A method for identifying a fossil skeleton based on XRD data

Abstract

The application provides a method for identifying the authenticity of XRD data, and relates to the technical field of identification of dragon bones. The method comprises the following steps: obtaining XRD spectrum data of known authenticity as a reference set, and constructing a support vector machine authenticity identification model; constructing a target function for evaluating the classification error rate, generating a particle swarm, and taking each particle position as a set of model parameters; calculating the Voronoi neighbor topology, substituting the corresponding parameters of each particle into the model to calculate the classification error rate as the fitness; combining the Voronoi neighbor calculation to obtain the alignment term and the rotational hydrodynamic interaction term, and obtaining the heading vector and the Voronoi neighbor average velocity, and then obtaining the hydrodynamic interaction velocity; updating the inertia weight factor and judging whether to update the hydrodynamic interaction learning factor, updating the particle velocity and position; iterating until the termination condition is met, and outputting the optimal parameter configuration model to identify the authenticity of the sample to be identified. The application can improve the identification accuracy of traditional Chinese medicine dragon bones.

Description

Technical Field

[0001] This application relates to the field of keel identification technology, and in particular to a method for keel authentication based on XRD data. Background Technology

[0002] As a traditional mineral-based Chinese medicinal material, the authenticity of dragon bone is directly related to the safety and efficacy of clinical medication. In recent years, utilizing XRD technology to obtain the crystal structure characteristics of materials and combining it with machine learning or deep learning to construct digital authentication models has become a research hotspot in this field. However, XRD data has complex characteristics such as high dimensionality, nonlinearity, and severe overlap of diffraction peaks, which poses a significant challenge to the selection of hyperparameters in authentication models: the search space contains a large number of local extrema, and traditional manual tuning or exhaustive search often fails to balance global optimization efficiency with accurate matching of model parameters. Particle Swarm Optimization (PSO), as an evolutionary computational technique that simulates swarm intelligence, exhibits natural applicability in handling such high-dimensional nonlinear optimization problems due to its advantages of not relying on gradient information, fast convergence speed, and ease of parallelization. PSO can achieve efficient search in complex parameter terrains through cooperation and competition among particles. However, when faced with highly complex objective functions induced by XRD data, the standard PSO algorithm is prone to "premature convergence" phenomena such as loss of population diversity and getting trapped in local optima in the later stages of evolution. Therefore, exploring improved optimization algorithms that can enhance global search capabilities and maintain population vitality is of great significance for improving the identification accuracy and robustness of XRD keel identification models.

[0003] Currently, various learning algorithms have been proposed for multi-objective optimization problems (MOOPs) such as task allocation and path planning. Both classical and novel learning algorithms are widely used to solve these problems. In decentralized multi-agent systems, learning algorithms can iteratively update the state of agents in a short time. Learning algorithms used to solve multi-objective optimization problems must ensure convergence and approximate Pareto optimal solutions.

[0004] Extensive theoretical research has been conducted on the application of learning algorithms in multi-objective optimization problems (MOOPs). These studies typically assume that the multi-agent system exists in an ideal state, such as a non-interactive cyberspace where there are no interactions between agents. While these methods are suitable for solving problems in general scenarios, real-world applications of multi-agent systems often face more constraints. To meet the needs of real-world MOOPs, researchers have proposed several multi-agent learning methods tailored to real-world constraints. For example, in disaster relief scenarios, there is an urgent need to find and rescue trapped survivors within a short timeframe. Decentralized partially observable Markov decision processes (Dec-POMDPs) provide a general framework for sequential decision-making in uncertain environments. Furthermore, in large-scale and partially observable stochastic environments, domain models are often unavailable or simulators are difficult to use due to high costs or security concerns. Therefore, some researchers have proposed a policy-based reinforcement learning method for policy learning in macro-action scenarios.

[0005] Particle Swarm Optimization (PSO) can be applied to such scenarios. Inspired by the foraging behavior of bird flocks, PSO utilizes this evolutionary computational technique to find robust solutions through a stochastic and adaptive process. While basic PSO has advantages in resource cost and global optimum search, it still suffers from some drawbacks, such as premature convergence and loss of diversity. Numerous studies have explored PSO variants, primarily improving the learning algorithm through four different approaches. First, convergence speed can be directly improved by modifying learning strategies (such as mutual learning PSO and orthogonal learning PSO). Another improvement method is parameter-based optimization, such as inertia weighting factors and acceleration coefficients. These two parameters significantly impact the convergence rate. Furthermore, other learning algorithms (such as Genetic Algorithm (GA), Extremum Optimization (EO), and Ant Colony Optimization (ACO)) can be integrated with PSO. This novel hybrid optimization algorithm combines the exploratory capabilities of PSO with the development capabilities of other optimization algorithms. Finally, researchers have also explored particle neighbor topology to enhance the exploratory capabilities of PSO. Related topology-improved PSO variants include Full Information Particle Swarm Optimization (FIPS) and Dynamic Multi-Swarm Particle Swarm Optimization (DMSPS).

[0006] However, the above-mentioned improvement strategies still have the following shortcomings: (1) Although the improvement methods based on learning strategies or parameter optimization can improve the convergence speed to a certain extent, they fail to fundamentally solve the problem of particle swarm diversity loss in the later stage of evolution. In highly complex objective functions with a large number of local extrema, such as XRD verification model parameter search, the algorithm is still prone to premature convergence to local optima; (2) The strategy of mixing PSO with other algorithms increases the complexity of the algorithm and makes it difficult to dynamically balance exploration and development capabilities at different stages of parameter search; (3) Most of the existing improvement methods based on topology adopt fixed neighbor selection rules and fail to fully consider the actual distribution characteristics of particles in the parameter space. The update of neighbor relationships lacks adaptability, resulting in the population topology structure not being able to effectively reflect the dynamic changes in the search process; (4) More importantly, the existing improvement methods do not consider the fluid dynamic interaction characteristics between particles. In the parameter search process, each particle independently updates its own state based on individual optimal and global optimal information. There is a lack of modeling of local cooperative behavior between particles, making it difficult to simulate the adaptive search behavior of biological groups in complex environments and limiting the global optimization capability of the algorithm in high-dimensional nonlinear parameter space.

