Multi-objective optimization and cost prediction method and system for concealed conduit salt elimination project
By employing a deep learning approach based on physical information, the problems of nonlinear parameter relationships and data scarcity in underground salt drainage projects were solved, achieving high-precision multi-objective optimization and cost prediction, and improving the physical interpretability and engineering applicability of the model.
Patent Information
- Application Number
- CN202511741158.9
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-11-25
- Publication Date
- 2026-03-10
AI Technical Summary
Existing technologies struggle to accurately characterize the nonlinear relationships between parameters in underground salt drainage projects. The scarcity of measured data and insufficient regional coverage limit the generalization ability of the models. Traditional methods cannot effectively handle multi-parameter coupling and complex geological conditions, resulting in low cost prediction accuracy and a lack of physical interpretability.
A physical information-based deep learning approach was adopted to generate soil hydraulic parameters through the Van Genuchten-Mualem model. Combined with HYDRUS-2D simulation, the water and salt transport process was simulated to construct spatial topology, water and salt dynamics, and economic cross-features. Multi-objective optimization was performed using a PG-RAN network, with physical constraints of the Richards equation embedded, and the model was trained using a hybrid loss function.
It significantly improves prediction accuracy. In cross-regional sample validation, the coefficient of determination R² = 0.969, explaining 96.9% of the variation of the target variable, shortening the design iteration cycle, realizing multi-objective collaborative optimization, and controlling the prediction error within ±2.1%, which is significantly better than traditional methods.
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Figure CN121638543A_ABST
Abstract
Description
TECHNICAL FIELD
[0001] The present application relates to the technical field of agricultural engineering, in particular to a multi-objective optimization and cost prediction method and system for a buried pipe salt drainage project. BACKGROUND
[0002] Saline-alkali soil improvement is a key measure to ensure food security and promote ecological sustainable development. Among them, the buried pipe salt drainage as an efficient underground water salt regulation technology has been widely used. Whether the engineering design and cost estimation of this technology are scientific and reasonable directly affects the economic benefit and popularization value of the project. At present, the traditional cost prediction method of buried pipe salt drainage project mainly depends on empirical formula or linear regression, which is difficult to effectively cope with the challenges brought by multi-parameter coupling, nonlinear constraints and complex geological conditions. In recent years, deep learning has shown great modeling potential in engineering prediction field, but its application in agricultural water conservancy engineering still faces problems such as lack of physical interpretability and need to improve engineering applicability. SUMMARY
[0003] The technical problems solved by the present application mainly include: how to overcome the problem that the existing empirical model in the prior art cannot accurately describe the nonlinear relationship between parameters, and the lack of actual measurement data and insufficient regional coverage, which limits the generalization ability of the model.
[0004] In a first aspect, an embodiment of the present application provides a multi-objective optimization and cost prediction method for a buried pipe salt drainage project, the method comprising:
[0005] determining soil hydraulic parameters, water-salt transport parameters and a first predicted total cost;
[0006] constructing spatial topological features, water-salt dynamic features and economic cross features according to the soil hydraulic parameters, the water-salt transport parameters and the linear predicted cost;
[0007] inputting the spatial topological features, the water-salt dynamic features and the economic cross features into a prediction model to obtain a buried pipe spacing, a pipe diameter, an irrigation water volume and a predicted cost.
[0008] In an embodiment of the present application, the method further comprises:
[0009] predicting the saturated hydraulic conductivity and the pore distribution index of the soil by using a predicted soil hydraulic feature model, wherein a KL divergence test is performed on the saturated hydraulic conductivity and the pore distribution index, and the predicted soil hydraulic feature model is a Van Genuchten-Mualem model.
[0010] In an embodiment of the present application, the method further comprises:
[0011] A two-dimensional grid model is used to simulate the process of field water and salt transport, and corresponding control equations are obtained, wherein the control equations are as follows:
[0012]
[0013] wherein, is the soil volumetric water content, is the solute (salt) concentration, is the water dynamic dispersion coefficient tensor, is the Darcy flow velocity vector, is the solute source and sink term.
[0014] In specific embodiments of the application, the method further comprises:
[0015] A linear economic cost function is constructed
[0016] wherein, , , respectively are the pipeline length, irrigation water volume and construction time, and alpha, beta and gamma are corresponding cost coefficients, is a regional economic correction term, wherein the first predicted total cost is obtained through the linear economic cost function.
[0017] In specific embodiments of the application, the spatial topological features include an aspect ratio lambda=L / W describing the shape of the plot, and a pipeline density rho_p= / A reflecting the degree of pipeline layout density, wherein A is the plot area;
[0018] The water and salt dynamic features include a unit area salt flux, which is used to reflect the amount of salt migration in a certain time t.
[0019] The economic cross features include a labor-material cost ratio R_cm=C_labor / C_material, which is used to capture the internal relationship of the cost structure, wherein C_labor is the labor cost and C_material is the material cost.
[0020] In specific embodiments of the application, the model input of the prediction model is a 19-dimensional feature vector, which includes 16 basic features and 3 derived features.
[0021] The feature extraction layer is composed of 4 PG-RAN modules, wherein each layer contains 256 neurons and a feature pyramid network to realize deep fusion of multi-scale features.
[0022] The output layer is provided with 12 independent prediction tasks, respectively for calculating the distance between buried pipes, the diameter of the pipe, the irrigation water volume and the predicted cost.
[0023] In specific embodiments of the present application, the method further comprises training the prediction model using a hybrid loss function,
[0024]
[0025] wherein, is the weighted mean squared error of the 11 prediction tasks, excluding the prediction task for predicting cost; is the weight value of the i-th prediction task, is the true value of the i-th task, is the predicted value of the i-th task;
[0026] is a physical regularization term imposed on the gradient of the cost function with respect to the parameter subsurface pipe spacing, pipe diameter, and irrigation water volume, is the cost function is the absolute value of the partial derivative with respect to the parameter subsurface pipe spacing, pipe diameter, and irrigation water volume, respectively, wherein, is a parameter set , ={subsurface pipe spacing, pipe diameter, irrigation water volume}, =1, 2, 3.
