Soil infiltration rate fitting method, device and readable storage medium

Abstract

The present application relates to the field of soil hydrology calculation, specifically to a soil infiltration rate fitting method and device, original observation data of soil infiltration test is collected to generate an infiltration rate-time sequence; the data set corresponding to the infiltration rate-time sequence is filtered according to a preset rule to obtain a target data set; a fractional order infiltration rate fitting model is constructed; a target function is constructed based on the target data set and the fractional order infiltration rate fitting model; the target function is optimized for parameters based on a particle swarm optimization method to obtain optimal parameters; a soil infiltration rate fitting curve is generated and a soil infiltration rate fitting result is output according to the optimal parameters. By incorporating exponential decay and power law decay characteristics into a unified mathematical framework, the infiltration decay process under different soil textures and test conditions is uniformly represented, the fitting accuracy and robustness are improved, the model selection sensitivity is reduced, and the stability and realizability of soil infiltration rate numerical calculation are ensured.

Description

Technical Field

[0001] This invention relates to the field of soil hydrological calculation, and more particularly to a method, apparatus, and readable storage medium for fitting soil infiltration rates. Background Technology

[0002] Soil infiltration is a key hydrological process in rainfall recharge, surface runoff formation, irrigation efficiency assessment, and soil and water conservation engineering design. Soil infiltration rate typically decreases gradually from a relatively high initial value over time and tends to stabilize. Accurately characterizing its variation pattern is of great significance for flood risk assessment, farmland irrigation regulation, and slope runoff prediction.

[0003] Currently, empirical infiltration models are commonly used to fit experimental data, estimating model parameters through methods such as least squares to provide a basis for subsequent engineering analysis. Common empirical models include exponential models, represented by the Horton model, and power-law models, represented by the Kostiakov model. The Horton model describes the decay process of infiltration over time using an exponential function. However, in reality, the infiltration rate of many soils exhibits a significant power-law decay characteristic in the middle and later stages, which the exponential function cannot fit. When dealing with this type of data, the Horton model sacrifices fitting accuracy in later stages to fit the rapid initial decay, making it difficult to achieve accurate fitting across the entire time frame. The Kostiakov model describes the decay process of infiltration over time using a power-law function, but its ability to fit rapid changes in infiltration in the initial stage is insufficient.

[0004] In summary, existing empirical infiltration models generally rely on a single functional form. The limitations of their mathematical form make it difficult to uniformly represent the complex and varied infiltration attenuation patterns under different soil textures and experimental conditions (especially the mixed patterns that simultaneously include rapid initial attenuation and power-law attenuation in the middle and later stages). Furthermore, they also suffer from problems such as strong subjectivity in model selection, sensitivity of parameter estimation to data noise, and unstable fitting results. Summary of the Invention

[0005] Considering the problems of existing soil infiltration rate fitting methods, such as limited model form, difficulty in achieving fitting accuracy across different decay stages, sensitivity of parameter estimation to noise and sampling, and poor numerical stability, this invention provides a soil infiltration rate fitting method, which includes the following steps: S100: Collect raw infiltration observation data from soil infiltration tests to generate infiltration rate-time series; S200: Filter the data group corresponding to the infiltration rate-time series according to preset rules to obtain the target dataset; S300: Construct a fractional infiltration rate fitting model; based on the target dataset and the fractional infiltration rate fitting model, construct an objective function; based on the particle swarm optimization method, optimize the parameters of the objective function to obtain the optimal parameters; S400: Based on the optimal parameters, generate a soil infiltration rate fitting curve and output the soil infiltration rate fitting result.

[0006] Preferably, in S100, raw infiltration observation data from soil infiltration tests are collected to generate an infiltration rate-time series, specifically: Collect the cumulative infiltration rate sequence and its corresponding time series during the soil infiltration test; associate the cumulative infiltration rate sequence and the time series to generate cumulative infiltration rate-time data; The cumulative infiltration-time data is subjected to backward difference calculation to obtain the infiltration rate-time series; wherein, the infiltration rate-time series includes the sampling time and the corresponding observed infiltration rate during the soil infiltration test.

[0007] Preferably, in S200, the data set corresponding to the infiltration rate-time series is filtered according to preset rules to obtain the target dataset, specifically as follows: The infiltration rate-time series data set is subjected to outlier data set removal to obtain the target dataset; wherein, the outlier data set includes at least one of the following: data set missing necessary soil attribute information, data set containing outliers, and data set not showing typical decay patterns.

[0008] Preferably, in S300, a fractional-order infiltration rate fitting model is constructed, including: Based on the following formula, a fractional-order infiltration rate fitting model is constructed. f ( t )= f c + bE α (- λt ᵅ) In the above formula, f ( t ) represents any time. t The predicted infiltration rate, E α () represents the Mittag-Leffler function. α , λ , b , f c These represent the model parameters.

