METHOD AND SYSTEM FOR INVERTING EVOLUTIONARY PARAMETERS OF GROUNDWATER CIRCULATION BASED ON A PARTICLE Swarm Optimization Algorithm

Description

2. Conventional methods often retain a large number of low-quality particles during iteration, leading to unnecessary computational overhead and hindering efficient and accurate parameter identification with limited computing resources. Therefore, the question of how to achieve intelligent control, dynamic focusing, and efficient filtering of particle swarms while considering multiple influencing factors has become a central challenge in improving the practicality of groundwater parameter inversion. Therefore, the present invention proposes a method and a system for inverting evolutionary parameters of groundwater circulation based on a particle swarm optimization algorithm. 10. CONTENT OF THE PRESENT INVENTION To solve the aforementioned technical problems,The present invention proposes a method and a system for inverting evolutionary parameters of groundwater circulation based on a particle swarm optimization algorithm and thereby solves the problems existing in the prior art. To achieve the aforementioned objectives, this invention provides a method for inverting evolutionary parameters of groundwater circulation based on a particle swarm optimization algorithm, which comprises the following: initializing a particle swarm based on observational data of a residual water level and a flow balance to obtain an initial particle set; Integrating water level residual and flow balance for fitness assessment based on the initial particle set to obtain a subset of highly fitting particles; 25 Extracting response features of geological heterogeneity based on the subset of highly fitting particles and activating a local search,when the reaction characteristics of the geological heterogeneity exceed a threshold value to obtain an optimized particle swarm; calculating a conformance deviation of the water quality based on 30 of the optimized particle swarm and integrating it into the fitness assessment to obtain an exclusion list of suboptimal particles; Performing a crossing operation using a genetic algorithm based on the exclusion list of suboptimal particles to generate new particles, and obtaining a set of expanded particles; 35 BE2026 / 7007 3 Filtering out flow-balance-satisfying particles based on the set of expanded particles, and adjusting a distribution density if aggregation is insufficient to obtain a stable particle swarm; and determining deviation values ​​by simulating the groundwater based on the stable particle swarm, and updating parameter space boundaries 5 based on the deviation value by Bayesian optimization,to obtain a final parameter combination. Optionally, a process from initializing the particle swarm based on observational data of the water level residual and flow balance to obtain the initial particle set includes: calculating an index to minimize the residual based on the observational data; determining a parameter space range based on the index to minimize the residual; randomly distributing particle velocities and positions within the parameter space range to obtain sampling points of a position distribution; and obtaining the initial particle set by integrating based on the sampling points of the position distribution. Optionally, a process from integrating the water level residual and flow balance to fitness assessment based on the initial particle set includes obtaining the subset of particles with high fit.The following: Updating particle positions and velocities using the particle swarm optimization algorithm based on the initial particle set, and calculating fitness values; calculating a comprehensive evaluation index by a weighted summation of the water level residual value and the flow balance based on the fitness values; and filtering out a subset of highly matching particles based on comparison results between the comprehensive evaluation index and a preset threshold.30 Optionally, a process from obtaining the optimized particle swarm based on the subset of highly matching particles includes: extracting response features of the geological heterogeneity based on the subset of highly matching particles, and generating activation signals based on the response features of the geological heterogeneity;35 BE2026 / 7007 4 activating a local search mechanism based on the activation signals,and updating an aggregation position of the particles in the parameter space; determining an optimization direction and fitting a particle swarm based on the updated aggregation position and analysis results of a reaction of the geological heterogeneity; and obtaining clustering results of a reaction pattern based on the fitted particle swarm and subsequent updating to obtain the optimized particle swarm. Optionally, a process from calculating the conformity deviation of the water quality based on the optimized particle swarm to obtain the exclusion list of suboptimal particles includes: preprocessing collected data samples of the water quality to obtain a standardized index; calculating a difference with the standardized index using the Euclidean distance formula based on a position of each particle in the optimized particle swarm.to obtain the water quality conformance deviation; integrating the water quality conformance deviation by means of a weighted summation into the fitness score to obtain updated fitness scores; and filtering out the exclusion list of suboptimal particles based on the 20 updated fitness scores. Optionally, a process from performing a crossing operation using the genetic algorithm based on the exclusion list of suboptimal particles to generate the new particles, and obtaining the set of expanded particles, includes the following: 25 Performing a crossing operation using the genetic algorithm on remaining particles based on the exclusion list of suboptimal particles to generate a new generation of particles; Calculating fitness values ​​based on the new generation of particles and selecting particles with high fit according to the fitness values; 30 Performing a position mean fusion processing based on particles with high fit,to obtain a diversified particle swarm; and checking a coverage state of a positional distribution of the diversified particle swarm over potential areas of high fit to form the set of expanded particles. 