[0027] In a second aspect, embodiments of the present application provide a subsurface pipe salt drainage engineering multi-objective optimization and cost prediction system, the system comprising:
[0028] a physical constraint modeling module for determining soil hydraulic parameters, water and salt transport parameters, and a first predicted total cost;
[0029] a feature engineering module for constructing spatial topological features, water and salt dynamic features, and economic cross features based on the soil hydraulic parameters, the water and salt transport parameters, and the linear predicted cost;
[0030] a prediction module for inputting the spatial topological features, the water and salt dynamic features, and the economic cross features into a prediction model to obtain subsurface pipe spacing, pipe diameter, irrigation water volume, and predicted cost.
[0031] In specific embodiments of the present application, the physical constraint modeling module is configured to predict the saturated hydraulic conductivity and the pore distribution index of the soil using a predicted soil hydraulic feature model, wherein a KL divergence test is performed on the saturated hydraulic conductivity and the pore distribution index, and wherein the predicted soil hydraulic feature model is a Van Genuchten-Mualem model.
[0032] In specific embodiments of the present application, the physical constraint modeling module is used to simulate the field water and salt transport process by using a two-dimensional grid model, and the corresponding control equation is obtained, wherein the control equation is as follows:
[0033]
[0034] wherein, is the soil volumetric water content, is the solute (salt) concentration, is the water dynamic dispersion coefficient tensor, is the Darcy flow velocity vector, is the solute source and sink term.
[0035] In specific embodiments of the present application, the physical constraint modeling module is used to construct a linear economic cost function
[0036] wherein, , , respectively are the pipeline length, irrigation water volume and construction time, and α, β, γ are the corresponding cost coefficients, is the regional economic correction term, wherein the first predicted total cost is obtained by the linear economic cost function.
[0037] In specific embodiments of the present application, the feature engineering module is used to determine that the spatial topological features include the aspect ratio λ=L / W describing the shape of the plot, and the pipeline density ρ_p= / A, wherein A is the plot area;
[0038] The water and salt dynamic features include the salt flux per unit area, which is used to reflect the salt migration amount within a certain time t.
[0039] The economic cross features include the labor-material cost ratio R_cm=C_labor / C_material, which is used to capture the internal relationship of the cost structure, wherein C_labor is the labor cost and C_material is the material cost.
[0040] In specific embodiments of the present application, the model input of the prediction model is a 19-dimensional feature vector, which includes 16 basic features and 3 derived features.
[0041] The feature extraction layer is composed of 4 PG-RAN modules, wherein each layer contains 256 neurons and a feature pyramid network to realize the deep fusion of multi-scale features.
[0042] The output layer is provided with 12 independent prediction tasks, which are respectively used to calculate the distance between the hidden pipes, the pipe diameter, the irrigation water volume and the predicted cost.
[0043] In specific embodiments of the present application, the prediction module is further configured to train the prediction model using a hybrid loss function,
[0044]
[0045] wherein, is the weighted mean squared error of the 11 prediction tasks, excluding the prediction task for predicting the cost; is the weight value of the i-th prediction task, is the true value of the i-th task, is the predicted value of the i-th task;
[0046] is a physical regularization term imposed on the gradient of the cost function with respect to the parameter underground pipe spacing, pipe diameter, and irrigation water volume, is the cost function is the absolute value of the partial derivative with respect to the parameter underground pipe spacing, pipe diameter, and irrigation water volume, respectively, wherein, is a parameter set , ={underground pipe spacing, pipe diameter, irrigation water volume}, =1, 2, 3.
[0047] In a third aspect, embodiments of the present application provide a computer readable storage medium having stored thereon a computer program, which, when executed by a processor, implements the steps of the multi-objective optimization and cost prediction method for underground pipe salt drainage projects.
[0048] In a fourth aspect, embodiments of the present application provide an electronic device comprising a memory, a processor, and a computer program stored on the memory and executable on the processor, wherein the processor implements the steps of the multi-objective optimization and cost prediction method for underground pipe salt drainage projects when executing the program.
[0049] Compared with related prior art, the present application has the following outstanding beneficial effects:
[0050] The method of the present application has advantages in multiple aspects through the construction of a multi-objective optimization and cost prediction method for underground pipe salt drainage projects:
[0051] Significant improvement in prediction accuracy: In a cross-regional 1,500-sample verification, the coefficient of determination R²=0.969, which can explain 96.9% of the variation of the target variable, significantly exceeds the engineering application threshold (R²>0.7); compared with benchmark models (DNN, XGBoost, etc.), the performance is significantly improved.
[0052] Engineering application value: Realize the multi-objective collaborative optimization of the salt drainage engineering, and reduce the design iteration cycle to 1 / 5 of the traditional method; In the test of the verification point in Wuyuan County of Hetao Irrigation District, the predicted MAE of construction days is only 0.82 days.
[0053] Technical breakthrough: Solve the problem of multi-physical field coupling modeling, and provide a design paradigm with physical interpretability (embedding Richards equation constraint) and decision-making intelligence. BRIEF DESCRIPTION OF DRAWINGS
[0054] The drawings described herein are used to provide further understanding of the present application, and form a part of the present application. The illustrative embodiments of the present application and their descriptions serve to explain the present application, and do not constitute an improper limitation on the present application. In the drawings:
[0055] Figure 1a The figure is a model structure schematic diagram of the multi-objective optimization and cost prediction method of the salt drainage engineering in the embodiment of the present application;
[0056] Figure 1b The figure is a model structure schematic diagram of the multi-objective optimization and cost prediction method of the salt drainage engineering in the embodiment of the present application;
[0057] Figure 1c The figure is a model structure schematic diagram of the multi-objective optimization and cost prediction method of the salt drainage engineering in the embodiment of the present application;
[0058] Figure 1d The figure is a model structure schematic diagram of the multi-objective optimization and cost prediction method of the salt drainage engineering in the embodiment of the present application;
[0059] Figure 2a The figure is a performance schematic diagram of the multi-objective optimization and cost prediction method of the salt drainage engineering in the embodiment of the present application;
[0060] Figure 2b The figure is a performance schematic diagram of the multi-objective optimization and cost prediction method of the salt drainage engineering in the embodiment of the present application;
[0061] Figure 2c The figure is a performance schematic diagram of the multi-objective optimization and cost prediction method of the salt drainage engineering in the embodiment of the present application;
[0062] Figure 3a The figure is a precision schematic diagram of the multi-objective optimization and cost prediction method of the salt drainage engineering in the embodiment of the present application;
[0063] Figure 3b The figure is a precision schematic diagram of the multi-objective optimization and cost prediction method of the salt drainage engineering in the embodiment of the present application;
[0064] Figure 3c The figure is a precision schematic diagram of the multi-objective optimization and cost prediction method of the salt drainage engineering in the embodiment of the present application;
[0065] Figure 3d The precision diagram of the multi-objective optimization and cost prediction method of the underground pipe salt drainage engineering in the embodiment of the present application is shown in the figure.
