor modulus. The structure factor calculation formula is as follows: ; In the formula, For structural factors; For the first The occupancy rate of each atom; N is the total number of atoms in the unit cell; Let be the atomic scattering factor of the j-th atom; , , is the fractional coordinate of the j-th atom in the unit cell; h, k, l are the crystal plane indices; i is the imaginary unit.

5. The COF structure determination method combining XRD data and artificial intelligence according to claim 4, characterized in that, The formula for calculating the fitness function value is: ; In the formula, The fitness function value; Let be the bond length of the i-th chemical bond in the constructed COF candidate structure; The average bond length of chemical bonds of the same type in the COF database; Let J be the bond angle of the j-th chemical bond in the constructed COF candidate structure; The average bond angle of the same type of chemical bond in the COF database; The diffraction angle is The intensity of the diffraction peaks obtained from the time simulation; The diffraction angle is The intensity of the diffraction peaks measured in the experiment.

6. The COF structure determination method combining XRD data and artificial intelligence according to claim 5, characterized in that, When iteratively adjusting the parameters of the COF candidate structure using the particle swarm optimization heuristic optimization algorithm, each COF candidate structure is treated as a particle, and the high-dimensional parameter vector representing the COF candidate structure is updated using velocity update formula and position update formula. The expression for the speed update formula is: ; In the formula, Let be the velocity of particle k in the (t+1)th iteration; Let be the velocity of particle k in the t-th iteration; Inertial weights; , As an acceleration factor; , Let be a random number in the range [0,1]. This is the best position found so far for particle k; This is the best global position found for all particles to date. Let K be the position of particle k in the t-th iteration; The expression for the position update formula is: ; In the formula, Let be the position of particle k in the (t+1)th iteration.

7. A COF structure determination apparatus combining XRD data and artificial intelligence, employing the COF structure determination method combining XRD data and artificial intelligence as described in any one of claims 1-6, characterized in that, include: The precursor information collection and input module is used to collect precursor information of covalent organic frameworks (COFs) by setting a resource library, and input the precursor information into the AI ​​model; The initial COF candidate structure construction and screening module is used to construct an initial COF candidate structure in the global search space based on the precursor information using a particle swarm optimization heuristic optimization algorithm, and to screen the initial COF candidate structure to obtain an effective COF candidate structure. The bond length and bond angle calculation and theoretical XRD pattern simulation module is used to calculate the bond length and bond angle parameters corresponding to the effective COF candidate structure by using crystallographic calculation tools and combining the atomic coordinates, unit cell parameters and space group information of the effective COF candidate structure, and to simulate and generate theoretical XRD patterns. The fitness function value calculation module is used to define and calculate the fitness function based on the theoretical XRD pattern, the bond length and the bond angle, combined with the experimentally obtained real XRD pattern and the average bond length and average bond angle in the COF database, to obtain the fitness function value; and to quantify the difference between the effective COF candidate structure and the real COF structure through the fitness function. The final crystal structure acquisition module is used to iteratively adjust the parameters of the effective COF candidate structures based on the fitness function value using the particle swarm optimization heuristic optimization algorithm and generate new COF candidate structures; perform XRD simulation, bond length, bond angle and fitness function iterative calculation on the new COF candidate structures until the fitness function value converges or the maximum number of iterations is reached, stop the iteration, output the COF candidate structures that meet the convergence conditions, and use them as the final crystal structure of the target COF.

8. The COF structure determination device combining XRD data and artificial intelligence according to claim 7, characterized in that, In the precursor information collection and input module, the precursor information includes: chemical structure information, preliminary unit cell parameters, and space group information of the organic molecular building blocks; the chemical structure information of the organic molecular building blocks includes: chemical formula, atomic coordinates, and bond connectivity; the atomic coordinates are three-dimensional Cartesian coordinates or fractional coordinates; the bond connectivity is represented by an adjacency matrix; the preliminary unit cell parameters include: unit cell axis length and unit cell axis angle; and the space group information is represented by international symbols.

9. The COF structure determination device combining XRD data and artificial intelligence according to claim 8, characterized in that, In the initial COF candidate structure construction and screening module, during the process of constructing the initial COF candidate structure, the translation vectors and rotation parameters of all non-equivalent organic molecular building units in the unit cell are integrated into a high-dimensional parameter vector to characterize the initial COF candidate structure; the translation vector is the three-dimensional Cartesian coordinates or fractional coordinates of the geometric center of the organic molecular building unit in the unit cell; the rotation parameter is the rotation matrix or Euler angles.

10. The COF structure determination device combining XRD data and artificial intelligence according to claim 9, characterized in that, In the bond length and bond angle calculation and theoretical XRD pattern simulation module, during the simulation generation of the theoretical XRD pattern, the diffraction peak intensity is calculated using the structure factor calculation formula based on the proportional relationship between diffraction peak intensity and the square of the structure factor modulus. The structure factor calculation formula is as follows: ; In the formula, For structural factors; For the first The occupancy rate of each atom; N is the total number of atoms in the unit cell; Let be the atomic scattering factor of the j-th atom; , , represents the fractional coordinates of the j-th atom in the unit cell; h, k, and l are crystal plane indices; i is the imaginary unit; In the fitness function value calculation module, the formula for calculating the fitness function value is as follows: ; In the formula, The fitness function value; Let be the bond length of the i-th chemical bond in the constructed COF candidate structure; The average bond length of chemical bonds of the same type in the COF database; Let J be the bond angle of the j-th chemical bond in the constructed COF candidate structure; The average bond angle of the same type of chemical bond in the COF database; The diffraction angle is The intensity of the diffraction peaks obtained from the time simulation; The diffraction angle is The intensity of the diffraction peaks measured in the experiment; In the final crystal structure acquisition module, when iteratively adjusting the COF candidate structure parameters through the particle swarm optimization heuristic optimization algorithm, each COF candidate structure is treated as a particle, and the high-dimensional parameter vector characterizing the COF candidate structure is updated through the velocity update formula and the position update formula. The expression for the speed update formula is: ; In the formula, Let be the velocity of particle k in the (t+1)th iteration; Let be the velocity of particle k in the t-th iteration; Inertial weights; , As an acceleration factor; , Let be a random number in the range [0,1]. This is the best position found so far for particle k; This is the best global position found for all particles to date. Let K be the position of particle k in the t-th iteration; The expression for the position update formula is: ; In the formula, Let be the position of particle k in the (t+1)th iteration.