[0009] Preferably, in S300, based on the target dataset and the fractional-order infiltration rate fitting model, an objective function is constructed, specifically as follows: The time series data is used as the input to the fractional infiltration rate fitting model to fit the model parameters. α , λ , b , f c The corresponding fitted infiltration rate curve is calculated under the following conditions; Based on the observed infiltration rate sequence and the fitted infiltration rate curve contained in the target dataset, an objective function is constructed; the objective function is used to measure the error between the predicted infiltration rate sequence corresponding to the fitted infiltration rate curve and the observed infiltration rate sequence.

[0010] Preferably, in step S300, the objective function is optimized using a particle swarm optimization method to obtain the optimal parameters, specifically as follows: The objective function is set as the root mean square error between the predicted infiltration rate sequence and the observed infiltration rate sequence. The objective function is optimized by using particle swarm optimization to obtain the optimal parameters.

[0011] Preferably, the objective function is optimized using a particle swarm optimization method to obtain the optimal parameters, specifically as follows: Set the parameters of the fitting model α , λ , b , f c The parameter search interval; the particle swarm is initialized within the parameter search interval, and the particle swarm update termination condition is set; For the fitted model parameters α , λ , b , f c For each candidate parameter group, determine its corresponding predicted infiltration rate sequence, and calculate the root mean square error between the predicted infiltration rate sequence and the observed infiltration rate sequence. After updating the particle swarm optimization, refit the model parameters. α , λ , b , f c For each candidate parameter group, determine its corresponding predicted infiltration rate sequence, and calculate the root mean square error between the predicted infiltration rate sequence and the observed infiltration rate sequence until the particle swarm update termination condition is met. Compare all root mean square errors, and output the candidate parameter group corresponding to the root mean square error with the minimum value as the optimal parameter.

[0012] Preferably, in step S400, based on the optimal parameters, a soil infiltration rate fitting curve is generated and the soil infiltration rate fitting result is output, specifically as follows: Based on the optimal parameters, the time series is input into the fractional infiltration rate fitting model to generate a soil infiltration rate fitting curve. Based on the candidate parameter set corresponding to the optimal parameters and the time series, the independent variables are obtained. z =- λt α And perform lower bound pruning on the independent variable; Based on the independent variables and the fractional infiltration rate fitting model, the soil infiltration rate fitting results are obtained.

[0013] The present invention also provides a soil infiltration rate fitting device, the device comprising: The data acquisition and processing module is used to collect raw infiltration observation data from soil infiltration tests and generate infiltration rate-time series. The data filtering module is used to filter the data groups corresponding to the infiltration rate-time series according to preset rules to obtain the target dataset; The model building module is used to build a fractional-order infiltration rate fitting model. The objective function construction module is used to construct an objective function based on the target dataset and the fractional-order infiltration rate fitting model; The optimization module is used to construct an objective function based on the target dataset and the fractional-order infiltration rate fitting model; and to optimize the parameters of the objective function using the particle swarm optimization method to obtain the optimal parameters. The fitting module is used to generate a soil infiltration rate fitting curve based on the optimal parameters and output the soil infiltration rate fitting result.

[0014] The present invention also provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the above-described soil infiltration rate fitting method.

[0015] The present invention also provides an electronic device, the electronic device comprising: processor; Memory for storing computer programs that can run on the processor; When the computer program is executed by the processor, the above-described soil infiltration rate fitting method is implemented.

[0016] Compared with the prior art, the present invention has the following beneficial effects: This invention constructs a fractional-order infiltration model incorporating Mittag-Leffler function terms, integrating exponential and power-law decay characteristics into a unified mathematical framework. It also constructs an objective function for the root mean square error and employs a particle swarm optimization algorithm to globally optimize the model parameters. During the optimization process, a global Padé rational approximation combined with a lower bound pruning strategy for independent variables is introduced to achieve stable numerical calculations of the Mittag-Leffler function terms. This enables a unified characterization of the infiltration decay process under different soil textures and experimental conditions, improves fitting accuracy and robustness, reduces model selection sensitivity, and ensures the stability and feasibility of numerical calculations of soil infiltration rates.

[0017] The soil infiltration rate fitting method and apparatus of the present invention have the following advantages: First, the soil infiltration rate fitting method and device of the present invention have strong model uniformity. By constructing a fractional infiltration model that includes Mittag-Leffler function terms, the exponential decay and power-law decay characteristics are incorporated into a unified mathematical framework, avoiding the difficulty of subjective selection between the Horton model and the Kostiakov model, and significantly reducing the uncertainty of model form selection.

[0018] Secondly, the soil infiltration rate fitting method and device of the present invention have high fitting accuracy throughout the entire time period. Since the fractional infiltration model has the characteristics of both exponential and power functions, it can simultaneously adapt to the curve shape changes of the two stages of rapid decay in the early stage of infiltration and slow decay in the middle and late stages, overcoming the defect that a single exponential function model or power function model cannot take into account the fitting accuracy throughout the entire time period.