[0066] Figure 3e The precision diagram of the multi-objective optimization and cost prediction method of the underground pipe salt drainage engineering in the embodiment of the present application is shown in the figure.
[0067] Figure 3f The precision diagram of the multi-objective optimization and cost prediction method of the underground pipe salt drainage engineering in the embodiment of the present application is shown in the figure.
[0068] Figure 3g The precision diagram of the multi-objective optimization and cost prediction method of the underground pipe salt drainage engineering in the embodiment of the present application is shown in the figure.
[0069] Figure 3h The precision diagram of the multi-objective optimization and cost prediction method of the underground pipe salt drainage engineering in the embodiment of the present application is shown in the figure.
[0070] Figure 3i The precision diagram of the multi-objective optimization and cost prediction method of the underground pipe salt drainage engineering in the embodiment of the present application is shown in the figure.
[0071] Figure 3j The precision diagram of the multi-objective optimization and cost prediction method of the underground pipe salt drainage engineering in the embodiment of the present application is shown in the figure.
[0072] Figure 3k The precision diagram of the multi-objective optimization and cost prediction method of the underground pipe salt drainage engineering in the embodiment of the present application is shown in the figure.
[0073] Figure 3l The precision diagram of the multi-objective optimization and cost prediction method of the underground pipe salt drainage engineering in the embodiment of the present application is shown in the figure.
[0074] Figure 4 The flowchart of the multi-objective optimization and cost prediction method of the underground pipe salt drainage engineering in the embodiment of the present application is shown in the figure.
[0075] Figure 5 The module diagram of the multi-objective optimization and cost prediction system of the underground pipe salt drainage engineering in the embodiment of the present application is shown in the figure.
[0076] Figure 6 The computer hardware diagram of the present application is shown in the figure. DETAILED DESCRIPTION
[0077] In the present application, "at least one" means one or more, and "multiple" means two or more. "At least one of the following" or the like means any combination of the items, including any combination of single item or multiple items. For example, at least one of a, b, or c can mean a, b, c, a-b, a-c, b-c, or a-b-c, where a, b, and c can be single or multiple.
[0078] It should also be understood that the term "and / or" in the present application is only a description of the association relationship of the associated objects, which means that there can be three relationships, for example, A and / or B can mean that A exists alone, A and B exist together, and B exists alone, where A and B can be singular or plural. In addition, the character " / " in the present application generally represents an "or" relationship between the associated objects before and after it, but it can also represent an "and / or" relationship, which can be understood according to the context before and after it.
[0079] It should also be understood that in various embodiments of the present application, the size of the sequence number of the above-mentioned processes does not mean the order of execution, and the execution order of the processes should be determined according to its function and inherent logic, and should not constitute any limitation on the implementation process of the embodiments of the present application.
[0080] In several embodiments provided by the present application, it should be understood that the disclosed devices, apparatuses and methods can be implemented in other ways. For example, the above-described device embodiments are only schematic. For example, the division of the units is only a logical function division, and there can be another division manner in actual implementation. For example, a plurality of units or components can be combined or integrated into another device, or some features can be ignored or not executed. In addition, the coupling or direct coupling or communication connection between the units shown or discussed can be indirect coupling or communication connection through some interface, device or unit, and can be electrical, mechanical or in other forms.
[0081] The units described as separate components can or can not be physically separate, and the components shown as units can or can not be physical units, i.e. they can be located in one place or distributed on multiple network units. Some or all of the units can be selected according to actual needs to achieve the purpose of the present embodiment.
[0082] In addition, each functional unit in each embodiment of the present application can be integrated into a processing unit, or each unit can exist physically, or two or more units can be integrated into one unit.
[0083] If the functions are implemented in the form of software function units and sold or used as independent products, they can be stored in a computer readable storage medium. Based on this understanding, the technical essence of the present application or the part that contributes to the prior art or the part of the technical invention can be embodied in the form of a software product. The computer software product is stored in a storage medium and includes a plurality of instructions for causing a computer device (which can be a personal computer, a server, or a network device, etc.) to execute all or part of the steps of the method described in the various embodiments of the present application. The aforementioned storage medium includes various media that can store program codes, such as a U disk, a mobile hard disk, a read-only memory (ROM), a random access memory (RAM), a magnetic disk or an optical disk.
[0084] In order to make the above features and effects of the present application more clear and easy to understand, the following embodiments are specifically described below with reference to the accompanying drawings. The present specification discloses one or more embodiments comprising the features of the present application. The disclosed embodiments are only used for illustration. The protection scope of the present application is not limited to the disclosed embodiments, and the present application is defined by the appended claims.
[0085] The following is a system embodiment corresponding to the above method embodiment. The present embodiment can be implemented in cooperation with the above embodiments. The related technical details mentioned in the above embodiments are still valid in the present embodiment. In order to reduce repetition, they will not be described again here. Correspondingly, the related technical details mentioned in the present embodiment can also be applied in the above embodiments.
