Soil groundwater monitoring distribution point optimization method and system based on Monte Carlo simulation

Abstract

The invention discloses a Monte Carlo simulation-based soil groundwater monitoring distribution point optimization method and system, and relates to the field of environmental monitoring and groundwater pollution prevention and control, and the optimization method comprises the following steps: S1, obtaining multi-source prior data and initial sampling data; s2, constructing a mixed probability distribution prior model and a probability distribution model; s3, performing posteriori updating on the prior model, and outputting a posteriori mean value and a confidence interval; s4, executing random sampling and spatial diffusion simulation; forming an extended scene set; s5, forming a high-credibility scene subset; s6, dividing risk levels and generating a pollution probability distribution diagram; s7, determining an optimal monitoring point position combination through an optimization algorithm; and S8, updating the model, the scene set and the point distribution scheme. According to the method, the problems of underestimation of high-concentration tail probability and overestimation of low-concentration area probability are effectively avoided, so that the risk of leak detection of pollution hot spots is reduced, and the identification capability of a monitoring network on a high-risk area is improved.

Description

Technical Field

[0001] This invention relates to the field of environmental monitoring and groundwater pollution control technology, and in particular to a method and system for optimizing the layout of soil and groundwater monitoring points based on Monte Carlo simulation. Background Technology

[0002] Heavy metal pollution in soil and groundwater is a key issue in the ecological environment monitoring and risk control of farmland surrounding mining areas. The sources of heavy metal pollution in mining areas are complex. Influenced by multiple factors such as tailings dam dust diffusion, historical leakage events, and long-term infiltration of irrigation water from polluted farmland, heavy metals (such as cadmium and lead) exhibit significant spatial heterogeneity in the soil medium. Concentration distribution often presents a complex pattern of intermingling local high-value "hot spots" and background low-value "cold spots." This heterogeneous pollution characteristic poses a severe challenge to the deployment strategies of traditional environmental monitoring systems. Especially given limited monitoring resources, achieving efficient coverage and accurate early warning of pollution risks has become an urgent problem to be solved.

[0003] Traditional environmental monitoring widely employs a systematic sampling method, whose core logic is to achieve spatial coverage through uniformly spaced sampling points. However, this method is essentially an experience-driven, static strategy that fails to consider the inherent differences in pollution distribution. In high-risk "hotspot" areas, insufficient sampling density may lead to missed detections, while in low-risk "coldspot" areas, there is a large amount of redundant sampling, resulting in a waste of monitoring resources. Specifically, on the one hand, high-concentration pollution areas near mining areas may be missed due to excessively large grid spacing, leading to misjudgments of pollution plume migration trends; on the other hand, oversampling in low-concentration background areas in the suburbs crowds out limited monitoring resources, reducing the overall risk response efficiency of the monitoring network. This contradiction between "missed hotspots" and "redundant coldspots" makes traditional sampling methods unable to meet the precise monitoring needs of complex pollution scenarios, necessitating a deep integration of experience-driven and data-driven approaches. Summary of the Invention

[0004] This invention overcomes the shortcomings of the prior art and provides a method and system for optimizing the layout of soil and groundwater monitoring points based on Monte Carlo simulation.

[0005] To achieve the above objectives, the technical solution adopted by the present invention is as follows: Firstly, the present invention provides a method for optimizing the layout of soil and groundwater monitoring points based on Monte Carlo simulation, comprising the following steps:

[0006] S1. Obtain multi-source prior data and initial sampling data;

[0007] S2. Based on prior data, construct a prior model of mixed probability distribution of heavy metal concentration for different polluted areas, and establish corresponding probability distribution models for soil physicochemical parameters.

[0008] S3. Using the initial sampled data as the observation vector, the prior model is updated posteriorly through statistical inference methods, and the posterior mean and confidence interval of the distribution parameters are output.

[0009] S4. Random sampling is performed based on the updated posterior distribution to generate multiple sets of parameter combinations, which are then input into the pollutant migration model for spatial diffusion simulation; extreme pollution scenarios are also included to form an extended scenario set.

[0010] S5. Calculate the error between each simulated scenario and the initial sampled data, retain the scenarios that meet the preset threshold, and form a subset of high-confidence scenarios;

[0011] S6. Based on high-confidence scenarios, calculate the probability of exceeding the standard for each spatial unit, classify the risk level, and generate a pollution probability distribution map;

[0012] S7. Based on the pollution probability distribution map, under the constraints of point spacing and boundary restrictions, determine the optimal combination of monitoring points through optimization algorithms;

[0013] S8. When receiving new monitoring data, repeat steps S2-S7 to update the model, scene set, and deployment plan.