[0019] Third, the soil infiltration rate fitting method and device of the present invention have good parameter estimation robustness. Taking the root mean square error (RMSE) as the objective function, the particle swarm optimization algorithm is introduced for global optimization. Combined with physical heuristic initialization and Latin hypercube sampling strategy, it effectively avoids the problems of traditional least squares method being prone to getting trapped in local optima and being sensitive to initial values, thereby improving the stability of parameter estimation and the ability to resist noise interference.

[0020] Fourth, the soil infiltration rate fitting method and device of the present invention have high numerical calculation stability. In view of the floating-point underflow problem that is prone to occur in the Mittag-Leffler function on long time scales, the global Padé rational approximation method is used for numerical solution, and the lower bound pruning constraint is applied to the independent variable to ensure the reliable calculation of function values ​​in the entire parameter optimization process, thereby improving the applicability of the algorithm in extreme time scales.

[0021] Fifth, the soil infiltration rate fitting method and device of the present invention have strong engineering practicality, and can provide good adaptability to different soil textures (such as sandy soil or clay) and different test conditions (such as indoor constant water head or field double ring infiltration). Moreover, the process steps are clear, the parameter settings are well defined, and it is easy to package into a computer program module or device, which is convenient for integration and application in engineering fields such as hydrological calculation, irrigation decision-making, and soil and water conservation. Attached Figure Description

[0022] To more clearly illustrate the technical solutions in the embodiments of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort. Wherein: Figure 1 This is a flowchart of the soil infiltration rate fitting method provided by the present invention.

[0023] Figure 2 This is a structural diagram of the soil infiltration rate fitting device provided by the present invention.

[0024] Figure 3 This is a structural diagram of an electronic device. Detailed Implementation

[0025] To make the above-mentioned objects, features, and advantages of the present invention more apparent and understandable, the specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings. It should be understood that the specific embodiments described herein are only for explaining the present invention and not for limiting the present invention. Furthermore, it should be noted that, for ease of description, only the parts related to the present invention are shown in the accompanying drawings, not all structures. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without inventive effort are within the scope of protection of the present invention.

[0026] The terms "comprising" and "having," and any variations thereof, used in this invention are intended to cover non-exclusive inclusion. For example, a process, method, product, or apparatus that includes a series of steps or units is not limited to the steps or units listed, but may optionally include steps or units not listed, or may optionally include other steps or units inherent to such process, method, product, or apparatus.

[0027] In this document, the term "embodiment" means that a particular feature, structure, or characteristic described in connection with an embodiment may be included in at least one embodiment of the invention. The appearance of this phrase in various places throughout the specification does not necessarily refer to the same embodiment, nor is it a separate or alternative embodiment mutually exclusive with other embodiments. It will be explicitly and implicitly understood by those skilled in the art that the embodiments described herein can be combined with other embodiments.

[0028] Please see Figure 1 As shown, this invention provides a method for fitting soil infiltration rate, which includes the following steps: S100: Collect raw infiltration observation data from soil infiltration tests to generate infiltration rate-time series; S200: Filter the data sets corresponding to the infiltration rate-time series according to preset rules to obtain the target dataset; S300: Construct a fractional infiltration rate fitting model; construct an objective function based on the target dataset and the fractional infiltration rate fitting model; optimize the parameters of the objective function using the particle swarm optimization method to obtain the optimal parameters; S400: Based on the optimal parameters, generate a soil infiltration rate fitting curve and output the soil infiltration rate fitting results.

[0029] The soil infiltration rate fitting method of this invention constructs a fractional-order infiltration model containing a Mittag-Leffler function term, incorporating exponential and power-law decay characteristics into a unified mathematical framework. It also constructs an objective function for the root mean square error and employs a particle swarm optimization algorithm to globally optimize the model parameters. During the optimization process, a global Padé rational approximation combined with a lower bound pruning strategy for independent variables is introduced to achieve stable numerical calculation of the Mittag-Leffler function term. This enables a unified characterization of the infiltration decay process under different soil textures and experimental conditions, improves fitting accuracy and robustness, reduces model selection sensitivity, and ensures the stability and feasibility of numerical calculation of soil infiltration rate.

[0030] Furthermore, in S100, raw infiltration observation data from soil infiltration tests are collected to generate an infiltration rate-time series, specifically: Collect the cumulative infiltration rate sequence and its corresponding time series during the soil infiltration test; correlate the cumulative infiltration rate sequence and the time series to generate cumulative infiltration rate-time data; The cumulative infiltration-time data were subjected to backward difference calculation to obtain the infiltration rate-time series; the infiltration rate-time series includes the sampling time and the corresponding observed infiltration rate during the soil infiltration test.