[0086] The subsurface drainage can be understood as a "minimally invasive drainage surgery" for the earth. Specifically, PVC or HDPE pipes with holes are laid according to scientific planning below the critical depth of groundwater, and the salt in the soil surface is dissolved through irrigation (such as Yellow River irrigation, fresh water leaching), and the salt water seeps into the ground under the action of gravity, collects in the pipe through the pipe hole, and then relies on the pipe slope to naturally collect in the water collection well, and finally is discharged from the project area through pumping or self-flowing, so as to permanently remove the salt from the soil. Subsurface drainage can quickly and continuously control the salt in the root layer of the soil below the crop tolerance threshold. Compared with traditional open channel drainage, subsurface drainage does not occupy surface land and is conducive to mechanized farming. Once the investment is made, the benefits can be enjoyed for decades. However, subsurface drainage is a simple trenching and pipe burying, but it is a complex system engineering. First of all, it needs to be accurately positioned at a depth that can effectively intercept salt water. If the pipe spacing is too large, the salt removal effect will be poor, forming a "blind area". If the spacing is too small, the cost will increase sharply. The optimal spacing is a core problem. The pipe diameter and slope determine the drainage capacity and whether there will be sedimentation. These parameters interact with each other and are strongly dependent on the specific hydrogeological conditions of the local area. Therefore, the project investment is huge, including materials, construction, and post-maintenance.
[0087] The traditional subsurface drainage engineering cost prediction method relies on empirical formula or linear regression. Such methods are not up to the task in the face of complex reality and are difficult to cope with "multi-parameter coupling": the cost is affected by dozens of factors such as soil texture, groundwater depth and salinity, climate (evaporation / rainfall), crop salt tolerance, material price, construction difficulty, etc., and these factors are interrelated and mutually constrained. Traditional methods are difficult to depict this complex coupling relationship and cannot handle nonlinear constraints because many relationships are not simple straight lines. For example, reducing the pipe spacing from 20 meters to 10 meters may double the cost, but the improvement in salt removal efficiency may only be 30%, which is a nonlinear relationship. Therefore, a linear model cannot capture this complex change. Under complex geological conditions, the traditional model based on the assumption of homogeneity will have a sharp decline in prediction accuracy when there are impermeable layers, lenses or uneven soil texture. In short, the traditional method is like using a simple static map to navigate a dynamic, multi-dimensional complex terrain, which is bound to have many flaws.
[0088] Deep learning is a branch of machine learning that has the core advantage of being able to automatically learn and extract extremely complex, non-linear features and patterns from massive amounts of high-dimensional historical data through multi-layer neural networks. When applied to subsurface drainage, it can build an "intelligent model" that inputs various geological, climatic, and design parameters to more accurately predict the final drainage effect and project cost, thereby assisting engineers in optimal design. However, there are two major bottlenecks in using deep learning: Poor physical interpretability: Traditional empirical formulas are simple, but each parameter has a clear physical meaning (such as permeability coefficient, specific yield), while the internal logic of deep learning models in making decisions is often opaque. Engineers have difficulty understanding why the model gives a certain prediction result based on which physical laws. This makes it difficult for engineers to fully trust the output of the model, especially when there are abnormal predictions, and it is difficult to investigate and explain from the physical mechanism. Engineering applicability needs to be improved: Deep learning requires a large amount of high-quality, standardized engineering data for training. However, in the field of agricultural water conservancy, data is often insufficient, inconsistent in format, and of varying quality. A model trained in one area may not be directly applicable to another area with completely different geological and hydrological conditions. How to embed known soil water dynamics, solute transport, and other physical laws into neural networks to form "physics information driven machine learning" rather than purely data-driven is a key frontier direction to improve its scientificity, reliability, and engineering applicability.
[0089] Therefore, current subsurface drainage design and cost evaluation mainly rely on empirical formulas (such as Darcy's law) and linear regression models, which have the following defects:
[0090] Multi-parameter coupling is difficult to handle: Soil salinity, pipe spacing, and burial depth have non-linear coupling (such as salinity-pipe spacing relationship), which is difficult to accurately describe by traditional models.
[0091] Lack of physical consistency: Pure data-driven models ignore soil water and salt transport (Richards equation), pipe hydraulics, and other physical constraints, resulting in low engineering feasibility of prediction results.
[0092] Cost prediction bias: Artificial cost functions are significantly influenced by regional factors, and existing models lack generalization ability.
[0093] Multi-objective coordination is insufficient: It cannot simultaneously optimize drainage efficiency (desalination rate η ≥ 85%) and economic cost, and lacks Pareto frontier search capability.
[0094] The existing method cannot simultaneously meet the requirements of physical interpretability, multi-parameter coupling prediction and engineering applicability. Technical difficulties include: physical-data fusion: how to embed Richards equation and Darcy's law into the deep learning framework to ensure that the prediction conforms to the soil water and salt transport law. Multi-task collaboration: how to avoid task conflict when synchronously outputting 12 parameters (water absorption pipe spacing, water collector depth, total cost, etc.). Small sample adaptation: the measured data is scarce, and high-quality synthetic data needs to be generated (verified by KL divergence test D_KL=0.041, p>0.05 to verify the consistency of the distribution).
[0095] The existing model cannot accurately depict the nonlinear relationship between parameters, resulting in poor collaborative optimization effect; the measured data is scarce and the regional coverage is insufficient, which limits the generalization ability of the model; the traditional single-objective optimization method cannot effectively handle the competition between multiple parameters, resulting in the lack of Pareto frontier. Therefore, the application proposes a multi-objective optimization and cost prediction system for underground drainage salt drainage engineering based on physical information deep learning.
[0096] The specific optimization includes: physical constraint data generation, generating soil hydraulic parameters based on the Van Genuchten model, verifying the consistency with the measured distribution by KL divergence test (D_KL=0.041); combining HYDRUS-2D simulation and Monte Carlo simulation to enhance data reliability; multi-scale feature decoupling network, embedding residual attention mechanism and physical regularization loss to improve feature-cost gradient significance by 37.6%; optimizing feature skewness through Box-Cox transformation, KMO test value reaches 0.83; PG-RAN network architecture, physically guided residual attention network (including non-negative constraint, channel attention module); multi-task head joint prediction of 12 parameters (water absorption pipe spacing, water collector depth, irrigation water quantity, total cost, etc.).