[0014] In a preferred embodiment of the present invention, in step S1, the multi-source prior data includes records of historical pollution events in the mining area, heavy metal concentration files of remediated sites, regional soil background value database, agricultural irrigation water usage records, and topographic and geomorphological layer data; the initial sampling data includes heavy metal concentration values, soil pH values, organic matter content, cation exchange capacity, soil texture classification, and groundwater depth parameters measured at multiple sampling points arranged in a preset sparse grid within the target cultivated land area.

[0015] In a preferred embodiment of the present invention, in step S2, the prior model of the mixed probability distribution is a bimodal mixed normal distribution model, which divides the target area into a near-field area and a far-field area, corresponding to the main pollution peak and the secondary pollution peak, respectively. Its probability density function expression is as follows:

[0016] ;

[0017] Where N represents the normal distribution function; Indicates the weighting coefficient; and This represents the mean and standard deviation of the main pollution peak in the near-field region; and This represents the mean and standard deviation of secondary pollution peaks in suburban areas.

[0018] In a preferred embodiment of the present invention, in step S3, the statistical inference method is the Markov chain Monte Carlo algorithm, which combines the student distribution likelihood function to perform posterior updates on the prior model and outputs the posterior mean, confidence interval and convergence index of the distribution parameters.

[0019] In a preferred embodiment of the present invention, in step S4, the extreme pollution scenario is reconstructed based on historical dam failure events, assuming that the tailings dam instantaneously collapses and releases pollutants, generating an extreme concentration field and injecting it into the extended scenario set.

[0020] In a preferred embodiment of the present invention, in step S5, the error is the root mean square error, the preset threshold is 0.30 mg / kg, and a supplementation mechanism is activated when the number of scenes is insufficient.

[0021] In a preferred embodiment of the present invention, in step S7, the optimization algorithm is an improved genetic algorithm or a multi-objective optimization algorithm, and the constraints include the distance between any two points being ≥80 m, the point being located within the boundary of cultivated land, and the elevation change rate being ≤15%.

[0022] Secondly, the present invention provides an optimization system for a method of optimizing the layout of soil and groundwater monitoring points based on Monte Carlo simulation, comprising:

[0023] The multi-source data acquisition module is used to acquire multi-source prior data and initial sampling data;

[0024] The parametric probability modeling module is used to construct a prior model of the mixed probability distribution of heavy metal concentration and a probability distribution model of soil physicochemical parameters.

[0025] The Bayesian correction module is used to perform posterior updates on the prior model;

[0026] The Monte Carlo scene generation module is used to generate extended scene sets;

[0027] The credibility filtering module is used to filter a subset of high-credibility scenarios;

[0028] The site selection optimization module is used to determine the optimal combination of monitoring points;

[0029] The dynamic update module is used to update the monitoring point layout plan when new monitoring data is received.

[0030] In a preferred embodiment of the present invention, the prior model of the mixed probability distribution constructed by the parametric probability modeling module is a bimodal mixed normal distribution model, which divides the near-field area and the far-suburb area into primary and secondary pollution peaks.

[0031] In a preferred embodiment of the present invention, the point optimization module adopts an improved genetic algorithm to maximize the coverage of high-risk areas, while satisfying the constraints of point spacing, boundary restrictions and elevation change rate.

[0032] This invention addresses the shortcomings of the prior art and has the following beneficial effects:

[0033] (1) This invention provides a method and system for optimizing the layout of soil and groundwater monitoring points based on Monte Carlo simulation. By constructing a bimodal mixed probability distribution model to characterize the spatial distribution characteristics of heavy metal concentration, the target area is divided into near-field area and far-field area, corresponding to the main pollution peak and secondary pollution peak, respectively. This enables it to accurately capture the bimodal or even multimodal distribution characteristics of heavy metals in mining areas due to the combined effects of intermittent leakage, local irrigation and soil adsorption and desorption kinetics. This can improve the realism and representativeness of the Monte Carlo simulation scenario set. Compared with the existing methods based on the single distribution assumption, this invention effectively avoids the underestimation of the probability of high concentration tails and the overestimation of the probability of low concentration areas. This makes the parameter probability structure more consistent with the complex evolution mechanism of the real pollution system, thereby reducing the risk of missed detection of pollution hotspots and improving the ability of the monitoring network to identify high-risk areas.