[0007] To address the aforementioned issues in existing technologies, in the XRD keel authentication scenario, the selection of hyperparameters (such as the penalty coefficient C and kernel function parameter γ) of the authentication model (e.g., support vector machine) directly determines the model's analytical sensitivity and feature extraction weights regarding diffraction peak position shifts and intensity changes in XRD patterns. Due to the complex characteristics of XRD data, such as high dimensionality, nonlinearity, and severe diffraction peak overlap, its corresponding parameter search space contains numerous local extrema. Standard PSO algorithms and their improved variants struggle to maintain global search while preserving population diversity in the later stages of evolution. They are prone to losing the ability to explore better regions in the parameter space due to particle convergence, resulting in the final output model parameter combination being only a locally optimal solution. This prevents the authentication model from accurately locking onto the unique crystal structure fingerprint features of genuine keel, thus limiting the identification accuracy and robustness of the authentication model. Therefore, there is an urgent need to provide a parameter optimization strategy that can simulate the cooperative search behavior of particles in a fluid environment. In the process of XRD verification model parameter search, a local interaction mechanism between particles is introduced to maintain population diversity and enhance global optimization ability, thereby effectively avoiding premature convergence of the algorithm and obtaining a better combination of verification model parameters to improve the accuracy of keel verification. Summary of the Invention

[0008] This application provides a method for keel identification based on XRD data. Addressing the technical challenges of numerous local optima in the parameter search space of XRD identification models and the tendency of standard PSO algorithms to suffer from population diversity loss and premature convergence in later evolutionary stages, this method introduces a hydrodynamic interaction velocity term into the PSO velocity update framework and constructs a local interaction structure between particles based on Voronoi neighbor topology. By calculating alignment and rotational hydrodynamic interaction terms, it simulates particle cooperative behavior in a fluid environment. Simultaneously, it adaptively adjusts the inertia weight factor and hydrodynamic interaction learning factor to maintain particle swarm diversity during the search process and enhance global optimization capabilities. This method utilizes the hydrodynamic interaction mechanism to guide particles in cooperative search within the parameter space, effectively avoiding getting trapped in local optima. Finally, it outputs the optimal model parameter combination to configure the identification model, thereby solving the technical problem of insufficient optimization accuracy in XRD keel identification scenarios using existing parameter optimization methods and improving the identification accuracy of keels.

[0009] To achieve the above objectives, this application adopts the following technical solution: This application provides a method for keel authentication of XRD data, the method comprising: Obtain sample data of X-ray diffraction patterns of keel with known authenticity as a reference dataset; A keel authentication model based on support vector machine is constructed. The keel authentication model takes X-ray diffraction pattern data as input and outputs the authenticity category of keel samples. A multinomial objective function is constructed to analyze the correlation of classified data, and the parameters are initialized to generate a particle swarm consisting of N particles. The multinomial objective function is used to evaluate the classification error rate of the keel identification model under different combinations of model parameters, and the initial position of each particle represents a set of model parameter combinations to be optimized for the keel identification model. Calculate the Voronoi neighbor topology for each particle based on the positions of all particles in the current parameter space; The model parameters represented by the current position of each particle are substituted into the keel verification model. The reference dataset is used for training and testing. The classification error rate of the keel verification model is calculated as the fitness value of the particle. The individual historical best position and global best position of each particle are recorded. The alignment term and rotational hydrodynamic interaction term are calculated by combining Voronoi neighbors; Calculate the orientation vector and the average velocity of Voronoi neighbors based on the alignment term and the rotational hydrodynamic interaction term; Calculate the hydrodynamic interaction velocity based on the orientation vector and the average velocity of the Voronoi neighbors; Update the inertia weight factor; Determine whether to update the fluid dynamics interaction learning factor based on the current iteration number; Based on the fluid dynamics interaction velocity, inertia weight factor, and fluid dynamics interaction learning factor, the velocity and position of each particle are updated according to the velocity and position update formulas to generate a new generation of model parameter combinations. Based on the new generation of model parameter combinations, the Voronoi neighbor topology of each particle is recalculated, and the model parameter combinations are updated until the termination condition is met, and the optimal keel verification model parameter combination is output. The optimal keel authentication model parameter combination is used to configure the keel authentication model, obtain the X-ray diffraction pattern data of the keel sample to be identified, and use the configured keel authentication model to authenticate the X-ray diffraction pattern data of the keel sample to be identified, and output the authentication result.

[0010] Furthermore, updating the velocity and position of each particle according to the velocity and position update formula includes: Based on the particle's current individual historical best position, global best position, and hydrodynamic interaction velocity, the updated velocity of the particle is calculated according to the following velocity update formula: in, Indicates the current iteration number. The current velocity of the particle. The velocity of the particle after the update. As the inertia weighting factor, As the first acceleration weight, As the second acceleration weight, As a fluid dynamics interaction acceleration learning factor, , , All are random factors that are uniformly distributed in the interval [0,1]. This is the particle's current position. For fluid dynamic interaction velocity, For the individual's optimal position, The globally optimal position; Based on the updated velocity, calculate the particle's new position using the following position update formula: in, This represents the updated position of the particle.

[0011] Furthermore, the fluid dynamic interaction velocity is determined by the following formula: in, For the orientation vector, The average velocity of Voronoi's neighbors.

[0012] Furthermore, the orientation vector is determined by the following formula: in, For alignment items, For rotating fluid dynamics interaction terms, It is a unit vector.

[0013] Furthermore, the average velocity of the Voronoi neighbors is determined by the following formula: in, Let V be the set of Voronoi neighbors of the target particle. The number of Voronoi neighbors. For the first j The velocity of the Voronoi neighbor particles.

[0014] Furthermore, based on the distance and angular relationship between the current particle and its Voronoi neighbor particles, the alignment term is calculated using the following formula: in, For alignment strength parameters, denoted as , where is the distance between the target particle and its Voronoi neighbors. The first angle parameter, This is the second angle parameter.

[0015] Furthermore, the velocities induced by each Voronoi neighbor particle at the current particle position are obtained, and the rotating hydrodynamic interaction term is calculated based on the induced velocities using the following formula: in, Let be the orientation vector of the current particle. Let be the vertical orientation vector of the current particle. Voronoi neighbor particles j The velocity induced at the target particle's location This is the gradient operator.

[0016] Furthermore, the method for obtaining the velocity induced by the Voronoi neighbor particles at the target particle's location includes: Based on the dipole strength parameter, the distance and angle between the Voronoi neighbor particles and the target particle, the following formula is used to calculate... : in, The dipole strength parameter, and These are the polar coordinate components defined in the local reference frame of the neighboring particle. For the third angle parameter, denoted as , where is the distance between the target particle and its Voronoi neighbors.