[0097] Through the above optimization, the multi-objective optimization and cost prediction system for underground drainage salt drainage engineering based on physical information deep learning constructed by the application has advantages in many aspects: prediction accuracy is significantly improved: in the cross-regional 1,500 sample verification, the determination coefficient R²=0.969, which can explain 96.9% of the variation of the target variable, significantly exceeding the engineering application threshold (R²>0.7); compared with the benchmark model (DNN, XGBoost, etc.), the performance is significantly improved; engineering application value: realizing multi-objective collaborative optimization of underground drainage salt drainage engineering, reducing the design iteration cycle to 1 / 5 of the traditional method; in the verification point test in Wuyuan County of Hetao Irrigation District, the construction day prediction MAE is only 0.82 days; technical breakthrough: solving the problem of multi-physical field coupling modeling, providing a design paradigm with physical interpretability (embedding Richards equation constraint) and decision-making intelligence.
[0098] The implementation process of the multi-objective optimization and cost prediction system for the salt drainage engineering based on physical information deep learning comprises four core modules.
[0099] The physical constraint modeling module comprises a soil parameter generation unit, a water-salt dynamic simulation unit and an economic cost modeling unit; the soil parameter generation unit synthesizes soil hydraulic parameters by using a Van Genuchten-Mualem model, and ensures consistency with the measured distribution through KL divergence test (D_KL≤0.05); the water-salt dynamic simulation unit solves the Richards equation by constructing a two-dimensional grid model with a precision of 0.1m based on HYDRUS-2D; and the economic cost modeling unit generates a cost function and quantifies a regional economic correction term epsilon by using the engineering quantity bill valuation method combined with 10 4 times Monte Carlo simulation.
[0100] The feature engineering module comprises a feature construction unit and a feature optimization unit; the feature construction unit generates spatial topological features (aspect ratio λ=L / W), water-salt dynamic features (unit area salt flux) and economic cross features (labor-material cost ratio); and the feature optimization unit performs Box-Cox transformation and optimizes the effectiveness of the feature set through KMO test (KMO≥0.8).
[0101] The PG-RAN (Physical Regularizer Residual Attention Network) prediction module adopts a feature pyramid network (256 neurons per layer) with four PG-RAN blocks to connect 12 independent task headers; the module implements the physical constraint (constraint strength λ=0.01) of the Richards equation by using the Physics Regularizer, and balances the prediction error and the cost gradient physical constraint by using a hybrid loss function.
[0102] The application provides a multi-objective optimization and cost prediction system for a salt drainage engineering based on physical information deep learning, which comprises the following modules:
[0103] 1. The physical constraint modeling module comprises three units, namely a soil parameter generation unit, a water-salt dynamic simulation unit and an economic cost modeling unit.
[0104] In the soil parameter generation unit, the Van Genuchten-Mualem model is used to synthesize soil hydraulic parameters, including saturated hydraulic conductivity and pore distribution index. To ensure that the generated parameters meet the actual soil conditions, a strict KL divergence test is further performed, requiring that the distribution consistency of the synthesized parameters and the regional measured soil data satisfies KL≤0.05, thereby ensuring the physical authenticity of subsequent simulation. 4
[0105] 2. Feature engineering module, which includes two units, feature construction unit and feature optimization unit.
[0106] In the feature construction unit, three types of features are generated, including spatial topological features (such as plot length-width ratio λ=L / W), water-salt dynamic features (such as unit area salt flux), and economic cross features (such as labor-material cost ratio). The feature optimization unit normalizes the features through Box-Cox transformation, and uses KMO test (KMO≥0.8) to ensure the effectiveness and applicability of the feature set.
[0107] 3. PG-RAN prediction module, which is the core network structure. It uses a feature pyramid network containing 4 PG-RAN blocks as the backbone, with 256 neurons in each layer, and finally connects 12 independent task heads for multi-target parameter prediction. The Richards equation is introduced as a physical constraint through a physics regularizer, with a constraint strength λ of 0.01.
[0108] During training, a hybrid loss function is used, taking into account both prediction error and cost gradient physical constraints to ensure that the model output meets engineering reality.
[0109] Figure 1 is a multi-objective optimization method for underground salt drainage engineering that combines physical mechanisms and data-driven methods. Through a systematic modeling, simulation, and machine learning process, accurate prediction of key engineering parameters and costs is achieved. The specific implementation steps are as follows:
[0110] Step 1: Soil hydraulic parameter modeling
[0111] In the soil parameter generation unit, the Van Genuchten-Mualem model is used to generate soil hydraulic parameters, including saturated hydraulic conductivity and pore distribution index. To ensure that the generated parameters meet the actual soil conditions, a strict KL divergence test is further performed, requiring that the distribution consistency of the synthesized parameters and the regional measured soil data satisfies KL≤0.05, thereby ensuring the physical authenticity of subsequent simulation.
[0112] Step 2: Numerical simulation of water and salt transport
[0113] In the water and salt dynamic simulation unit, a high-resolution two-dimensional grid model (spatial resolution of 0.1 m) is constructed based on the professional software HYDRUS-2D to accurately simulate the process of water and salt transport in the field. This process is controlled by the Richards equation, which has the following specific form:
[0114]
[0115] where, is the volumetric water content of the soil, is the solute (salt) concentration, is the water dynamic dispersion coefficient tensor, is the Darcy flow velocity vector, is the solute source and sink term.
[0116] The Richards equation completely describes the migration, diffusion, and reaction processes of water and solutes in the soil.
[0117] Step 3: Construction of economic cost function
[0118] To conduct economic evaluation, a linear economic cost function is constructed based on the bill of quantities valuation method:
[0119]
[0120] where, , , are the pipe length, irrigation water volume, and construction time, respectively, and α, β, γ are the corresponding cost coefficients.