[0034] (2) In this invention, a Bayesian posterior update mechanism is introduced, and the parameter distribution is dynamically corrected by combining the Markov chain Monte Carlo algorithm. The high-confidence simulation scenario is screened by the root mean square error test, so that the parameter posterior distribution is continuously optimized using limited observation data. At the same time, extreme pollution scenarios are forcibly included to cover the peak area formed by historical leakage events. This can effectively solve the problem of missing high-risk extreme values ​​caused by insufficient initial sampling data, so that the simulation scenario is closer to the actual pollution situation. Compared with the problem of incomplete hot spot coverage caused by ignoring extreme values ​​in the traditional Monte Carlo method, this invention can adapt to the data-scarce environment and continuously optimize the model, so as to reduce the missed detection rate of the optimized layout scheme in high-risk areas, thereby improving the response sensitivity of the monitoring network to complex pollution events.

[0035] (3) Based on the pollution probability distribution map, the present invention uses an improved genetic algorithm to achieve spatial optimization of monitoring points. The objective function takes into account the maximization of risk coverage, the constraint of the distance between points and the operability of sampling. The algorithm dynamically adjusts the influence area and constraint conditions of the monitoring points, ensuring coverage of high-risk areas while avoiding spatial redundancy. It can solve the contradiction between hot spot missed detection and cold point redundancy in the traditional system point layout method, thereby achieving accurate allocation of monitoring resources and effectively improving the risk warning benefits of unit monitoring cost. Thus, it provides an economical and efficient technical solution for long-term monitoring in complex environments such as mining areas and farmland. Attached Figure Description

[0036] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments recorded in the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0037] Figure 1 This is a time-series schematic diagram of a preferred embodiment of the present invention for optimizing the layout of soil and groundwater monitoring points based on Monte Carlo simulation.

[0038] Figure 2 This is a schematic diagram of a soil and groundwater monitoring point optimization system based on Monte Carlo simulation, according to a preferred embodiment of the present invention. Detailed Implementation

[0039] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0040] Many specific details are set forth in the following description in order to provide a full understanding of the invention. However, the invention may also be practiced in other ways different from those described herein. Therefore, the scope of protection of the invention is not limited to the specific embodiments disclosed below.

[0041] Application Overview:

[0042] To overcome the limitations of traditional system-based monitoring methods, some studies have attempted to introduce the Monte Carlo simulation framework to enhance the scientific rigor and adaptability of monitoring point placement. Monte Carlo simulation, based on limited initial sampling data, assumes that key parameters follow a specific probability distribution and then generates multiple possible spatial distribution scenarios of pollution through extensive random sampling to reflect the uncertainty of pollution plumes during migration. Finally, based on the spatial distribution of high-uncertainty areas in the simulation results, monitoring points are prioritized for placement, achieving risk-oriented dynamic response. This strategy possesses strong theoretical foresight and flexibility, especially demonstrating superior potential compared to deterministic methods in handling parameter uncertainty, and is therefore considered an important transitional path from traditional grid-based monitoring to intelligent monitoring.

[0043] However, the applicant discovered that in non-steady-state environments like mining areas, characterized by numerous pollution sources, strong historical interference, and weak data foundations, the Monte Carlo method based on a single prior distribution assumption has deep-seated limitations at the theoretical level. Fundamentally, the problem does not stem from the simulation algorithm itself, but from its simplified modeling of the parameter probability structure, which is ill-suited to the complex evolutionary mechanisms of real pollution systems. Specifically, the distribution of heavy metal concentrations in mining areas often exhibits bimodal or even multimodal characteristics (the main peak is concentrated in the near-field region of the tailings dam, while the secondary peaks are distributed in a band along irrigation canals). Traditional methods, by mechanically employing single-modal assumptions such as log-normal distribution, systematically underestimate the probability of high-concentration tailings and overestimate the probability of low-concentration areas, leading to a distortion of the risk profile in the simulated scenario set. Furthermore, because initial sampling is often limited by cost and accessibility, it is difficult to cover the peak areas formed by historical extreme leakage events. This results in the inability to effectively incorporate high-risk extreme values ​​during the simulation process, causing the generated pollution plume "hotspots" to cover only about 60% of the actual area. Ultimately, this leads to a high rate of missed detections in high-risk areas by the optimized sampling scheme, severely weakening the early warning capability of the monitoring system.