[0031] The soil infiltration rate fitting method of this invention can fit soil infiltration test data under different soil textures and experimental conditions, thereby obtaining a fitting curve of infiltration rate changing over time and the corresponding model parameters, improving the accuracy and stability of infiltration rate curve fitting. The aforementioned original infiltration observation data can be, but is not limited to, the cumulative infiltration rate sequence collected during the soil experiment. F ( t ) and its corresponding time series t The cumulative infiltration amount F ( t The unit for time can be cm (centimeter). t The unit can be h (hour). Then, in terms of time... t As a correlation factor, the cumulative infiltration series and time series are correlated to generate cumulative infiltration-time data, thereby arranging the cumulative infiltration data in a time-domain order.

[0032] Infiltration rate-time series refers to the sequence formed by the observed infiltration rate (in cm / h) and time (in h) obtained by differential calculation of the above cumulative infiltration rate series. In practice, the cumulative infiltration rate-time data is first obtained ( t k , F k ),in F k Indicates cumulative penetration. t k The time is represented; then, backward differencing is used to calculate the observed infiltration rate by differentiating the above cumulative infiltration-time data. i k And form an infiltration rate-time series ( t k , i k This refers to the observed infiltration rate sequence. The aforementioned backward differencing refers to the quantification based on adjacent sampling points (…). t k-1 , F k-1 )and( t k , F k The time was calculated. t k Corresponding observed infiltration rate i k ,Right now i k =( F k - F k-1 ) / ( t k -t k-1 Preferably, when the time interval is equal, a fixed time step can be used for calculation (in this case...). t k - t k-1 (For fixed values); when the sampling time interval is unequal, it can be used... t k - t k-1 Calculations are performed to ensure the accuracy of the infiltration rate calculation.

[0033] It is understandable that the aforementioned backward differencing calculation can be performed as a preprocessing step before the fitting calculation. The infiltration rate-time series obtained through preprocessing can be used as input data for subsequent model fitting, thus not requiring the aforementioned backward differencing calculation to be completed within the same main program. By performing the aforementioned preprocessing on the cumulative infiltration-time data to obtain the infiltration rate-time series, a unified data foundation is provided for the subsequent fractional-order infiltration rate fitting model.

[0034] Furthermore, in S200, the data sets corresponding to the infiltration rate-time series are filtered according to preset rules to obtain the target dataset, specifically: The infiltration rate-time series data sets are processed by removing outlier data sets to obtain the target dataset. Outlier data sets include at least one of the following: data sets that lack necessary soil property information, data sets that contain outliers, and data sets that do not show typical decay patterns.

[0035] Considering the influence of external and internal interference factors during the acquisition of raw infiltration observation data, infiltration rate-time series inevitably contains interference noise, reducing its reliability. To improve the accuracy of infiltration rate-time series, it can be filtered according to preset rules to obtain a dataset for parameter estimation of fractional-order infiltration rate fitting models, i.e., the target dataset. The preset rules can be a set of rules for excluding data groups that do not meet the fitting requirements and / or have obvious anomalies.

[0036] It is understandable that the data sets corresponding to the infiltration rate-time series are selected according to the preset rules, which may include, but are not limited to, removing data sets that lack necessary soil attribute information; wherein the necessary soil attribute information may include, but is not limited to, soil texture category information, etc.; removing data values ​​with obvious outliers; wherein the outliers may include, but are not limited to, negative infiltration rate, abnormal deviation of infiltration rate in the initial stage, abnormal deviation of infiltration rate in the final stage, etc.; removing data sets that do not show a typical decay pattern; wherein the typical decay pattern refers to the trend of infiltration rate decreasing as a whole over time and gradually stabilizing.

[0037] Furthermore, the above screening can be performed manually according to preset rules, or automatically by a computer program according to preset rules. By obtaining data sets that better conform to the infiltration attenuation law through this screening, the interference of outlier data sets on parameter optimization can be reduced, improving the stability and reliability of the fitting process.

[0038] Furthermore, in S300, a fractional-order infiltration rate fitting model is constructed, including: Based on the following formula, a fractional-order infiltration rate fitting model is constructed. f ( t )= f c + bE α (- λt ᵅ) In the above formula, f ( t ) represents any time. t The predicted infiltration rate, E α () denotes the Mittag-Leffler function (corresponding to the global Padé rational approximation method). α , λ , b , f c These represent the model parameters.

[0039] It is understandable that the above fractional infiltration rate fitting model can be pre-defined based on the derivation and used to characterize the fractional function model of infiltration rate decaying over time and tending to stabilize.

[0040] Furthermore, in S300, based on the target dataset and the fractional-order infiltration rate fitting model, an objective function is constructed, specifically as follows: Using time series data as input to a fractional infiltration rate fitting model, the model parameters are fitted. α , λ , b , f c The corresponding fitted infiltration rate curve is calculated under the following conditions; Based on the observed infiltration rate sequence and the fitted infiltration rate curve contained in the target dataset, an objective function is constructed; the objective function is used to measure the error between the predicted infiltration rate sequence corresponding to the fitted infiltration rate curve and the observed infiltration rate sequence.