[0121] To quantify the uncertainty brought by regional economic factors, a regional economic correction term ε is introduced, and its fluctuation range is statistically analyzed through 10 4 Monte Carlo simulations to ensure that its standard deviation is controlled within ±5%, thereby improving the robustness of cost estimation.
[0122] Step 4: Feature construction project
[0123] To achieve deep learning of physical and economic laws, three types of features are systematically constructed:
[0124] Spatial topological features: including the aspect ratio λ = L / W describing the shape of the plot, and the pipe density ρ_p= / A, where A is the plot area, reflecting the density of pipe layout.
[0125] Water salt dynamic characteristics: Taking the salt flux per unit area Φ_s = c·q_avg·t as the core, it comprehensively reflects the salt migration amount within a certain time.
[0126] Economic cross characteristics: The artificial-material cost ratio R_cm = C_labor / C_material is constructed to capture the internal relationship of the cost structure.
[0127] Step 5: Feature optimization engineering
[0128] Before model training, the above features are optimized. First, Box-Cox transformation is used to process the feature data to eliminate its skew distribution and make it closer to normal distribution, improving the model training effect. Then, KMO test is used to evaluate the overall quality of the feature set. In this case, the KMO value is 0.83, indicating that the feature set is very suitable for factor analysis and model learning.
[0129] Step 6: PG_RAN model construction and training
[0130] This step is the construction and training of the core machine learning model. The Figure 1a , Figure 1b , Figure 1c and Figure 1d are exploded views of the schematic diagram of the network architecture of the model, where the modules in 1a, 1b, 1c and 1d are repeatedly displayed to accommodate the modules in the above figures. For example, the dense3 module in 1a and the module in dense3 in 1b are repeated, and so on. 1b and 1c also have repeatedly displayed modules. As shown in Figure 1a , Figure 1b , Figure 1c and Figure 1d , the model input is a 19-dimensional feature vector (including 16 basic features and 3 derived features). The feature extraction layer is composed of 4 PG-RAN modules (each layer contains 256 neurons) and a feature pyramid network to realize the deep fusion of multi-scale features. The output layer has 12 independent task heads, which are used to predict the key target variables such as buried pipe spacing, pipe diameter, irrigation water volume, and total cost.
[0131] Training strategy:
[0132] Loss function: A custom hybrid loss function is used to balance prediction accuracy and physical constraints. Its expression is:
[0133]
[0134] where, is the weighted mean square error sum of 11 prediction tasks (excluding cost). A physical regularization term is applied to the cost function gradient of the key design parameters Ω = {dark pipe spacing, pipe diameter, irrigation water volume} to force the model to learn variable relationships that conform to economic laws.
[0135] An adaptive optimizer was used with an initial learning rate of η = 5 × 10 and a cyclic learning rate strategy (decay factor γ = 0.8) to accelerate convergence and avoid getting trapped in local optima.
[0136] During training, the validation set loss is continuously monitored. If it does not decrease for 15 consecutive rounds, training is terminated early to prevent overfitting.
[0137] Step 7: Project Deployment and Verification
[0138] To comprehensively evaluate model performance, large-scale testing was conducted at three levels:
[0139] Test scenario: Synthetic data: 10,000 samples, generated through Latin hypercube sampling, covering a wide range of design parameter spaces. Measured data: 1,500 samples, derived from field observations in the first irrigation district. External validation: 300 independent samples collected from the second irrigation district to verify the model's generalization ability.
[0140] As attached Figure 2a As shown in Figures 2b and 2c, performance metrics include: Explanatory power: The model's coefficient of determination R² on the test set reaches 0.969, meaning it can explain 96.9% of the variance in the target variable, far exceeding the engineering application threshold (R²>0.7). Prediction accuracy and convergence: The mean absolute error (MAE) on the validation set is 0.065, and the mean absolute percentage error (MAPE) is as low as 0.5%, a decrease of 53.5% compared to the training set. Simultaneously, the mean squared error (MSE=0.03) and final loss value (0.17) on the validation set decrease by 40% and 22% respectively compared to the training set, demonstrating the model's excellent convergence and generalization ability. Industrial-grade reliability: As shown in the attached figure. Figure 3a To be continued Figure 3l As shown, the true-to-predicted scatter plots of all parameters are densely distributed within the ±3% confidence interval of the Y=X baseline, with no systematic shift. This demonstrates that the synergistic effect of physical constraints and feature engineering enables the model to achieve industrial-grade prediction accuracy, with the error stably controlled at ±2.1%, significantly outperforming traditional engineering estimation methods (typical error of ±10~15%), and fully meeting the industrial deployment requirements for multi-objective optimization of underground pipe salt drainage projects.
[0141] Next, the method of the present invention will be described in detail with reference to another specific embodiment. For example... Figure 4 As shown, a multi-objective optimization and cost prediction method for concealed pipe salt drainage projects is proposed. The method includes:
[0142] 110, determining soil hydraulic parameters, water-salt transport parameters and a first predicted total cost;
[0143] 120, constructing spatial topological features, water-salt dynamic features and economic cross features according to the soil hydraulic parameters, the water-salt transport parameters and the linear predicted cost;
[0144] 130, inputting the spatial topological features, the water-salt dynamic features and the economic cross features into a prediction model to obtain an underground pipe spacing, a pipe diameter, an irrigation water volume and a predicted cost.
[0145] In specific embodiments of the application, the method further comprises:
[0146] predicting a saturated hydraulic conductivity and a pore distribution index of the soil using a predicted soil hydraulic feature model, wherein a KL divergence test is performed on the saturated hydraulic conductivity and the pore distribution index, and wherein the predicted soil hydraulic feature model is a Van Genuchten-Mualem model.
[0147] In specific embodiments of the application, the method further comprises:
[0148] simulating a water-salt transport process in the field using a two-dimensional grid model to obtain a corresponding control equation, wherein the control equation is as follows:
[0149]
[0150] wherein, is a soil volumetric water content, is a solute (salt) concentration, is a hydrodynamic dispersion coefficient tensor, is a Darcy flow velocity vector, is a solute source-sink term.