[0017] Furthermore, the methods for updating the inertia weight factor include: Based on the current iteration number, the maximum iteration number, and the kinetic energy of the particle swarm, the inertia weight factor is adaptively updated according to the following formula: in, This is the initial value for the inertia weight. This is the termination value for the inertia weight. This represents the current iteration number. The maximum number of iterations, A random number selected within the interval [0,1]. This represents the kinetic energy of the particle swarm.

[0018] Furthermore, the method for determining whether to update the fluid dynamics interaction learning factor based on the current iteration number is expressed as follows: in, As the inertia weighting factor, This is a fluid dynamics interaction acceleration learning factor.

[0019] The keel identification method for XRD data provided in this application has at least the following beneficial effects: (1) This application addresses the technical challenge of optimizing parameters in XRD keel verification models due to the high dimensionality, nonlinearity, and severe overlap of diffraction peaks in XRD data. It introduces a fluid dynamics interaction velocity term into the particle velocity update framework to simulate the cooperative behavior between particles in a fluid environment, enabling each particle to adjust its motion direction based on the state of its Voronoi neighbors during the evolution process. Here, the position of each particle represents a set of model parameters to be optimized, and the particle velocity represents the adjustment direction and magnitude of this set of model parameters in the search space. Since the XRD verification model parameter search space contains numerous local extrema, standard methods are prone to losing their ability to explore better parameter regions in the later stages of evolution due to particle convergence. This application, through a fluid dynamics interaction mechanism, ensures that each particle is continuously disturbed by its local neighbors during the parameter search process, effectively maintaining the diversity of particle distribution in the parameter space and preventing particles from prematurely converging in local optimal regions. This allows the final searched model parameter combination to enable the verification model to more accurately analyze the unique diffraction peak shifts and intensity changes of genuine keel in the XRD pattern.

[0020] (2) This application uses a Voronoi diagram to construct the neighbor topology of particles, and dynamically determines the neighbor relationship based on the actual distribution position of each particle in the parameter space, so that the interaction objects of each particle change adaptively with the search process. Among them, the Voronoi neighbors of each particle refer to other particles in the parameter space that are closest to the particle and whose Voronoi units are adjacent. This neighbor relationship is dynamically reconstructed as the particle position is updated. Since there is a serious overlap between different diffraction peaks in XRD data, the parameter combinations corresponding to different peak position analytical sensitivities in the parameter space may belong to different local optimal regions. This application enables particles to adaptively adjust their interaction range according to the local aggregation characteristics in the parameter space through dynamic Voronoi neighbor topology. Both edge particles and internal particles obtain a reasonable number of neighbors, which avoids the problem of loss of individual characteristics due to too many neighbors, and also avoids ineffective interaction with particle groups far away from themselves, thereby improving the diversity of parameter search and global optimization efficiency of the verification model.

[0021] (3) This application introduces a dipole flow field weight factor in the alignment term and the deflection effect of water flow on particle orientation in the rotation term, so that the particle's motion behavior in the parameter space simulates the dynamic law of a real fish swarm in a fluid environment. Among them, the alignment term is calculated based on the distance and angle relationship between the target particle and its Voronoi neighbor particles, which is used to make the particle's motion direction tend to be consistent with its neighbor particles, thereby enhancing the synergy of the particle swarm in the parameter search process; the rotational fluid dynamics interaction term is calculated based on the velocity induced by the Voronoi neighbor particles at the target particle's position, which is used to simulate the deflection effect of water flow on the particle's motion orientation. When the particle swarm tends to converge in a certain parameter region, the induced velocity generated by the rotational fluid dynamics interaction term can guide some particles to migrate to the unexplored region of the parameter space, thereby enabling the parameter search process of the authentication model to continuously jump out of local extrema. Through the above mechanism, this application can effectively distinguish the crystal structure differences between genuine and counterfeit products in the complex diffraction characteristics of XRD patterns, and avoid the model misjudging similar diffraction peaks in the XRD pattern of counterfeit products due to the convergence of parameters to local optima.

[0022] (4) This application adaptively and dynamically adjusts the inertia weight factor, allowing it to change its weight value in real time according to the kinetic energy changes of the particle swarm. It maintains a high hydrodynamic interaction learning factor in the early stages of iteration to preserve population diversity, and sets this learning factor to zero in the later stages of iteration to ensure optimization accuracy. Specifically, the inertia weight factor controls the influence of the particle's previous velocity on its current velocity, while the hydrodynamic interaction learning factor controls the contribution weight of the hydrodynamic interaction velocity term in velocity updates. This adaptive adjustment strategy enables the parameter search process to achieve a dynamic balance between global exploration and local development. It ensures both wide-area coverage in the early stages of the search, traversing a large range of model parameters in the parameter space, and fine optimization in the later stages of the search, enabling precise localization within the optimal parameter neighborhood, thereby obtaining a more accurate model parameter combination with a lower classification error rate.

[0023] (5) Through the synergistic effect of the above-mentioned fluid dynamics interaction mechanism and Voronoi topology, the optimal combination of model parameters output in this application is finally configured into the dragon bone authentication model based on support vector machine. The configured authentication model can effectively filter out background noise and interference signals caused by preparation differences in XRD patterns, while accurately locking the unique crystal structure fingerprint features of genuine dragon bone. Experimental statistical results show that this application is significantly better than traditional methods and other baseline methods in key indicators such as the optimal value, mean, standard deviation and median of the authentication model classification error rate. The actual identification effect verifies that this application can significantly improve the identification accuracy and robustness of the XRD dragon bone authentication model, and provides a reliable technical means for the digital identification of mineral Chinese medicinal materials. Attached Figure Description

[0024] The accompanying drawings, which are incorporated in and form part of this specification, illustrate embodiments consistent with this application and, together with the description, serve to explain the principles of this application.

[0025] Figure 1 The diagram illustrates different behavioral patterns of a school of fish provided in the embodiments of this application; wherein, (a) is swarming, which focuses on the tendency of individuals to gather towards the center of the group or a certain attraction source; (b) is swimming in a group, which focuses on the synchronous movement, formation maintenance, and coordinated turning of the group in space; and (c) is circling, which is often used to describe the behavior of particles performing local circling search near the optimal solution. Figure 2 A flowchart of a keel authentication method for XRD data provided in this application embodiment; Figure 3 A hydrodynamic interaction analysis diagram between the target particle and its Voronoi neighbor particles provided in the embodiments of this application; Figure 4 Another flowchart of a keel authentication method for XRD data provided in this application embodiment; Figure 5 The test samples used in this experiment are provided for the embodiments of this application; wherein, (a) and (b) are genuine keel bones, and (c) and (d) are counterfeit keel bones.