[0044] To address the aforementioned issues, this invention proposes a method and system for optimizing the layout of soil and groundwater monitoring points based on Monte Carlo simulation. By constructing a bimodal mixed probability distribution model that integrates multi-source prior knowledge and small sample observation data, and combining a Bayesian posterior update mechanism with a high-confidence scenario screening strategy, a high-fidelity Monte Carlo simulation scenario set reflecting the complex pollution risk pattern of mining areas is generated. Based on this scenario set, spatial optimization of monitoring point layout is implemented, thereby effectively solving the problem of missed pollution hotspots caused by the single distribution assumption in traditional methods. This significantly improves the accuracy and coverage of the monitoring network in identifying high-risk areas, thereby enhancing the timeliness and reliability of pollution early warning.

[0045] like Figure 1 As shown, a method for optimizing the placement of soil and groundwater monitoring points based on Monte Carlo simulation includes the following steps:

[0046] S1. Obtain multi-source prior data and initial sampling data;

[0047] S2. Based on prior data, construct a prior model of mixed probability distribution of heavy metal concentration for different polluted areas, and establish corresponding probability distribution models for soil physicochemical parameters.

[0048] S3. Using the initial sampled data as the observation vector, the prior model is updated posteriorly through statistical inference methods, and the posterior mean and confidence interval of the distribution parameters are output.

[0049] S4. Random sampling is performed based on the updated posterior distribution to generate multiple sets of parameter combinations, which are then input into the pollutant migration model for spatial diffusion simulation; extreme pollution scenarios are also included to form an extended scenario set.

[0050] S5. Calculate the error between each simulated scenario and the initial sampled data, retain the scenarios that meet the preset threshold, and form a subset of high-confidence scenarios;

[0051] S6. Based on high-confidence scenarios, calculate the probability of exceeding the standard for each spatial unit, classify the risk level, and generate a pollution probability distribution map;

[0052] S7. Based on the pollution probability distribution map, under the constraints of point spacing and boundary restrictions, determine the optimal combination of monitoring points through optimization algorithms;

[0053] S8. When receiving new monitoring data, repeat steps S2-S7 to update the model, scene set, and deployment plan.

[0054] In some specific implementations, in step S1, the multi-source prior data includes records of historical pollution events in the mining area, heavy metal concentration archives of remediated sites, regional soil background value databases, agricultural irrigation water usage records, and topographic and geomorphological layer data; the initial sampling data includes heavy metal concentration values, soil pH values, organic matter content, cation exchange capacity, soil texture classification, and groundwater depth parameters measured at multiple sampling points arranged in a preset sparse grid within the target cultivated land area.

[0055] Among them, the heavy metal concentration values ​​were mainly controlled by Cd and Pb; the collected multi-source prior data and initial sampling data were registered in a unified coordinate system (WGS-84 UTM Zone 50N) and stored in a local SQLite relational database.

[0056] In some specific implementations, in step S2, based on the statistical results of historical leakage events, the target area is divided into a near-field zone (≤500 m from the tailings dam) and a far-field zone (>500 m from the tailings dam), corresponding to the spatial distribution ranges of the primary and secondary pollution peaks, respectively. The prior distribution of the heavy metal concentration C is defined as a bimodal mixed normal distribution, and its probability density function expression is as follows:

[0057] ;

[0058] Where N represents the normal distribution function; weighting coefficients The value was determined by normalizing the frequency of historical leakage events in the near-field region, ranging from 0.65 to 0.85; the average value of the main peak... Based on the historical maximum values ​​of known high-concentration points around the tailings dam, the range is set at 8.2 mg / kg ≤ ≤12.6 mg / kg; Standard deviation of main peak Based on the empirical range of 0.35-0.55 for the near-field coefficient of variation (CV), ... The product is calculated to obtain the mean of the second peak. Based on the background superposition increment setting along the irrigation canal, the range is 2.1 mg / kg ≤ ≤3.8 mg / kg; second peak standard deviation Based on the fitting of measured soil heterogeneity data from suburban areas, the range was determined to be 0.7 mg / kg ≤ ≤1.3 mg / kg.

[0059] Furthermore, the marginal distributions of soil physicochemical parameters were modeled using a β distribution for pH value, with shape parameters α=4.2 and β=2.1; and a gamma distribution for organic matter content, with shape parameter k=3.5 and scale parameter θ=0.8%. The distribution parameters were obtained by inversion of the mean and variance from the regional agricultural census report.

[0060] In some specific implementations, in step S3, the observation vector Y = {C1,C2,...,C...} formed by the initial sampled data n}, where n is the number of valid sampling points. Likelihood function The Student's t-distribution is used to enhance robustness to outliers, with its degrees of freedom ν fixed at 4 and location parameters... With scale parameters It is jointly determined by the component parameters in the bimodal mixing model.