[0151] In specific embodiments of the application, the method further comprises:
[0152] a linear economic cost function is constructed ;
[0153] wherein, , , respectively are a pipe length, an irrigation water volume and a construction time, and α, β, γ are corresponding cost coefficients, is a regional economic correction term, wherein the first predicted total cost is obtained by the linear economic cost function.
[0154] In specific embodiments of the application, the spatial topological features include an aspect ratio λ=L / W describing a shape of a plot, and a pipe density ρ_p= A, wherein A is the plot area;
[0155] The water salt dynamic characteristic includes a unit area salt flux Φ_s=c·q_avg·t, which is used to reflect the salt migration amount within a certain time t.
[0156] The economic cross characteristic includes a labor-material cost ratio R_cm=C_labor / C_material, which is used to capture the internal relationship of the cost structure, wherein C_labor is the labor cost, and C_material is the material cost.
[0157] In specific embodiments of the application, the model input of the prediction model is a 19-dimensional feature vector, which includes 16 basic features and 3 derived features.
[0158] The feature extraction layer is composed of 4 PG-RAN modules, each containing 256 neurons and a feature pyramid network, to realize deep fusion of multi-scale features.
[0159] The output layer is provided with 12 independent prediction tasks, respectively for calculating the buried pipe spacing, pipe diameter, irrigation water volume and predicting the cost.
[0160] In specific embodiments of the application, the method further includes training the prediction model using a hybrid loss function,
[0161]
[0162] wherein, is the weighted mean square error of the 11 prediction tasks, excluding the prediction task for predicting the cost; is the weight value of the i-th prediction task, is the true value of the i-th task, is the predicted value of the i-th task;
[0163] is a physical regularization term applied to the cost function gradient of the parameters buried pipe spacing, pipe diameter, irrigation water volume, is the cost function is the absolute value of the partial derivative with respect to the parameter buried pipe spacing, pipe diameter, irrigation water volume, respectively, wherein, is a parameter set , ={buried pipe spacing, pipe diameter, irrigation water volume}, =1, 2, 3.
[0164] Next, another specific embodiment is combined to describe the method of the embodiment of the application in detail. As Figure 5As shown, a multi-objective optimization and cost prediction system for a buried pipe salt drainage project, the system comprises:
[0165] a physical constraint modeling module for determining soil hydraulic parameters, water-salt transport parameters and a first predicted total cost;
[0166] a feature engineering module for constructing spatial topology features, water-salt dynamic features and economic cross features according to the soil hydraulic parameters, the water-salt transport parameters and the linear predicted cost;
[0167] a prediction module for inputting the spatial topology features, the water-salt dynamic features and the economic cross features into a prediction model to obtain a buried pipe spacing, a pipe diameter, an irrigation water volume and a predicted cost.
[0168] In specific embodiments of the present application, the physical constraint modeling module is configured to predict the saturated hydraulic conductivity and the pore distribution index of the soil using a predicted soil hydraulic feature model, wherein a KL divergence test is performed on the saturated hydraulic conductivity and the pore distribution index, and wherein the predicted soil hydraulic feature model is a Van Genuchten-Mualem model.
[0169] In specific embodiments of the present application, the physical constraint modeling module is configured to simulate a field water-salt transport process using a two-dimensional grid model to obtain corresponding control equations, wherein the control equations are as follows:
[0170]
[0171] wherein, is the soil volumetric water content, is the solute (salt) concentration, is the hydrodynamic dispersion coefficient tensor, is the Darcy flow velocity vector, is the solute source-sink term.
[0172] In specific embodiments of the present application, the physical constraint modeling module is configured to construct a linear economic cost function .
[0173] wherein, , , are the pipe length, the irrigation water volume and the construction time, respectively, and α, β, γ are corresponding cost coefficients, is a regional economic correction term, and wherein the first predicted total cost is obtained through the linear economic cost function.
[0174] In specific embodiments of the present application, the feature engineering module is configured to determine the spatial topology features including a length-width ratio λ=L / W describing the shape of the land plot, and a pipe density ρ_p / A, where A is the area of the land plot;
[0175] The water-salt dynamic features include a salt flux per unit area Φ_s=c·q_avg·t, which is used to reflect the amount of salt migration within a certain time t.
[0176] The economic cross features include a labor-material cost ratio R_cm=C_labor / C_material, which is used to capture the internal relationship of the cost structure, where C_labor is the labor cost and C_material is the material cost.
[0177] In specific embodiments of the present application, the model input of the prediction model is a 19-dimensional feature vector, which includes 16 basic features and 3 derived features.
[0178] The feature extraction layer includes 4 PG-RAN modules, each of which includes 256 neurons and a feature pyramid network, to realize deep fusion of multi-scale features.
[0179] The output layer is provided with 12 independent prediction tasks, respectively for calculating the buried pipe spacing, pipe diameter, irrigation water volume, and predicting the cost.
[0180] In specific embodiments of the present application, the prediction module is further configured to train the prediction model using a hybrid loss function,
[0181]
[0182] wherein, is the weighted mean square error of the 11 prediction tasks, excluding the prediction task for predicting the cost; is the weight value of the i-th prediction task, is the true value of the i-th task, is the predicted value of the i-th task;
[0183] is a physical regularization term applied to the cost function gradient of the parameters buried pipe spacing, pipe diameter, and irrigation water volume, is the cost function is the absolute value of the partial derivative with respect to the parameter buried pipe spacing, pipe diameter, and irrigation water volume, respectively, wherein, is a parameter set , ={buried pipe spacing, pipe diameter, irrigation water volume}, =1, 2, 3.
[0184] In addition, in this application, voice interaction and adaptive fine-tuning can be introduced in the demand input layer to introduce a speech recognition engine (such as BERT-CTC), and natural language instructions (such as "sandy soil budget <= 800,000") are parsed into engineering constraint parameters; at the same time, a pluggable adapter is deployed in the model inference layer, and different crops (coupling FAO-56 water demand model) and regional characteristics (such as saline-alkali land coefficient) are dynamically adapted through lightweight fine-tuning (parameter ratio <0.1%).