35 BE2026 / 7007 5 Optionally, a process comprising determining deviation values ​​by simulating the groundwater based on the stable particle swarm, and updating parameter space boundary based on the deviation value by means of Bayesian optimization to obtain the final parameter combination, as follows: obtaining an initial parameter combination from a distribution of geological 5 heterogeneity based on the stable particle swarm and simulating to obtain a total amount of groundwater flow; comparing the total amount of groundwater flow with the observational data,to obtain the deviation values; obtaining a posterior distribution and updating the parameter space boundary by means of Bayesian optimization based on the deviation values; and obtaining the final parameter combination from the updated boundaries after a convergence adjustment of the parameter space boundary. The present invention also provides a system for inverting evolution parameters of groundwater circulation based on a particle swarm optimization algorithm, which is used to implement the method, and the system comprises: a particle initialization module for initializing a particle swarm based on observational data of a residual water level and a flow balance to obtain an initial particle set; a fitness assessment module for integrating the residual water level and the flow balance to assess fitness based on the initial particle set.to obtain a subset of particles with high fit; an activation module for local search to extract response features of geological heterogeneity based on the subset of particles with high fit, and to activate a local search when the response features of geological heterogeneity exceed a threshold, in order to obtain an optimized particle swarm; a module for excluding suboptimal particles to calculate a conformity deviation of water quality based on the optimized particle swarm and integrate into the fitness assessment to obtain an exclusion list of suboptimal particles; a module for expanding the particles to perform a crossing operation using a genetic algorithm based on the exclusion list of suboptimal particles to generate new particles,and to obtain a set of 35 expanded particles; BE2026 / 7007 6 a module for selecting stable particles to filter out particles that satisfy flow balance constraints based on the set of expanded particles, and to adjust a distribution density if aggregation is insufficient to obtain a stable particle swarm; and a parameter inversion module to determine deviation values ​​by means of a 5 simulation of the groundwater based on the stable particle swarm, and to update parameter space limits based on the deviation value by means of Bayesian optimization to obtain a final parameter combination. In comparison to the prior art, the present invention offers the following advantages and technical effects: 10 This invention enables intelligent control and focusing of the particle swarm in parameter space by designing a weighted fitness assessment mechanism under multidimensional boundary conditions, the water level residual value,Flow balance and water quality indicators are integrated, as well as through the dynamic activation of local search in combination with the 15 response features of geological heterogeneity. Furthermore, the introduction of suboptimal particle exclusion and crossing operation using genetic algorithms effectively reduces the computational effort while maintaining population diversity. Ultimately, while maintaining inversion accuracy, the method significantly improves the convergence rate and stability of the 20 parameter identification in complex heterogeneous aquifers and thus provides efficient and reliable technical support for scientific management and decision-making in the field of groundwater resources. DESCRIPTION OF THE DRAWING 25 The attached drawings, which form part of this application,For the purpose of a better understanding of this application. The exemplary embodiments and descriptions of this application serve to explain this application and do not constitute an unreasonable limitation of this application. In the drawings: Fig. 1 is a flow diagram of a process according to an embodiment of the present invention; and Fig. 2 is a structure diagram of a system according to an embodiment of the present invention. 35 BE2026 / 7007 7 DETAILED DESCRIPTION It should be noted that, in the absence of any conflict, the implementation forms of this application and the features within these implementation forms may be combined with one another. The present application is now described in detail with reference to the attached drawings and in conjunction with implementation forms.5 It should be noted that the steps shown in the flowchart of the drawings may be executed in a computer system, for example as a series of computer-executable instructions. Furthermore, it should be noted thatthat although the flowchart shows a logical sequence, the steps shown or described may, under certain circumstances, be carried out in a different order than the one shown here. 10 Embodiment 1 As shown in Figure 1, this embodiment provides a method and a system for inverting evolutionary parameters of groundwater circulation based on a particle swarm optimization algorithm, including the following steps: 1. Initializing the position