[0061] Furthermore, the posterior distribution The solution is obtained using the Markov Chain Monte Carlo (MCMC) algorithm, specifically employing an adaptive Metropolis-Hastings sampling strategy. Five independent Markov chains are initialized, each undergoing 10,000 iterations. The first 2,000 iterations are discarded as a pre-burning period, and the remaining 8,000 iterations are used for posterior statistical inference. The parameter vector θ contains... The convergence of the five core variables was measured using the Gelman-Rubin diagnostic statistic. Validation, when all parameters Convergence is determined at a certain time. The final output includes the posterior mean, 95% confidence interval, and posterior standard deviation of each parameter, stored in a database table with fields including `param`. name (Text type), posterior mean (Floating-point type), posterior std (Floating-point type), ci lower (Floating-point type), ci upper (Floating-point type), r hat (Floating-point type).

[0062] Furthermore, if the relative error of any parameter estimate exceeds 15%, a data supplementation collection command is automatically triggered, and a supplementary task is sent to the on-site UAV-assisted sampling system via the Modbus TCP protocol. The target area is the grid cell with the highest posterior uncertainty at present.

[0063] In some specific implementations, in step S4, the Monte Carlo scene generation performs large-scale random sampling based on the corrected posterior distribution of the parameters to generate M=1000 independent parameter combinations. (m=1,2,…,1000), each set of parameters is input into a coupled pollutant migration model for spatial diffusion simulation. The model is composed of the MODFLOW-2005 groundwater flow module and the MT3DMS solute transport module. The model domain is divided into 1000 m×1000 m, with a spatial grid resolution of 10 m×10 m, totaling 10,000 computational cells. Vertically, it is divided into 3 layers: topsoil (1m), vadose zone (15m), and aquifer (5~10m). The time step is set to 1 day, and the total simulation period is 365 days.

[0064] Furthermore, the boundary conditions were set based on measured water level data: the northern boundary was a constant head boundary with a head value of 35.2 m; the southern boundary was a river drainage boundary with a drainage coefficient of 0.05 m / d; and the east and west sides were zero flux boundaries. The source term loading method was as follows: continuous release from a surface source in the near-field region, with the release rate determined by the posterior concentration. Driven by, the flux released per unit area is kg / (m 2 •yr); In suburban areas, pulsed input is triggered by irrigation events, with a frequency set to twice a month based on agricultural water usage records, each lasting for 3 days, and an input concentration of .

[0065] Furthermore, during the simulation, the adsorption-desorption behavior of heavy metals was described using a linear partitioning model, with the partition coefficient Kd determined by empirical formulas based on measured pH value and organic matter content. Dynamic calculations were performed, with units of L / kg, an effective porosity of 0.35, and a horizontal permeability coefficient of 5.0 × 10⁻⁶. -4 m / s, vertical dispersion is 0.1m.

[0066] Preferably, the Monte Carlo scenario generation forcibly incorporates K=20 extreme pollution scenarios to ensure the integrity of coverage for high-risk tailing events. The extreme pollution scenarios are reconstructed based on historical dam failure events: assuming a momentary tailings dam collapse with a total release of Q0=1.2×10⁻⁶. 5kg of cadmium pollutant was released at a time T0 = 2 h, and the pollutant entered the downstream farmland system via surface runoff. The initial diffusion direction was determined by the slope vector extracted from the digital elevation model (DEM), with an average slope of 2.3%. In this scenario, the initial pollutant concentration field was generated by coupling the two-dimensional shallow water equation with the convection-diffusion equation, improving the spatial resolution to 2 m × 2 m and compressing the time step to 10 s. The finite volume method was used for discretization, and the k-ε model was selected as the turbulence closure model, with the Manning roughness coefficient set to 0.035.

[0067] It should be noted that the generated extreme concentration fields are injected as additional input into the Monte Carlo scene set, resulting in an expanded total number of scenes M'=1020. All scene files are stored in HDF5 format in the / scenarios / directory. Each file contains the following datasets: / concentration_map (a 100×100 floating-point two-dimensional array), / pH_map (a floating-point two-dimensional array), / OM_map (a floating-point two-dimensional array), and / metadata (a JSON string recording parameter combinations and simulation configurations).