[0041] In practice, the infiltration rate-time series of the target dataset mentioned above can be used as an example. t k , i k ) as the fitting data, where the time seriesi k As input to the fractional infiltration rate fitting model, this is used to fit the candidate parameter set ( α , λ , b , f c The corresponding fitted infiltration rate curve is calculated under the following conditions. f ( t ). Observation infiltration rate sequence i k This is used to construct the objective function to measure the error between the predicted infiltration rate sequence and the observed infiltration rate sequence. The parameters are... α , λ , b , f c The parameters are used as substitutes for subsequent parameter optimization based on the objective function. By calling the fractional infiltration rate fitting model as the fitting model, the infiltration rate decay curves in the form of exponential and power functions can be characterized and their parameters identified within a unified model framework.

[0042] Furthermore, in S300, based on the particle swarm optimization method, the parameters of the objective function are optimized to obtain the optimal parameters, specifically: The objective function is set as the root mean square error between the predicted infiltration rate sequence and the observed infiltration rate sequence. The particle swarm optimization method is used to perform parameter optimization on the objective function to obtain the optimal parameters.

[0043] Understandably, the particle swarm optimization method described above is a global optimization method that minimizes the objective function through a swarm of particles. It can be used for parameter estimation under non-convex, multi-modal objective function conditions. The objective function of particle swarm optimization is set as the root mean square error. RMSE This is used to characterize the difference between the predicted infiltration rate sequence and the observed infiltration rate sequence. The root mean square error mentioned above... RMSE This can be expressed by the following formula: , In the above formula, N represents the total number of time points.

[0044] Optionally, the particle swarm size can be set to 120, and the maximum number of iterations can be set to 600. This is achieved by using the root mean square error... RMSE By using the objective function and combining it with particle swarm optimization for global optimization, we can obtain model parameters that minimize the fitting error, thereby improving fitting accuracy and robustness.

[0045] Furthermore, the objective function is optimized using the particle swarm optimization method to obtain the optimal parameters, specifically as follows: Set the parameters of the fitting modelα , λ , b , f c The parameter search range is defined; the particle swarm is initialized within the parameter search range, and the particle swarm update termination condition is set; the above particle swarm update termination condition can be, but is not limited to, the upper limit of the number of particle swarm updates. When the above upper limit of the number of particle swarm updates is met, the particle swarm update is terminated. For the fitted model parameters α , λ , b , f c For each candidate parameter group, determine its corresponding predicted infiltration rate sequence and calculate the root mean square error between the predicted infiltration rate sequence and the observed infiltration rate sequence. After updating the particle swarm optimization, refit the model parameters. α , λ , b , f c For each candidate parameter group, determine its corresponding predicted infiltration rate sequence and calculate the root mean square error between the predicted infiltration rate sequence and the observed infiltration rate sequence until the particle swarm update termination condition is met. Compare all root mean square errors, and output the candidate parameter group corresponding to the root mean square error with the minimum value as the optimal parameter.

[0046] Furthermore, in S400, based on the optimal parameters, a soil infiltration rate fitting curve is generated and the soil infiltration rate fitting result is output, specifically as follows: Based on the optimal parameters, the time series is input into the fractional infiltration rate fitting model to generate the soil infiltration rate fitting curve. Based on the candidate parameter set and time series corresponding to the optimal parameters, the independent variables are obtained. z =- λt α And perform lower bound pruning on the independent variable; Based on the independent variable and the fractional infiltration rate fitting model, the soil infiltration rate fitting results are obtained.

[0047] In practice, particle swarm initialization can employ a hybrid strategy. Core particles are generated from physically heuristic information such as steady-state infiltration rate, initial infiltration rate, and characteristic time. These core particles, along with other particles, are generated through Latin hypercube sampling within the constraint parameter boundaries, balancing global coverage and physical plausibility. Optionally, the model parameters are fitted... α , λ , b , f c The parameter search range can be set as follows: b∈[0.01, 200]; α ∈[0.1001, 0.9999], and the initial value is 0.5; λ ∈[0.01, ub λ ],in ub λ Indicates parameters λ The upper limit; f c The search range is adaptively determined by the tail information of the original observation data.

[0048] Due to the independent variable z =- λt α Simultaneously affected by parameters λ and α The impact of this, in order to ensure the observation tail end t max Satisfying | z ( t max If |≤600, then it can be determined. λ ≤ 600 / t max α ,in t max This refers to the observation time at the very end of the soil infiltration test. z ( t max )= λt max α Furthermore, parameters can be preferred. α =0.8 is used as a representative empirical value, parameter λ The upper limit can be defined as: ub λ =min(100, 600 / t max 0.8 ), where min(100, 600 / t max 0.8 ) indicates taking 100 and 600 / t max 0.8 The smaller one.