[0026] The accompanying drawings illustrate specific embodiments of this application, which will be described in more detail below. These drawings and descriptions are not intended to limit the scope of the concept in any way, but rather to illustrate the concepts of this application to those skilled in the art through reference to specific embodiments. Detailed Implementation

[0027] Exemplary embodiments will now be described in detail, examples of which are illustrated in the accompanying drawings. When the following description relates to the drawings, unless otherwise indicated, the same numbers in different drawings denote the same or similar elements. The embodiments described in the following exemplary embodiments do not represent all embodiments consistent with this application. Rather, they are merely examples of apparatuses and methods consistent with some aspects of this application as detailed in the appended claims.

[0028] The technical solution of this application and how the technical solution of this application solves the above-mentioned technical problems are described in detail below with specific embodiments. These specific embodiments can be combined with each other, and the same or similar concepts or processes may not be described again in some embodiments. The embodiments of this application will now be described with reference to the accompanying drawings.

[0029] To address the problem of limited classification accuracy in XRD identification of dragon bone (a traditional Chinese medicine) due to the difficulty in determining parameters in the authentication model, this application provides a method for dragon bone authentication based on XRD data. In real-world authentication scenarios, the high complexity of XRD data poses a significant challenge to the convergence speed and global search capability of optimization algorithms. To improve model performance, interaction mechanisms from fluid dynamics are introduced into the particle swarm optimization process. This method enhances population diversity and spatial distribution rationality by introducing Voronoi neighbor topology; simultaneously, it constructs a hydrodynamic interaction mechanism to simulate particle cooperative behavior in a fluid environment, effectively preventing the algorithm from getting trapped in local optima. This embodiment also provides a theoretical analysis of the computational complexity of this method in the parameter search task of the XRD authentication model, and the results confirm that it is within the ideal range for engineering applications. Statistical analysis of experimental results shows that in the parameter optimization task of the dragon bone authentication model, the HIIPSO algorithm significantly outperforms traditional algorithms and other baseline algorithms in key indicators such as the optimal value, mean, standard deviation, and median of the objective function. Experimental data show that the HIIPSO algorithm can significantly improve the robustness and identification accuracy of the XRD dragon bone identification model, and is the preferred solution for solving the parameter optimization problem in the digital identification of complex mineral medicinal materials.

[0030] To enable those skilled in the art to fully understand the method of this application, several background studies related to the method of this application will be introduced below, including the basic particle swarm optimization (PSO) algorithm, fish behavior research, and topological methods in fish swarms (neighborhood partitioning based on Voronoi diagrams).

[0031] Particle swarm optimization (PSO) searches for the optimal solution by iteratively updating the positions of particles. A particle's next position depends on its current velocity. Each particle records its best position found in the search history, called its individual best position (pbest). Among all the individual best positions, the position with the best fitness (i.e., the best fit) is marked as the global best position (gbest). The velocity and position update formulas of the basic PSO algorithm for the target search space are described as follows: Where k represents the number of iterations in the evolutionary process, and Let be a random factor that is uniformly distributed in the interval [0,1]. Acceleration weights (learning factors) are used to guide particles toward their individual optimal position (pbest). Acceleration weights are used to guide particles toward their global optimum (gbest). The particle's new velocity is determined by its relative position to its individual optimum. and global optimal position This is derived through weighted calculation. Inertia weighting factor. This is used to control the degree to which the particle's previous velocity affects its current velocity. Finally, by combining the particle's old position with the velocity increment, the particle's new position can be calculated.

[0032] One of the differences between the basic particle swarm optimization algorithm (PSO) and the method in this application lies in the neighbor topology. To solve multi-objective optimization problems (MOOPs) under fluid environment constraints, drawing on bionic experience is the best approach. Multi-agent behavior is widely present in various biological groups, such as mosquito swarms, starling flocks, and fish schools. Birds have good eyesight and flexible flight capabilities, so each bird can interact with more individuals, and their neighbor topology is generally considered to be organized according to the "three A rules" (repulsion, alignment, and attraction). In contrast, the topology of fish schools is organized differently

[22] . Unlike birds, fish sense the movement of their neighbors through lateral lines (hair-like sensors distributed along the sides of the fish's body). In the underwater environment, although the range of hydrodynamic interactions is not as wide as that of birds, it has extremely high sensitivity and is very suitable for rapid interaction with nearby neighbors. In this way, fish schools exhibit different behavioral patterns such as swarming, milling, and schooling. The different behaviors of fish schools are as follows Figure 1 As shown.

[0033] New research on fish swarm biomimicry offers novel insights into organizing neighbor topologies. The swarming mechanism of fish allows marginal individuals to keep pace with the group. Under the traditional "3A rule," internal individuals possess a large number of neighbors, causing them to lose most of their own characteristics (or individual traits). However, under the fish swarm rule, the number of neighbors for internal individuals is reasonably limited, which helps improve the basic particle swarm optimization (PSO) algorithm.

[0034] Existing research has demonstrated that fish swarms tend to use Voronoi neighbors to construct their neighborhood topology. A Voronoi graph (Thieson polygon) is a method of dividing a plane into regions based on the distances between points in a specific subset of the plane. This set of points (called seed points, agents, or generators) is pre-given, and for each seed point, there exists a corresponding region where all points within that region are less distant from the seed point than from any other seed point. These regions are called Voronoi cells. The Voronoi graph of a point set and its Delaunay triangulation are dual graphs.

[0035] The rigorous mathematical definition of a Voronoi diagram is as follows: in, Representation space An ordered set of intelligent agents. Point Distance to that subset. Space. Any intelligent agent in the current context The distance is no greater than that to other intelligent agents All points at a distance belong to the Voronoi region. .

[0036] This embodiment proposes using Voronoi neighbors as a new neighbor topology. If two agents belong to adjacent Voronoi regions, then these two agents are Voronoi neighbors. Agents located in edge Voronoi regions tend to have fewer neighbors; while other internal agents, although having more neighbors, still have far fewer neighbors than when using the "3A rule".

[0037] Based on the above background research, the implementation process of the method in this application will be described in detail below.