[0068] In some specific implementations, step S5 involves performing a consistency check on all M' simulated scenarios, calculating the root mean square error (RMSE) between the simulated and measured values. For the m-th scenario, simulated concentrations are extracted at the n initial sampling points. , compared with the measured concentration The RMSE calculation formula is as follows:

[0069] ;

[0070] Among them, the THR screening threshold is set. RMSE = 0.30 mg / kg, retaining RMSE⁽ᵐ⁾ ≤ THR RMSE All scenarios constitute the high-believability scenario subset S. high Its cardinality is denoted as M. h If M is filtered h If the error is less than 300, the scene reweighting mechanism is activated: the inverse error weight for each scene is calculated. , where ε = 1 × 10 -6 Then, according to weight Sampling with replacement was performed to supplement the sample to 300 groups. The final S... high It contains 300 high-fidelity simulation scenes, whose numbers are stored in a database table, with fields including scenario. id (Plastic) RMSE value (Floating-point type), weight factor (Floating-point type), source type(Text type, value can be normal or extreme).

[0071] In some specific implementations, in step S6, based on the high-confidence scenario subset S high Generate a pollution probability distribution map. For any location (x, y) in the spatial grid, count the number of times it exceeds the national soil environmental quality risk control standard (Cd limit of 0.3 mg / kg in GB 15618-2018) in 300 scenarios. Calculate the probability of exceeding the standard .

[0072] Furthermore, The risk level is divided into six levels with an interval of 0.1: [0, 0.1) is extremely low risk, [0.1, 0.3) is low risk, [0.3, 0.5) is medium risk, [0.5, 0.7) is relatively high risk, [0.7, 0.9) is high risk, and [0.9, 1.0] is extremely high risk. The pollution probability distribution map is generated in GeoTIFF format with a band depth of 32-bit floating point, a projected coordinate system of WGS-84 UTM Zone 50N, and a pixel size of 10m × 10m. World and projection files are included.

[0073] In some specific implementations, in step S7, the optimal monitoring point location is calculated spatially based on the pollution probability distribution map. The total number of monitoring points to be deployed is set to K=12, and the objective function is defined as maximizing the coverage of high-risk areas, expressed mathematically as follows:

[0074] ;

[0075] in, The influence area of ​​the j-th monitoring point is defined by its location coordinates. The constraint is a circular neighborhood centered at a point with a radius R = 50m. The constraints include the distance between any two points. m; all points must be located within the farmland boundary, which is defined by polygon vector data in Shapefile format; the elevation change rate of the points must not exceed 15%.

[0076] Furthermore, an improved genetic algorithm was used for optimization, with a population size of 200, a crossover probability Pc = 0.8, a mutation probability Pm = 0.02, a tournament selection mechanism (tournament size = 3), and a termination condition of no significant improvement in the optimal solution for 50 consecutive generations (ΔF < 1 × 10⁻⁶). -4 Chromosome coding uses real numbers, with each gene representing a single location. The coordinates are used to form a chromosome of length 24, with 12 points arranged sequentially. The fitness function is the objective function F. Each iteration outputs the current optimal point placement scheme, and the final result is stored in the table `optimized`. network In the text, the fields include point id (Integer), x coord (Floating-point type), y coord (Floating-point type), elevation (floating-point type), risk contribution (Floating-point type, unit: %).

[0077] Furthermore, multi-objective optimization is supported, allowing users to switch optimization criteria via configuration files. Optional objective functions include: minimizing the average distance variance from monitoring points to the pollution plume front to enhance the consistency of early warning responses; or maximizing the information entropy gain, i.e., selecting the combination of points that minimizes posterior uncertainty, calculated based on the variance field update estimated by Kriging interpolation. In the multi-objective scenario, the NSGA-II algorithm is used for Pareto front search, generating a non-dominated solution set. The final solution is manually selected by decision-makers based on cost-benefit trade-offs.

[0078] In some specific implementations, in step S8, when a new batch of field monitoring data arrives, the system automatically triggers an update process: first, the new data is merged into the existing observation set, the MCMC iteration process is re-executed, and the posterior distribution of the parameters is updated; then, the Monte Carlo scenario is regenerated and a high-confidence subset is selected; finally, the optimal monitoring point is called to calculate the new scheme. The update cycle is set to once per quarter, or it can be event-driven (such as when a new leak event is detected).

[0079] like Figure 2 As shown, this invention provides a soil and groundwater monitoring site optimization system based on Monte Carlo simulation, comprising:

[0080] The multi-source data acquisition module is used to acquire multi-source prior data and initial sampling data from external databases, geographic information system servers, historical archive management systems and on-site portable sampling terminals, and to perform unified coordinate system registration and storage on the acquired data;

[0081] The parametric probability modeling module is used to construct a bimodal mixed normal distribution prior model of heavy metal concentration based on the multi-source prior data, and to use the β distribution to model soil pH and the gamma distribution to model organic matter content.