[0049] It is understandable that the above-mentioned soil infiltration rate fitting curve refers to the curve under the optimal parameter set ( α , λ, b, f c The infiltration rate-time curve is calculated by the fractional-order infiltration rate fitting model. The above soil infiltration rate fitting results are used as output content to characterize the fitting effect, and include at least the above soil infiltration rate fitting curve and the root mean square error.RMSE Indicators, model parameter values, etc. Also, the Mittag-Leffler function term refers to... E α (- λt The numerical calculation results of ᵅ), where the independent variable of the Mittag-Leffler function is - λt The above process uses a rational approximation form to numerically solve the Mittag-Leffler function, thereby achieving a global Padé approximation.

[0050] Furthermore, to improve numerical stability over long time scales, this invention modifies the independent variable... z Apply a lower bound clipping constraint: when z When <-600, z Cut to -600; when z When ≥-600, maintain z The original value remains unchanged, that is, by adjusting the independent variable. z Apply lower bound clipping z The value is ≥-600, thus mitigating floating-point underflow and preventing the function term from approaching zero over long time scales due to underflow. By using global Padé approximation combined with lower bound pruning, the computability and numerical stability of the Mittag-Leffler function term can be improved, providing a reliable basis for subsequent parameter optimization. Finally, by outputting the above soil infiltration rate fitting results, the fitting effect of the infiltration rate decay process can be intuitively characterized, and parameterized input can be provided for engineering calculations and subsequent analysis.

[0051] This invention employs infiltration test data from three sets of soils with different textures from the global soil infiltration database SWIG (Rahmati et al., 2018) to verify the adaptability and fitting accuracy of the soil infiltration fitting method of this invention for soils with different textures. The three sets of original observation data are all cumulative infiltration-time data, and the specific information is as follows: The first set of raw observation data corresponds to an infiltration experiment in sandy loam, dataset number I0011, containing 19 data points with a time range of 0–0.75 hours. The second set of raw observation data corresponds to an infiltration experiment in clay loam, dataset number I0012, containing 18 data points with a time range of 0–2.29 hours. The third set of raw observation data corresponds to an infiltration experiment in sandy clay loam, dataset number I0013, containing 21 data points with a time range of 0–4.30 hours.

[0052] For each set of raw observation data (i.e., cumulative infiltration amount minus time data), backward differencing was used to calculate the observed infiltration rate sequence. Due to unequal sampling intervals, a uniform differencing formula was adopted.i k =( F k - F k-1 ) / ( t k - t k-1 ),in F k Indicates time t k The cumulative infiltration amount. Three sets of infiltration rate-time series were obtained through the above processing. t k , i k ), which serve as input data for subsequent model fitting.

[0053] The above three sets of infiltration rate-time series ( t k , i k According to the preset rules, the soil texture information is complete, without outliers, shows a typical decay pattern, and meets the fitting requirements.

[0054] Then set up a fractional infiltration rate fitting model f ( t )= f c + bE α (- λt ᵅ), the parameter search range is uniformly set as follows: b ∈[0.01, 200]; α ∈[0.1001, 0.9999], and the initial value is 0.5; λ ∈[0.01, ub λ ],in ub λ =min(100, 600 / t max 0.8 ), t max This represents the maximum time value for each data set. For sandy loam soil data ( t max =0.75h), ub λ =min(100, 600 / t max 0.8 )=100; For clay loam soil data ( t max =2.29h), ub λ=min(100, 600 / t max 0.8 )=100; For sandy clay loam soil data ( t max =4.3h), ub λ =min(100, 600 / t max 0.8 )=100. And the parameter f c The search range is adaptively determined by the mean of the last 3 points of the infiltration rate sequence observed in each data group. The particle swarm optimization parameters are uniformly set as follows: population size 120, maximum number of iterations 600, and a hybrid initialization strategy combining physical heuristic seed and Latin hypercube sampling is adopted.

[0055] During the parameter optimization process, the independent variables of the Mittag-Leffler function are calculated for each candidate parameter set. z =- λt α and to z Values ​​less than -600 are pruned to -600 to mitigate floating-point underflow. The Mittag-Leffler function terms are computed using a global Padé rational approximation method. E α ( z This allows us to obtain the predicted infiltration rate sequence. f ( t k ), and calculate the root mean square error according to the corresponding formula. RMSE The three sets of data converged after 600 iterations, and the optimal parameters and fitting accuracy are as follows: For the first group of sandy loam soil data (dataset number I0011), the optimal parameter combination is: α =1, λ =13.05, b =17.57cm / h, f c =2.49cm / h. The fitting performance index is: root mean square error. RMSE = 1.05 cm / h, mean absolute error MAE = 0.73 cm / h, Nash efficiency coefficient NSE = 0.96. In comparison, the root mean square error of fitting this set of data using the traditional Horton model is... RMSE The mean absolute error is 1.05 cm / h. MAE The efficiency coefficient is 0.73 cm / h. NSEThe root mean square error of the fitted model using the Modified Kostiakov model is 0.96. RMSE The speed is 2.28 cm / h, with a mean absolute error. MAE The efficiency coefficient is 2.12 cm / h. NSE The accuracy is 0.83. Please refer to Table 1 below. The fitting accuracy of the method of the present invention on the first set of data is comparable to that of the Horton model, but significantly better than that of the Modified Kostiakov model.