[0038] This embodiment first describes the problem, and then introduces the method proposed to solve the problem (i.e., the method of this application).

[0039] Problem Description: Suppose there exists a cluster of N agents (particles) in the parameter search space of a keel XRD authentication model, aiming to find the optimal parameter combination that maximizes the recognition accuracy of the authentication model through single-objective optimization. Due to the complex characteristics of XRD data, such as high dimensionality, nonlinearity, and overlapping diffraction peaks, the selection of hyperparameters (e.g., penalty coefficient C, kernel function parameter γ) for authentication models (e.g., Support Vector Machines, SVMs) faces significant challenges, and the search space contains numerous local extrema. Therefore, any method applied to this problem should be constrained by the characteristics of keel XRD data. When agents move in the parameter space, each agent (i.e., a set of parameters) generates a polarization potential field, which decays with increasing distance between agents. The goal of this research is to propose an algorithm with superior performance and faster convergence speed in the parameter optimization task of a keel authentication model, effectively avoiding the model from getting trapped in local optima.

[0040] To address this, this application proposes a fluid dynamics interaction improvement strategy. Within the "displacement-velocity" framework, the fluid dynamics interaction between topological structures is introduced into the particle swarm optimization algorithm to optimize the parameters of the keel-based model. By introducing new terms, stronger adaptability is achieved, effectively preserving the swarming characteristics of fish and enhancing the diversity of parameter search and global optimization capabilities.

[0041] like Figure 2 As shown, the keel authentication method for XRD data includes the following steps S1-S13 in its specific implementation.

[0042] S1: Obtain sample data of X-ray diffraction patterns of keel with known authenticity as a reference dataset.

[0043] Specifically, genuine and counterfeit keel samples, verified by authoritative sources, were collected. X-ray diffraction (XRD) scans were performed on both samples to obtain their XRD patterns. The XRD patterns contain information on diffraction peak positions, intensities, and shapes reflecting crystal structure characteristics, forming a reference dataset for subsequent model training and testing. Each sample in the reference dataset has a known genuine / counterfeit category label, used for supervised learning model training and performance evaluation.

[0044] S2: Construct a keel authentication model based on support vector machine. The keel authentication model takes X-ray diffraction pattern data as input and outputs the authenticity category of the keel sample.

[0045] Specifically, Support Vector Machines (SVMs) are chosen as the basic architecture for the classification model. SVMs map the XRD pattern features in the input space to a high-dimensional space and perform category division by finding an optimal classifying hyperplane. The input to this keel authentication model is preprocessed XRD pattern data, and the output is the category label of the keel sample, including genuine and counterfeit labels. The keel authentication model internally includes hyperparameters such as the penalty coefficient C and the kernel function parameter γ. The values ​​of the penalty coefficient C and the kernel function parameter γ directly affect the model's classification accuracy and generalization performance.

[0046] S3: Construct a multinomial objective function to analyze the correlation of classified data, initialize the parameters, and generate a particle swarm consisting of N particles.

[0047] In this embodiment, the polynomial objective function is used to evaluate the classification error rate of the keel identification model under different combinations of model parameters. The initial position of each particle represents a set of model parameter combinations to be optimized for the keel identification model.

[0048] Specifically, step S3 first constructs a polynomial objective function, which is used to quantify the classification error rate of the keel-based model under different combinations of model parameters. During the initialization phase, it is necessary to determine the particle swarm size N, the initial and final values ​​of the inertia weight factor, and the initial values ​​of each acceleration factor. Subsequently, the initial positions and velocities of N particles are randomly generated in the parameter search space. The position vector of each particle includes multiple dimensions such as the penalty coefficient C and the kernel function parameter γ.

[0049] S4: Calculate the Voronoi neighbor topology for each particle based on the positions of all particles in the current parameter space.

[0050] Specifically, the Voronoi neighbor topology is calculated as follows: each particle is considered a generator in the parameter space. The entire parameter space is partitioned using Voronoi methods based on the position coordinates of each particle. After partitioning, each particle has a corresponding Voronoi cell. If the Voronoi cells corresponding to two particles share an edge, then these two particles are Voronoi neighbors. For each target particle, all Voronoi neighbors of that target particle are collected to form the Voronoi neighbor set of that target particle. Since the positions of each particle are continuously updated during the iteration process, the Voronoi neighbor set is recalculated in each iteration step.

[0051] S5: Substitute the model parameter combination represented by the current position of each particle into the keel verification model, use the reference dataset for training and testing, calculate the classification error rate of the keel verification model as the fitness value of the particle, and record the individual historical best position and global best position of each particle.

[0052] Specifically, for each particle in the particle swarm, the penalty coefficient C and kernel function parameter γ corresponding to the particle's current position are extracted, and the keel detection model is configured using this set of model parameter values. Then, the configured keel detection model is trained and tested using the reference dataset obtained in S1, employing K-fold cross-validation to obtain a classification error rate estimate. The calculated classification error rate is the fitness value of the particle; a lower classification error rate indicates better performance of the keel detection model under this set of model parameter values.

[0053] For each particle, the fitness value of its current position is compared with the fitness value of the best position it has experienced during the historical search. If the fitness value of the current position is better, the particle's individual historical best position pbest is updated. At the same time, the position with the best fitness value among all the individual historical best positions of all particles is determined as the global best position gbest.

[0054] S6: Combine Voronoi neighbors to calculate alignment terms and rotational hydrodynamic interaction terms.

[0055] Specifically, in keel parameter optimization, the alignment term adjusts the state of a particle by referencing its Voronoi neighbors, thereby enhancing the consistency of the particle swarm. Alignment Term It can be calculated using the following formula: in, For alignment strength parameters, denoted as , where is the distance between the target particle and its Voronoi neighbors. The first angle parameter, The second angle parameter, angle , and like Figure 3 As shown. Due to the characteristics of fluid dynamics interaction, weights are introduced into the alignment term. Intuitively, each fish generates a dipole flow field, and this weighting makes the influence behind the particle more significant.

[0056] The rotating hydrodynamic interaction term R characterizes the effect of water flow on the agent's orientation. In keel parameter optimization, this term simulates the induced velocity of the agent by the water flow, helping particles escape local extremum traps and explore a wider parameter space.

[0057] Rotating fluid dynamics interaction term The calculation formula is: in, Let be the orientation vector of the current particle. Let be the vertical orientation vector of the current particle. Voronoi neighbor particles j The velocity induced at the target particle's location This is the gradient operator.