[0082] The Bayesian correction module is used to take the initial sampled data as the observation vector, combine the Student t-distribution likelihood function and the Markov chain Monte Carlo algorithm to perform posterior updates on the prior model, output the posterior statistics of each distribution parameter, and trigger a data supplementation collection command when the parameter estimation error exceeds the limit.

[0083] The Monte Carlo scene generation module is used to perform large-scale random sampling based on the corrected parameter posterior distribution, generate multiple sets of parameter combinations and input them into the pollutant migration model for spatial diffusion simulation, while forcibly incorporating extreme pollution scenarios reconstructed based on historical dam failure events.

[0084] The credibility filtering module is used to calculate the root mean square error of each simulation scenario at the initial sampling point position, filter a subset of high credibility scenarios based on a preset threshold, and start a reweighting and supplementation mechanism when the number of scenarios is insufficient.

[0085] The site selection optimization module is used to calculate the optimal site selection scheme based on the pollution probability distribution map, with the goal of maximizing the cumulative risk coverage within the area affected by the monitoring points, while meeting spatial constraints.

[0086] The dynamic update module is used to automatically trigger a closed-loop iterative update process from Bayesian correction to point optimization when new monitoring data is received, and supports version archiving and rollback.

[0087] Specifically, a multi-source data acquisition module obtains multi-source prior data and initial sampling data from external databases, geographic information system servers, historical archive management systems, and portable sampling terminals. This multi-source prior data is then input into a parameter probability modeling module to construct a bimodal mixed normal distribution prior model of heavy metal concentration. The initial sampling data is used as an observation vector and input into a Bayesian correction module. The prior model is then updated posteriorly using a Student's distribution likelihood function and a Markov chain Monte Carlo algorithm, outputting the posterior mean and confidence interval of each distribution parameter. Based on the updated posterior distribution, a Monte Carlo scene generation module performs large-scale random sampling to generate M sets of independent parameter combinations, which are then input into a coupled pollutant migration model. The system performs spatial diffusion simulation and forcibly incorporates K groups of extreme pollution scenarios reconstructed based on dam failure events, forming an expanded total scenario set. A confidence screening module calculates the root mean square error of each simulation scenario at the initial sampling point location, retaining a subset of high-confidence scenarios that meet a set threshold. Based on the high-confidence scenario subset, the probability of exceeding the standard for each spatial grid unit is statistically analyzed, generating a pollution probability distribution map. A site optimization module performs spatial optimization calculations based on the pollution probability distribution map, maximizing the cumulative risk coverage within the monitoring point's influence area while satisfying minimum spacing constraints, boundary limitations, and terrain operability, outputting an optimized site layout scheme. A dynamic update module automatically triggers a closed-loop iterative update of the above process upon receiving new monitoring data.

[0088] It should be noted that the soil and groundwater monitoring site optimization system can implement the steps in the soil and groundwater monitoring site optimization method in the above embodiments and achieve the same technical effect. Refer to the description in the above embodiments, which will not be elaborated here.

[0089] The above description is based on the preferred embodiments of the present invention. It will be apparent to those skilled in the art that the present invention is not limited to the details of the exemplary embodiments described above, and that the invention can be implemented in other specific forms without departing from its spirit or essential characteristics. Therefore, the embodiments should be considered exemplary and non-limiting in all respects. The scope of the invention is defined by the appended claims rather than the foregoing description, and all variations falling within the meaning and scope of equivalents of the claims are intended to be included within the present invention. No reference numerals in the claims should be construed as limiting the scope of the claims.

[0090] Furthermore, it should be understood that although this specification describes embodiments, not every embodiment contains only one independent technical solution. This narrative style is merely for clarity. Those skilled in the art should consider the specification as a whole, and the technical solutions in each embodiment can also be appropriately combined to form other embodiments that can be understood by those skilled in the art.