[0056] Table 1

[0057] For the second set of clay loam soil data (dataset number I0012), the optimal parameter combination is: α =0.68, λ =15.26, b =47.03cm / h, f c =1.55cm / h. The fitting performance index is: root mean square error. RMSE = 1.40 cm / h, mean absolute error MAE = 1.08 cm / h, Nash efficiency coefficient NSE = 0.93. In comparison, the root mean square error of the Horton model is... RMSE The speed is 2.43 cm / h, and the mean absolute error is... MAE The efficiency is 1.81 cm / h, and the Nash efficiency coefficient is... NSE The root mean square error of the Modified Kostiakov model is 0.80. RMSE The mean absolute error is 1.17 cm / h. MAE The efficiency coefficient is 0.92 cm / h. NSE The value is 0.95. Please refer to Table 2 below. The fitting accuracy of the method of the present invention on the second set of data is better than that of the Horton model and comparable to that of the Modified Kostiakov model.

[0058] Table 2

[0059] For the third set of sandy clay loam soil data (dataset number I0013), the optimal parameter combination is: α =0.69, λ =4.05, b =52.57cm / h, f c =1.88cm / h. The fitting performance index is: root mean square error. RMSE= 0.69 cm / h, mean absolute error MAE = 0.53 cm / h, Nash efficiency coefficient NSE = 0.99. In comparison, the root mean square error of the Horton model is... RMSE The speed is 1.51 cm / h, and the mean absolute error is... MAE The efficiency coefficient is 1.26 cm / h. NSE The root mean square error of the Modified Kostiakov model is 0.97. RMSE The speed is 1.30 cm / h, and the mean absolute error is... MAE The efficiency is 1.16 cm / h, and the Nash efficiency coefficient is... NSE The value is 0.98. Please refer to Table 3 below. The fitting accuracy of the method of the present invention on the third set of data is significantly better than the two Horton models and the Modified Kostiakov model.

[0060] Table 3

[0061] In summary, the embodiments of the present invention, through three sets of raw infiltration observation data with different soil textures and time scales, fully demonstrate the entire process of the method of the present invention, from the preprocessing of raw cumulative infiltration data, model parameter setting, particle swarm optimization to result output, and fully prove that the method of the present invention has good universality, fitting accuracy and numerical stability.

[0062] Please see Figure 2 As shown, the present invention provides a soil infiltration rate fitting device, the device comprising: The data acquisition and processing module is used to collect raw infiltration observation data from soil infiltration tests and generate infiltration rate-time series. The data filtering module is used to filter data groups corresponding to infiltration rate-time series according to preset rules to obtain the target dataset; The model building module is used to build a fractional-order infiltration rate fitting model. The objective function building module is used to construct the objective function based on the target dataset and the fractional infiltration rate fitting model; The optimization module is used to construct an objective function based on the target dataset and a fractional-order infiltration rate fitting model; and to optimize the parameters of the objective function using the particle swarm optimization method to obtain the optimal parameters. The fitting module is used to generate a soil infiltration rate fitting curve based on the optimal parameters and output the soil infiltration rate fitting results.

[0063] The operation and effect of the soil infiltration rate fitting device of the present invention are consistent with the above-mentioned soil infiltration rate fitting method, and the soil infiltration rate fitting device will not be described again here.

[0064] In one embodiment of the present invention, the present invention also provides a computer-readable storage medium on which a computer program is stored, the computer program implementing the soil infiltration rate fitting method as described above when executed by a processor.

[0065] In one embodiment of the present invention, please refer to Figure 3 The present invention also provides an electronic device, wherein the computer device includes at least a memory and a processor, and a computer program is stored in the memory, which, when executed by the processor, implements the soil infiltration rate fitting method as described above.

[0066] Through the above description of the embodiments, those skilled in the art can clearly understand that each embodiment can be implemented by means of a necessary general-purpose hardware platform, or by a combination of hardware and software. Based on this understanding, the above technical solutions, in essence or the part that contributes to the prior art, can be embodied in the form of a computer product. The present invention can take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0067] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit it. Other embodiments may also be used. Although the present invention 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 of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for fitting soil infiltration rate, characterized in that, The method includes the following steps: S100: Collect raw infiltration observation data from soil infiltration tests to generate infiltration rate-time series; S200: Filter the data group corresponding to the infiltration rate-time series according to preset rules to obtain the target dataset; S300: Construct a fractional infiltration rate fitting model; based on the target dataset and the fractional infiltration rate fitting model, construct an objective function; based on the particle swarm optimization method, optimize the parameters of the objective function to obtain the optimal parameters; S400: Based on the optimal parameters, generate a soil infiltration rate fitting curve and output the soil infiltration rate fitting result.