[0058] Based on the dipole strength parameter, the distance and angle between the Voronoi neighbor particles and the target particle, the Voronoi neighbor particles are calculated using the following formula. j The velocity induced at the target particle's location : in, The dipole strength parameter, and These are the polar coordinate components defined in the local reference frame of the neighboring particle. For the third angle parameter, denoted as , where is the distance between the target particle and its Voronoi neighbors.

[0059] S7: Calculate the orientation vector and the average velocity of Voronoi neighbors based on the alignment term and the rotational hydrodynamic interaction term.

[0060] The fluid dynamics interaction velocity vector is determined by the orientation vector. Average speed with Voronoi neighbors It consists of the scalar product (dot product). Its definition is as follows: in, Let V be the Voronoi neighbor set of the focal particle. The number of Voronoi neighbors. The orientation of the target particle is subject to alignment terms. Interaction terms with rotating fluid dynamics The impact.

[0061] S8: Calculate the hydrodynamic interaction velocity based on the orientation vector and the average velocity of the Voronoi neighbors.

[0062] In this embodiment, the fluid dynamic interaction velocity is determined by the following formula: in, It is a direction vector. The average velocity of Voronoi's neighbors.

[0063] S9: Update the inertia weight factor.

[0064] Inertia weighting factor It is designed to dynamically fluctuate according to the spatial compactness of the particle swarm. During the keel parameter optimization process, a high inertial weight is required to prevent excessive particle aggregation (thus simulating the behavior of fish avoiding physical collisions). The adaptive calculation formula is as follows. in, and The dynamic range of the linearly decreasing weights. This is the initial value for the inertia weight. This is the termination value for the inertia weight. (Random number) Choose between 0 and 1. The current iteration number This represents the maximum number of iterations. By introducing the kinetic energy of the particle swarm, the inertia weight will decrease under a certain buffer, thus allowing the inertia weight to adaptively adjust according to the kinetic energy of the particle swarm. This adaptive update of the inertia weight not only helps improve the optimization accuracy of the keel-based model parameters but also achieves better convergence.

[0065] S10: Determine whether to update the fluid dynamics interaction learning factor based on the current iteration number.

[0066] Learning factor of fluid dynamics interaction improvement term It can maintain the diversity of the particle swarm. The update formula for this learning factor is shown in formula (13): During the iteration process, with the inertia weight As the coefficient of variation gradually decreases, particles gradually lose diversity. In the early stages of the algorithm, the learning factor of the hydrodynamic interaction improvement term should be increased, which helps avoid getting trapped in local optima and find better keel-based model parameters. In the later stages, it is desirable to maintain optimization accuracy. It is generally assumed that after two-thirds of the total iterations have been completed, there is a greater chance of converging to the global optimum. Therefore, at this point, [the following should be considered]. Set it to 0 because the particle swarm no longer needs to maintain diversity.

[0067] S11: Based on the fluid dynamics interaction velocity, inertia weight factor, and fluid dynamics interaction learning factor, update the velocity and position of each particle according to the velocity and position update formula to generate a new generation of model parameter combinations.

[0068] Specifically, based on the particle's current individual historical best position, global best position, and hydrodynamic interaction velocity, the updated velocity of the particle is calculated according to the following velocity update formula: in, Indicates the current iteration number. The current velocity of the particle. The velocity of the particle after the update. As the inertia weighting factor, As the first acceleration weight, As the second acceleration weight, As a fluid dynamics interaction acceleration learning factor, , , All are random factors that are uniformly distributed in the interval [0,1]. This is the particle's current position. For fluid dynamic interaction velocity, For the individual's optimal position, The globally optimal position; Based on the updated velocity, calculate the particle's new position using the following position update formula: in, This represents the updated position of the particle.

[0069] Fluid dynamics interaction improvement terms through random factors Interaction with fluid dynamics accelerates learning factors Make corrections.

[0070] S12: Based on the new generation of model parameter combinations, recalculate the Voronoi neighbor topology of each particle and update the model parameter combinations until the termination condition is met, and output the optimal keel verification model parameter combination.

[0071] Specifically, after S11 completes the position update of all particles, the process returns to step S4, where the Voronoi neighbor topology is recalculated based on the new positions of each particle. Then, steps S5-S11 are executed sequentially, forming a complete iterative cycle. In each iteration, the particle swarm gradually moves towards a more favorable region in the parameter space. This iterative process is repeated until the preset maximum number of iterations is reached. If the fitness value of the global optimal position no longer improves after several consecutive generations, then the model parameter combination represented by the current global optimal position will be output as the optimal keel verification model parameter combination.

[0072] S13: Configure the keel authentication model using the optimal combination of keel authentication model parameters, obtain the X-ray diffraction pattern data of the keel sample to be identified, and use the configured keel authentication model to authenticate the X-ray diffraction pattern data of the keel sample to be identified, and output the authentication results.

[0073] Specifically, the optimal model parameter combination output by S12 is configured into the keel authentication model constructed by S2 to achieve optimal classification performance. Then, the XRD pattern data of the keel sample to be authenticated is obtained and input into the configured keel authentication model. The keel authentication model automatically outputs the category label of the sample based on the input XRD pattern features. The category label includes genuine and counterfeit products, which serves as the final authentication result.

[0074] The main differences between genuine and counterfeit keel frames lie in the positional shifts and intensity variations of specific diffraction peaks in the XRD pattern. Therefore, the parameter combination determines the algorithm's sensitivity to the diffraction peaks (such as peak position and intensity) and the weighting of feature extraction. When the parameters are not optimized, the program is easily affected by background noise or misses key features. However, when the optimal parameter combination is obtained through the HIIPSO algorithm, the program can accurately locate the unique crystal structure fingerprint features of genuine keel frames and effectively filter out noise caused by manufacturing differences.

[0075] Therefore, analyzing the computational complexity of the proposed algorithm is very important and necessary. Figure 4 A flowchart of the proposed method is shown to analyze its computational complexity. The detailed execution process of the method can be described as follows: Step 1: Construct the XRD identification evaluation function for keel and initialize the particle swarm. First, obtain the X-ray diffraction (XRD) pattern data of the keel samples to be identified as input data. A multinomial objective function is constructed in the program to analyze the correlation of classified data. Then, the parameters of the HIIPSO algorithm are initialized and a particle swarm is generated. The initial position of each particle represents a set of input parameters to be optimized for the multinomial objective function.