distribution of the particles in the parameter space by the particle swarm optimization algorithm after acquiring the observational data, including the residual water level and the flow balance.to obtain an initial particle set for subsequent further adjustments.20 The observational data are obtained by recording the residual water level and the flow balance values ​​at monitoring stations of the river channel. For the aforementioned residual water level and flow balance values, an index for minimizing the residual value is calculated,The result of the balance error correction is determined by minimizing the sum of the squared differences between the residual water level and the values ​​of the 25 flow balances. Based on this result of the balance error correction, a parameter space is defined. By mapping the result of the balance error correction onto a multidimensional coordinate system, the limit of the particle position distribution is determined. The particles are initialized within the parameter space using a particle swarm optimization algorithm. 30 sample points of the position distribution are generated by randomly distributing particle velocities and positions. From these sample points of the position distribution, the initial particle set for the iterative adjustment during the calibration of the hydrological simulation parameters of the flow is integrated. As a concrete implementation of this design, the monitoring station is equipped with 35 water level sensors and flow meters.Data BE2026 / 7007 8 is automatically recorded hourly. The residual water level value represents the difference between the actually measured water level and the water level predicted by the simulation model. The flow balance value is an equilibrium index for the inflow and outflow in the riverbed, calculated based on the principle of conservation of water quantity. The index for minimizing the residual value is calculated for the recorded water level residual value and the value of the flow balance. In this implementation, the result of the balance error correction is obtained by determining the minimum value of the sum of the squares of the differences. The parameter space range is defined based on the result of the balance error correction. The corrected error values ​​are mapped in a three-dimensional space, where the x-axis represents the range of the water level residual value (e.g., -0.5 to 0.5 meters).The y-axis represents the range of the flow balance value (e.g., -100 to 100 cubic meters per second) and the z-axis the time factor. The boundary is thus defined as a multidimensional cube or sphere that encloses these points. Particle swarm optimization serves to initialize the particles in the parameter space.15 In this implementation, the sample points of the position distribution are generated by randomly distributing the particle velocities and positions. The parameter space includes dimensions such as soil permeability and riverbed roughness. Ten particles are randomly selected, with each particle having an initial position such as (0.01; 0.03) and a velocity such as (0.001; 0.002).20 These points represent possible parameter combinations. The initial particle set is integrated from the sample points to iteratively adjust the parameter calibration for the hydrological simulation of the river channel. p. 102Performing a fitness assessment under multidimensional boundary conditions based on the initial particle set, integrating water level residual, and flow balance using weighted summation to determine a subset of highly fitting particles and to control the dynamic change in distribution density. Multidimensional boundary conditions are derived from the initial particle set, and the fitness values ​​are calculated by updating position and velocity under the multidimensional boundary conditions using the particle swarm optimization algorithm. The fitness values ​​are used to fuse the water level residual and flow balance, assigning weights to the residual and balance using weighted summation and adding them to obtain a comprehensive assessment index. Based on this comprehensive assessment index, the subset of highly fitting particles is determined. BE2026 / 7007 9 If the valuation index exceeds a preset threshold,is included in the subset. For this subset of particles with high fit, distribution density parameters are determined, and the density distribution is dynamically controlled and updated based on the position of the subset. Hydrological parameters are calibrated from the density distribution, and the iterative result of the flood simulation is determined through iterative optimization of the five distribution density parameters. As a concrete implementation of this design, the geological properties and the flow dynamics of the river channel are considered as boundary conditions during the calibration of the hydrological simulation parameters of a river channel.when multidimensional boundary conditions are derived from the initial particle set. During the update of position and velocity using the particle swarm optimization algorithm, the difference between the current position of each particle and the globally optimal position is first calculated. Subsequently, the velocity vector is adjusted, taking into account boundary conditions such as the upper water level and the lower flow limit, to prevent particles from exceeding the permissible limits. In a specific simulation scenario of a river channel for a section of the middle course, the initial particle set consists of 100 particles, each corresponding to a parameter set, such as a Manning coefficient between 0.025 and 0.035. If, during the speed update, the particle velocity causes the position to exceed boundary conditions, e.g., a residual water level of more than 5 cm, the speed is halved using a penalty function.to ensure algorithm convergence. This update process helps to gradually approximate the optimal parameter configuration and improve the simulation accuracy. When fusing the water level residual and the flow balance using fitness values, a weighted summation method can be used, assigning a weight of 0.6 to the water level residual and a weight of 0.4 to the flow balance. These values ​​are then added to obtain a comprehensive rating index. S103, Extracting response features of geological heterogeneity from a subset of particles with high fit. If the response features exceed the preset threshold, the local search mechanism is activated to determine and update the aggregation position of the particles in the parameter space.This results in an optimized particle swarm for accuracy improvement. 