2. The method according to claim 1, characterized in that, In S100, raw infiltration observation data from soil infiltration tests are collected to generate an infiltration rate-time series, specifically: Collect the cumulative infiltration rate sequence and its corresponding time series during the soil infiltration test; associate the cumulative infiltration rate sequence and the time series to generate cumulative infiltration rate-time data; The cumulative infiltration-time data is subjected to backward difference calculation to obtain the infiltration rate-time series; wherein, the infiltration rate-time series includes the sampling time and the corresponding observed infiltration rate during the soil infiltration test.

3. The method according to claim 2, characterized in that, In S200, the data set corresponding to the infiltration rate-time series is filtered according to preset rules to obtain the target dataset, specifically as follows: The infiltration rate-time series data set is subjected to outlier data set removal to obtain the target dataset; wherein, the outlier data set includes at least one of the following: data set missing necessary soil attribute information, data set containing outliers, and data set not showing typical decay patterns.

4. The method according to claim 3, characterized in that, In S300, a fractional infiltration rate fitting model is constructed, including: Based on the following formula, a fractional-order infiltration rate fitting model is constructed. f ( t )= f c + bE α (- λt ᵅ), In the above formula, f ( t ) represents any time. t The predicted infiltration rate, E α () represents the Mittag-Leffler function. α , λ , b , f c These represent the model parameters.

5. The method according to claim 4, characterized in that, In S300, based on the target dataset and the fractional-order infiltration rate fitting model, an objective function is constructed, specifically as follows: The time series data is used as the input to the fractional infiltration rate fitting model to fit the model parameters. α , λ , b , f c The corresponding fitted infiltration rate curve is calculated under the following conditions; Based on the observed infiltration rate sequence and the fitted infiltration rate curve contained in the target dataset, an objective function is constructed; the objective function is used to measure the error between the predicted infiltration rate sequence corresponding to the fitted infiltration rate curve and the observed infiltration rate sequence.

6. The method according to claim 5, characterized in that, In S300, based on the particle swarm optimization method, the objective function is optimized to obtain the optimal parameters, specifically as follows: The objective function is set as the root mean square error between the predicted infiltration rate sequence and the observed infiltration rate sequence. The objective function is optimized by using particle swarm optimization to obtain the optimal parameters.

7. The method according to claim 6, characterized in that, The objective function is optimized using the particle swarm optimization method to obtain the optimal parameters, specifically: Set the parameters of the fitting model α , λ , b , f c The parameter search interval; the particle swarm is initialized within the parameter search interval, and the particle swarm update termination condition is set; For the fitted model parameters α , λ , b , f c For each candidate parameter group, determine its corresponding predicted infiltration rate sequence, and calculate the root mean square error between the predicted infiltration rate sequence and the observed infiltration rate sequence. After updating the particle swarm optimization, refit the model parameters. α , λ , b , f c For each candidate parameter group, determine its corresponding predicted infiltration rate sequence, and calculate the root mean square error between the predicted infiltration rate sequence and the observed infiltration rate sequence until the particle swarm update termination condition is met. Compare all root mean square errors, and output the candidate parameter group corresponding to the root mean square error with the minimum value as the optimal parameter.

8. The method according to claim 7, characterized in that, In S400, based on the optimal parameters, a soil infiltration rate fitting curve is generated and the soil infiltration rate fitting result is output, specifically as follows: Based on the optimal parameters, the time series is input into the fractional infiltration rate fitting model to generate a soil infiltration rate fitting curve. Based on the candidate parameter set corresponding to the optimal parameters and the time series, the independent variables are obtained. z =- λt α And perform lower bound pruning on the independent variable; Based on the independent variables and the fractional infiltration rate fitting model, the soil infiltration rate fitting results are obtained.

9. A soil infiltration rate fitting device, characterized in that, The device includes: The data acquisition and processing module is used to collect raw infiltration observation data from soil infiltration tests and generate infiltration rate-time series. The data filtering module is used to filter the data groups corresponding to the infiltration rate-time series according to preset rules to obtain the target dataset; The model building module is used to build a fractional-order infiltration rate fitting model. The objective function construction module is used to construct an objective function based on the target dataset and the fractional-order infiltration rate fitting model; The optimization module is used to construct an objective function based on the target dataset and the fractional-order infiltration rate fitting model; and to optimize the parameters of the objective function using the particle swarm optimization method to obtain the optimal parameters. The fitting module is used to generate a soil infiltration rate fitting curve based on the optimal parameters and output the soil infiltration rate fitting result.

10. A computer-readable storage medium storing a computer program that, when executed by a processor, implements the soil infiltration rate fitting method according to any one of claims 1-8.

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