[0076] Step 2: Calculate the Voronoi neighbor topology of all particles (i.e., each set of model parameters) in the current parameter space to simulate the local interaction of particles in the fluid environment and enhance the diversity of parameter search.

[0077] Step 3: Substitute the parameter combination represented by the particle's current position into the keel authentication model. Use real keel XRD data (including genuine and counterfeit products) for training and testing, and calculate the model's classification error rate as the particle's fitness value. The smaller the fitness value, the better the model's authentication performance under that parameter set. Record the individual historical best position of each particle. and global optimal position .

[0078] Step 4: Calculate the alignment term using Voronoi neighbors. Interaction terms with rotating fluid dynamics This guides particles to move towards a more optimal parameter region.

[0079] Step 5: Calculate the orientation vector Voronoi topological average velocity .

[0080] Step 6: Calculate the fluid dynamics interaction velocity .

[0081] Step 7: Update the inertia weight factor This is to balance the algorithm's global search and local exploitation capabilities.

[0082] Step 8: If the current iteration count does not exceed 2 / 3 of the maximum iteration count, then update the fluid dynamics interaction learning factor.

[0083] Step 9: Generate a new generation of model parameter combinations based on HIIPSO's velocity and position update formulas. Then, return to Step 2 to evaluate and iteratively optimize the new parameter combinations until termination conditions are met (such as reaching the maximum number of iterations or finding sufficiently optimal authentication model parameters).

[0084] Assuming the number of particles is The number of iterations is The number of operations performed in the above algorithm is as follows: Step 1: Initializing particle swarm position values ​​requires execution. This operation requires constant-level operations to initialize the parameters; Step 2: Calculating the Voronoi topology for the current iteration requires executing... This operation; Step 3: Finding the optimal position in the particle's history requires performing the following steps. This operation, finding the globally optimal position, requires execution. This operation; Step 4: Calculate the alignment item Interaction terms with rotating fluid dynamics Required to be executed This operation; Step 5: Calculating the orientation vector requires one operation, and calculating the Voronoi topological average velocity requires one operation. This operation; Step 6: Calculating the fluid dynamics interaction velocity requires one operation; Step 7: Updating the inertia weight factor requires one operation; Step 8: The judgment and update operations need to be performed as constant-level operations; Step 9: Update the velocity and position of the particle swarm. This is the second operation.

[0085] In summary, the method described in this application requires a total of [number] steps. The algorithm iterates several times to check the termination condition. Therefore, the computational complexity of the proposed algorithm is O(n log n). This is on the same order of magnitude as the original PSO algorithm.

[0086] To further illustrate the feasibility and advancement of the proposed method, it was compared with several highly relevant and recent semi-heuristic algorithms, including Differential Evolution (DE), Artificial Bee Colony (ABC), Genetic Algorithm (GA), and Firefly Swarm Optimization (FSO). All experiments used real keel samples as data sources, such as... Figure 5 As shown.

[0087] All experiments were conducted on a 64-bit Windows 7 operating system, with an Intel(R) Core(TM) i7-3770 processor (3.4 GHz) and 8 GB of RAM. The software environment was MATLAB 2017b. The experimental equipment used was a brand-new intelligent XRD diffractometer.

[0088] In this embodiment, the diffraction angle of the keel is divided into five equal parts from small to large, and the experimental data of the diffraction angle of each type is set as the coefficient of the objective function, resulting in five different objective functions.

[0089] To ensure a fair and reasonable comparison, all comparison algorithms are set to the same maximum number of iterations. =100. The population size is set to 50 times the number of decision variables. Furthermore, each method is run independently 50 times. Since the problem dimension of this experiment is set to 5, the population size is set to 5 × 50 = 250.

[0090] All parameter values ​​required for the classic algorithm are listed in Table 1. The classic learning algorithm, the PSO variant, and HIIPSO (the method of this application) all operate under the same hydrodynamic constraints as described above.

[0091] Table 1 Parameter Settings

[0092] For each objective function, HIIPSO was run independently 50 times. Statistical results included the minimum (Min), maximum (Max), standard deviation (Std), mean (Mean), and median (Mdn). Since the theoretical optimal value for each objective function is 0, the closer the output value of the learning algorithm is to 0, the more satisfactory the solution is considered. The statistical results were analyzed using the following criteria: Min (optimal fitness solution): The optimal fitness solution obtained in 50 runs.

[0093] Max (Worst Fitness Solution): The worst fitness solution obtained in 50 runs.

[0094] Std (Standard Deviation): Measures the degree of dispersion of the obtained solution.

[0095] Mean (average fitness solution): measures the accuracy (quality) of the results obtained by an algorithm in 50 runs within a given number of iterations.

[0096] Mdn (median fitness solution): The median of the fitness solutions obtained in 50 runs.

[0097] All experiments were conducted on problems with the same scaling scale. Statistical data for HIIPSO and classic learning algorithms are shown in Table 2, with the best-performing values ​​highlighted in bold. Experimental results show that HIIPSO outperforms all traditional algorithms on all five objective functions.

[0098] Furthermore, the proposed algorithm was compared with several state-of-the-art PSO variants. These variants include Enhanced Leader Particle Swarm Optimization (ELPSO), Chaotic Inertial Weighted Particle Swarm Optimization (CAIWPSO), Chaotic Stochastic Inertial Weighted Particle Swarm Optimization (CRIWPSO), and Time-Varying Acceleration Coefficient Particle Swarm Optimization (TVAPSO). The maximum number of iterations, problem dimension, and particle population size remained unchanged (100, 5, and 250, respectively). Statistical data for HIIPSO and the PSO variants are shown in Table 3. Experimental results show that HIIPSO outperforms all the improved PSO algorithms on all five objective functions.

[0099] Table 2 Statistical data of HIIPSO and classic learning algorithms

[0100] Table 3 Statistical data of HIIPSO and PSO variants

[0101] Based on the above experimental results, it can be seen that the method in this application draws on the characteristics of hydrodynamic interactions in nature and integrates them into the evolutionary mechanism of the basic particle swarm optimization (PSO) algorithm. The core improvements of HIIPSO are reflected in the following two aspects: Voronoi Neighbor Topology: This feature reveals new possibilities for organizing the spatial distribution of particle swarms, enhancing the algorithm's ability to cover complex solution spaces.

[0102] Hydrodynamic interaction mechanism in fluid environment: The velocity update term of particles was improved by introducing fluid dynamic interaction analysis.