Claims

1. A method for optimizing the layout of soil and groundwater monitoring points based on Monte Carlo simulation, characterized in that, Includes the following steps: S1. Obtain multi-source prior data and initial sampling data; S2. Based on prior data, construct a prior model of mixed probability distribution of heavy metal concentration for different polluted areas, and establish corresponding probability distribution models for soil physicochemical parameters. S3. Using the initial sampled data as the observation vector, the prior model is updated posteriorly through statistical inference methods, and the posterior mean and confidence interval of the distribution parameters are output. S4. Random sampling is performed based on the updated posterior distribution to generate multiple sets of parameter combinations, which are then input into the pollutant migration model for spatial diffusion simulation; extreme pollution scenarios are also included to form an extended scenario set. S5. Calculate the error between each simulated scenario and the initial sampled data, retain the scenarios that meet the preset threshold, and form a subset of high-confidence scenarios; S6. Based on high-confidence scenarios, calculate the probability of exceeding the standard for each spatial unit, classify the risk level, and generate a pollution probability distribution map; S7. Based on the pollution probability distribution map, under the constraints of point spacing and boundary restrictions, determine the optimal combination of monitoring points through optimization algorithms; S8. When receiving new monitoring data, repeat steps S2-S7 to update the model, scene set, and deployment plan.

2. The method for optimizing the layout of soil and groundwater monitoring points based on Monte Carlo simulation according to claim 1, characterized in that: In step S1, the multi-source prior data includes records of historical pollution events in the mining area, heavy metal concentration archives of remediated sites, regional soil background value database, agricultural irrigation water usage records, and topographic and geomorphological layer data; the initial sampling data includes heavy metal concentration values, soil pH values, organic matter content, cation exchange capacity, soil texture classification, and groundwater depth parameters measured at multiple sampling points arranged in a preset sparse grid within the target cultivated land area.

3. The method for optimizing the layout of soil and groundwater monitoring points based on Monte Carlo simulation according to claim 1, characterized in that: In step S2, the prior model of the mixed probability distribution is a bimodal mixed normal distribution model, which divides the target area into a near-field area and a far-field area, corresponding to the main pollution peak and the secondary pollution peak, respectively. Its probability density function expression is: ； Where N represents the normal distribution function; Indicates the weighting coefficient; and This represents the mean and standard deviation of the main pollution peak in the near-field region; and This represents the mean and standard deviation of secondary pollution peaks in suburban areas.

4. The method for optimizing the layout of soil and groundwater monitoring points based on Monte Carlo simulation according to claim 1, characterized in that: In step S3, the statistical inference method is the Markov chain Monte Carlo algorithm, which combines the student distribution likelihood function to perform posterior updates on the prior model and outputs the posterior mean, confidence interval, and convergence index of the distribution parameters.

5. The method for optimizing the layout of soil and groundwater monitoring points based on Monte Carlo simulation according to claim 1, characterized in that: In step S4, the extreme pollution scenario is reconstructed based on historical dam failure events, assuming that the tailings dam collapses instantaneously and releases pollutants, generating an extreme concentration field and injecting it into the extended scenario set.

6. The method for optimizing the layout of soil and groundwater monitoring points based on Monte Carlo simulation according to claim 1, characterized in that: In step S5, the error is the root mean square error, the preset threshold is 0.30 mg / kg, and a supplement mechanism is activated when the number of scenes is insufficient.

7. The method for optimizing the layout of soil and groundwater monitoring points based on Monte Carlo simulation according to claim 1, characterized in that: In step S7, the optimization algorithm is an improved genetic algorithm or a multi-objective optimization algorithm, and the constraints include a distance of ≥80 m between any two points, the point being located within the boundary of cultivated land, and an elevation change rate of ≤15%.

8. An optimization system based on any one of claims 1-7 for optimizing the layout of soil and groundwater monitoring points using Monte Carlo simulation, characterized in that, include: The multi-source data acquisition module is used to acquire multi-source prior data and initial sampling data; The parametric probability modeling module is used to construct a prior model of the mixed probability distribution of heavy metal concentration and a probability distribution model of soil physicochemical parameters. The Bayesian correction module is used to perform posterior updates on the prior model; The Monte Carlo scene generation module is used to generate extended scene sets; The credibility filtering module is used to filter a subset of high-credibility scenarios; The site selection optimization module is used to determine the optimal combination of monitoring points; The dynamic update module is used to update the monitoring point layout plan when new monitoring data is received.

9. The optimization system for the soil and groundwater monitoring point optimization method based on Monte Carlo simulation according to claim 8, characterized in that: The prior model of the mixed probability distribution constructed by the parametric probability modeling module is a bimodal mixed normal distribution model, which divides the near-field area and the far-suburb area into primary and secondary pollution peaks.

10. The optimization system for the method of optimizing soil and groundwater monitoring point layout based on Monte Carlo simulation according to claim 8, characterized in that: The site selection optimization module employs an improved genetic algorithm to maximize coverage of high-risk areas while satisfying constraints on site spacing, boundary limitations, and elevation change rate.

Images