35 BE2026 / 7007 10 Reaction features are extracted from the geological heterogeneity analysis. By associating these reaction features with the adaptation of the subset of particles, it is determined whether a predefined threshold is exceeded, thereby generating an activation signal. Based on this activation signal, the local search mechanism is initiated, whereby the aggregation positions are associatively updated by analyzing the aggregation in parameter space 5 and the particle positions in order to determine an updated position distribution. Based on the association between the updated position distribution and the analysis of the geological heterogeneity reaction, adaptation data of the particles are obtained from the feature association of the subset of particles.to determine the optimization direction.10 By associating the optimization direction with the extraction of the reaction features, the particle swarm is adapted according to the geological layer distribution map to obtain clustering results of the reaction patterns. Finally, the association between the clustering results of the reaction patterns and the optimization for accuracy improvement is maintained, and the 15 particle swarm is then updated and optimized to obtain a particle swarm for accuracy improvement. As a concrete implementation of this execution form, after generation of the activation signal, a local search mechanism, for example a neighborhood search strategy, is activated to aggregate particle positions in the parameter space. 20 Assuming that the parameter space includes hydrogeological parameters such as hydraulic conductivity and storage coefficient, the association between the current particle position and the activation signal is determined.by calculating the aggregation center as a weighted average position and updating it accordingly. If the activation signal points to a region of high heterogeneity, the particles are shifted in the direction of this region, resulting in a more compact cluster structure in the updated position distribution. This process is performed over several iterations to ensure that the distribution reflects geological heterogeneity, thereby providing more precise boundary conditions for the simulation of groundwater flows. 30 S104, Calculating a water quality conformance deviation based on the optimized particle swarm, Maintaining conformance deviation and integrating it into the fitness assessment,to determine an exclusion list of suboptimal particles and thus reduce the computational effort. Standardized indicators are determined from the collected samples by preprocessing the water quality data. Initialization is performed using the BE2026 / 7007 particle swarm optimization algorithm, whereby the initial positions and velocities are determined based on the standardized indicators. The standardized indicators serve as input to the particle swarm optimization algorithm, while the initial positions and velocities serve as output. The agreement deviation value is determined by calculating the degree of indicator agreement based on the initial positions. The calculation is performed by applying the Euclidean distance formula, where the square root of the sum of the squared differences between the individual indicators is taken to obtain the agreement deviation value. The agreement deviation value is integrated into the fitness assessment.where the integration is performed by weighted summation of the deviation value with the evaluation function to obtain the fitness value of the particles. Based on the fitness value of the particles, if it is below a predefined threshold, the exclusion list of suboptimal particles is determined. S105, Performing a crossing operation using the genetic algorithm on the exclusion list of suboptimal particles to generate a new generation of particles from the remaining particles, thereby obtaining a set of expanded particles to cover potential areas with high fit. Using the remaining particles, a genetic algorithm is applied to generate the new generation of particles through the crossing operation.and thus obtain the set of expanded particles. Fitness values ​​are determined from this initial expanded set. By comparing these fitness values ​​with a preset threshold, a subset of particles with fitness values ​​above the threshold is identified as a subset of particles with high matching. For this subset of particles with high matching, a method for fusing the 25 particle positions is used to increase diversity. This leads to a diverse particle swarm. The position distribution of this diverse particle swarm is then determined. By checking the intersection ratio between the position distribution and the potential area, if the position distribution covers the potential area, the fitness threshold is adjusted to generate additional particles. This results in a complete extended set. Based on the complete extended set, the overlap ratio between particle positions and regions is calculated as the regional coverage rate. This results in a particle set,which covers