[0103] This embodiment rigorously analyzes the computational complexity of the HIIPSO method proposed in this application, and the results confirm that it is within an acceptable range for engineering applications. Under the same experimental environment and constraints, this embodiment compares HIIPSO with traditional algorithms and several latest PSO variants. Statistical data shows that in most test scenarios, the proposed method significantly outperforms other learning algorithms in many aspects. Thanks to the improvement of the topology and the introduction of the hydrodynamic interaction mechanism, HIIPSO effectively overcomes the shortcomings of traditional PSO, which is prone to premature convergence. When dealing with the complex nonlinear parameter search task in the XRD keel identification model, its optimization depth is significantly better than the comparative algorithms. HIIPSO can significantly improve the performance of digital identification models for mineral-based Chinese medicinal materials and has broad application potential and practical value in the fields of automatic identification and complex decision-making of real Chinese medicinal materials.

[0104] The above embodiments are only used to illustrate the technical solutions of this application, and are not intended to limit them. Although this application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features therein. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of this application.

Claims

1. A method for keel authentication based on XRD data, characterized in that, The method includes: Obtain sample data of X-ray diffraction patterns of keel with known authenticity as a reference dataset; A keel authentication model based on support vector machine is constructed. The keel authentication model takes X-ray diffraction pattern data as input and outputs the authenticity category of keel samples. A multinomial objective function is constructed to analyze the correlation of classified data, and the parameters are initialized to generate a particle swarm consisting of N particles. The multinomial objective function is used to evaluate the classification error rate of the keel identification model under different combinations of model parameters, and the initial position of each particle represents a set of model parameter combinations to be optimized for the keel identification model. Calculate the Voronoi neighbor topology for each particle based on the positions of all particles in the current parameter space; The model parameters represented by the current position of each particle are substituted into the keel verification model. The reference dataset is used for training and testing. The classification error rate of the keel verification model is calculated as the fitness value of the particle. The individual historical best position and global best position of each particle are recorded. The alignment term and rotational hydrodynamic interaction term are calculated by combining Voronoi neighbors; Calculate the orientation vector and the average velocity of Voronoi neighbors based on the alignment term and the rotational hydrodynamic interaction term; Calculate the hydrodynamic interaction velocity based on the orientation vector and the average velocity of the Voronoi neighbors; Update the inertia weight factor; Determine whether to update the fluid dynamics interaction learning factor based on the current iteration number; Based on the fluid dynamics interaction velocity, inertia weight factor, and fluid dynamics interaction learning factor, the velocity and position of each particle are updated according to the velocity and position update formulas to generate a new generation of model parameter combinations. Based on the new generation of model parameter combinations, the Voronoi neighbor topology of each particle is recalculated, and the model parameter combinations are updated until the termination condition is met, and the optimal keel verification model parameter combination is output. The optimal keel authentication model parameter combination is used to configure the keel authentication model, obtain the X-ray diffraction pattern data of the keel sample to be identified, and use the configured keel authentication model to authenticate the X-ray diffraction pattern data of the keel sample to be identified, and output the authentication result.

2. The keel authentication method for XRD data according to claim 1, characterized in that, The process of updating the velocity and position of each particle according to the velocity and position update formula includes: Based on the particle's current individual historical best position, global best position, and hydrodynamic interaction velocity, the updated velocity of the particle is calculated according to the following velocity update formula: in, Indicates the current iteration number. The current velocity of the particle. The velocity of the particle after the update. As the inertia weighting factor, As the first acceleration weight, As the second acceleration weight, As a fluid dynamics interaction acceleration learning factor, , , All are random factors that are uniformly distributed in the interval [0,1]. This is the particle's current position. For fluid dynamic interaction velocity, For the individual's optimal position, The globally optimal position; Based on the updated velocity, calculate the particle's new position using the following position update formula: in, This represents the updated position of the particle.

3. The keel authentication method for XRD data according to claim 1, characterized in that, The fluid dynamic interaction velocity is determined by the following formula: in, For the orientation vector, The average velocity of Voronoi's neighbors.

4. The keel authentication method for XRD data according to claim 3, characterized in that, The orientation vector is determined by the following formula: in, For alignment items, For rotating fluid dynamics interaction terms, It is a unit vector.

5. The keel authentication method for XRD data according to claim 4, characterized in that, The average velocity of the Voronoi neighbors is determined by the following formula: in, Let V be the set of Voronoi neighbors of the target particle. The number of Voronoi neighbors. For the first j The velocity of the Voronoi neighbor particles.

6. The keel authentication method for XRD data according to claim 5, characterized in that, The alignment term is calculated based on the distance and angle relationship between the current particle and its Voronoi neighbor particles using the following formula: in, For alignment strength parameters, denoted as , where is the distance between the target particle and its Voronoi neighbors. The first angle parameter, This is the second angle parameter.

7. The keel authentication method for XRD data according to claim 5, characterized in that, Obtain the induced velocities of each Voronoi neighbor particle at the current particle position, and calculate the rotating hydrodynamic interaction term based on the induced velocities using the following formula: in, Let be the orientation vector of the current particle. Let be the vertical orientation vector of the current particle. Voronoi neighbor particles j The velocity induced at the target particle's location This is the gradient operator.

8. The keel authentication method for XRD data according to claim 7, characterized in that, The methods for obtaining the velocity induced by the Voronoi neighbor particles at the target particle's location include: Based on the dipole strength parameter, the distance and angle between the Voronoi neighbor particles and the target particle, the following formula is used to calculate... : in, The dipole strength parameter, and These are the polar coordinate components defined in the local reference frame of the neighboring particle. For the third angle parameter, denoted as , where is the distance between the target particle and its Voronoi neighbors.

9. The keel authentication method for XRD data according to claim 1, characterized in that, The methods for updating the inertia weight factor include: Based on the current iteration number, the maximum iteration number, and the kinetic energy of the particle swarm, the inertia weight factor is adaptively updated according to the following formula: in, This is the initial value for the inertia weight. This is the termination value for the inertia weight. This represents the current iteration number. The maximum number of iterations, A random number selected within the interval [0,1]. This represents the kinetic energy of the particle swarm.

10. The keel authentication method for XRD data according to claim 9, characterized in that, The method for determining whether to update the fluid dynamics interaction learning factor based on the current iteration number is expressed as follows: in, As the inertia weighting factor, This is a fluid dynamics interaction acceleration learning factor.

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