the potential area with high adaptation. As a concrete implementation of this execution form, step 35, determining fitness values ​​from the minimal extended set and determining the subset of particles with high conformity by comparison with a preset threshold, includes a mechanism for calculating and selecting the fitness values. In the field of water quality optimization, fitness values ​​are usually quantified values ​​based on the conformance deviation of the index. The preset threshold can be set to an empirical value, for example, 0.8, which represents the acceptable level of conformity. In this process, the fitness value for each newly generated particle is first calculated, for example, by using a weighting function to fuse the deviations of several water quality indicators. If the total deviation of a particle is below the threshold,It is classified as a high-fit. By comparison, all particles 10 above the threshold are classified as belonging to the subset of particles with a high fit. S106, Filtering out the particles that satisfy the flow balance constraint from the set of expanded particles, and iteratively fitting a distribution density if the filter result indicates insufficient aggregation of the particles 15, assessing and outputting a stable particle swarm as a basis for inversion accuracy. From the set of expanded particles, the particles that meet the flow balance constraint are determined, whereby the set of filtered particles is determined by comparing the difference between the particle position coordinates and the preset 20 threshold values ​​for the constraint. The degree of aggregation in the set of filtered particles is determined by calculating the average distance between the particles.to obtain a value for the degree of aggregation. Should this value of the degree of aggregation fall below a preset threshold, the distribution density is iteratively adjusted to obtain an updated particle distribution. From the updated particle distribution, the particles that meet the flow balance constraint are filtered again, and the aggregation rating is evaluated by calculating the particle density distribution. The stability of the particle swarm is determined based on this aggregation rating. The stable particle swarm is determined by comparing the rating with a stability threshold. This stable particle swarm is output as the basis for the inversion accuracy and thus forms the basis for the inversion accuracy. As a concrete implementation of this execution form, filtering the set of particles requires the evaluation of the particle aggregation level. This aggregation level is quantified by calculating the average distance between the particles.which reflects the spatial distribution density of the particles. If the average distance BE2026 / 7007 13 is below a preset threshold, for example below 2.0 units, this indicates an excessively high concentration of particles, which can potentially lead to local overload. In this case, the distribution density is iteratively adjusted, for example by stepwise increasing the distance between the particles using a uniform diffusion algorithm, until the average distance exceeds the threshold, thereby achieving an updated particle distribution. After selecting the particles that meet the flow balance constraint from the updated particle distribution,The assessment value of the aggregation can be determined by calculating the particle density distribution. The particle density distribution describes the distribution of the number of particles within a specific area. For the calculation, the space can be divided into grids and the number of particles in each grid counted. Subsequently, the density variance is calculated as the assessment value. A lower assessment value indicates a more uniform distribution. 15 S107, Simulating the total amount of groundwater flow based on the stable particle swarm, determining the deviation between simulation values ​​and observational data, subsequently updating the parameter space boundary by Bayesian optimization and determining the final parameter combination to achieve a highly precise inversion. 20 By optimizing the stable particle swarm, an initial parameter combination is obtained from the geological heterogeneity distribution.to obtain simulation values ​​of the total groundwater flow. By comparing the simulation values ​​with observational data, a deviation value is determined, which is used to calculate a fusion-based fit of the real-time water level measurement data. Using Bayesian optimization, a posterior distribution is derived from the deviation value to update the parameter space boundary. If the fitted boundary converges, the optimal parameter combination is obtained from the updated boundary, thereby determining the inversion of the geological permeability coefficient. Based on this parameter combination, highly precise inversion results are obtained. As a concrete implementation of this execution form, Bayes' method uses a posteriori distribution and a probability function to update the probability assumptions. For example, it is initially assumed that the parameter space boundary is a permeability coefficient between 0, 1, and 1.0 is. After deriving the posterior distribution from the deviation value, the limit can be narrowed to 0.3 to 0.7, thus refining the search space. If the limits converge after fitting, for example, if the standard deviation of the posterior distribution is less than 0.05, the optimal parameter combination is selected from the updated limit, for example, a permeability coefficient of 0.45, to determine the inversion of the geological permeability coefficient. This inversion process includes the inverse derivation of geological parameters to fit them to the observational data. Embodiment 2 As in,

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