[0185] The model in this application can construct a four-layer cache system, wherein the L1 edge layer: store high-frequency parameters (buried depth, real-time salt content), response <=5ms; the L2 regional layer: cache physical simulation results (HYDRUS-2D output); the L3 cloud layer: host Pareto optimization scheme; and the L4 blockchain layer: store evidence decision to prevent tampering.
[0186] Compared with the related prior art, the following outstanding beneficial effects are achieved:
[0187] The method has advantages in many aspects through the multi-objective optimization and cost prediction method system of the underground pipe salt drainage engineering:
[0188] The prediction accuracy is significantly improved: in the cross-regional 1,500 sample verification, the determination coefficient R²=0.969, which can explain 96.9% of the variation of the target variable, significantly exceeds the engineering application threshold (R²>0.7); compared with the benchmark model (DNN, XGBoost, etc.), the performance is significantly improved.
[0189] Engineering application value: realize multi-objective collaborative optimization of underground pipe salt drainage engineering, and reduce the design iteration cycle to 1 / 5 of the traditional method; in the verification point test in Wuyuan County of Hetao Irrigation District, the construction day prediction MAE is only 0.82 days.
[0190] Technical breakthrough: solve the problem of multi-physical field coupling modeling, and provide a design paradigm with physical interpretability (embedding Richards equation constraint) and decision intelligence.
[0191] The embodiment of the application provides a computer readable storage medium, which stores a computer program, and the program is executed by a processor to realize the steps of the multi-objective optimization and cost prediction method of the underground pipe salt drainage engineering.
[0192] The embodiment of the application provides an electronic device, which comprises a memory, a processor and a computer program stored on the memory and executable on the processor, and the processor executes the program to realize the steps of the multi-objective optimization and cost prediction method of the underground pipe salt drainage engineering.
[0193] In addition, in combination with Figure 4The multi-objective optimization and cost prediction method of the described salt drainage engineering can be implemented by an electronic device, such as a computer device. Figure 6 A schematic diagram of a hardware structure of the computer device according to an embodiment of the present application.
[0194] In some embodiments, the computer device can further include a communication interface 83 and a bus 80. As shown, the processor 81, the memory 82, and the communication interface 83 are connected through the bus 80 and complete communication with each other. Figure 6
[0195] Specifically, the processor 81 can include a central processing unit (CPU), or an application specific integrated circuit (ASIC), or can be configured as one or more integrated circuits that implement one or more embodiments of the present application.
[0196] The memory 82 can be used to store or buffer various data files required for processing and / or communication, and possible computer program instructions executed by the processor 81.
[0197] The processor 81 reads and executes the computer program instructions stored in the memory 82 to implement any of the multi-objective optimization and cost prediction methods of the salt drainage engineering described above.
[0198] The technical features of the above-described embodiments can be combined in any manner. To make the description concise, all possible combinations of the technical features in the above-described embodiments are not described, but it should be understood that any combination of the technical features that does not cause contradiction is within the scope of the present disclosure.
[0199] The above-described embodiments only express several embodiments of the present application, and the description is relatively specific and detailed, but it should not be understood as a limitation on the scope of the patent. It should be noted that for ordinary skilled in the art, without departing from the concept of the present application, a number of modifications and improvements can be made, which are within the scope of the present application. Therefore, the scope of protection of the present application should be subject to the appended claims.
Claims
1. A multi-objective optimization and cost prediction method for concealed pipe salt drainage projects, characterized in that, The method comprises: determining soil hydraulic parameters, water-salt transport parameters and a first predicted total cost; constructing spatial topological features, water-salt dynamic features and economic cross features according to the soil hydraulic parameters, the water-salt transport parameters and the linear predicted cost; inputting the spatial topological features, the water-salt dynamic features and the economic cross features into a prediction model to obtain the buried pipe spacing, the pipe diameter, the irrigation water volume and the predicted cost.
2. The method of claim 1, wherein, The method further comprises: predicting the saturated hydraulic conductivity and the pore distribution index of the soil by using a predicted soil hydraulic feature model, wherein a KL divergence test is performed on the saturated hydraulic conductivity and the pore distribution index, and the predicted soil hydraulic feature model is a Van Genuchten-Mualem model.
3. The method of claim 1, wherein, The method further comprises: simulating the water-salt transport process in the field by using a two-dimensional grid model to obtain corresponding control equations, wherein the control equations are as follows: where, is the volumetric water content of the soil, is the solute (salt) concentration, is the hydrodynamic dispersion coefficient tensor, is the Darcy velocity vector, is the solute source / sink term.
4. The method of claim 1, wherein, The method further comprises: A cost function was constructed wherein, , , are the pipeline length, irrigation water volume and construction time, respectively, and α, β, γ are the corresponding cost coefficients, is a regional economic correction term, wherein the first predicted total cost is obtained by the linear economic cost function.
5. The method of claim 1, wherein The spatial topological features include an aspect ratio λ=L / W describing the shape of the plot, and a pipe density ρ_p reflecting the degree of pipe layout density / A, where A is the plot area; The water-salt dynamic features include a salt flux per unit area, which is used to reflect the salt migration amount within a certain time. The economic cross features include a labor-material cost ratio R_cm = C_labor / C_material, which is used to capture the internal relationship of the cost structure, wherein C_labor is the labor cost and C_material is the material cost.
6. The method of claim 1, wherein, The model input of the prediction model is a 19-dimensional feature vector, which includes 16 basic features and 3 derived features; The feature extraction layer includes 4 PG-RAN modules, each of which contains 256 neurons and a feature pyramid network to realize deep fusion of multi-scale features; The output layer is provided with 12 independent prediction tasks for calculating the buried pipe spacing, the pipe diameter, the irrigation water volume and the predicted cost.
7. The method of claim 1, wherein, The method further comprises training the prediction model by using a hybrid loss function, wherein, is the weighted mean squared error sum for 11 prediction tasks, excluding the prediction task for predicting cost; is the weight value for the i-th prediction task, is the true value for the i-th task, is the predicted value for the i-th task; are absolute values of partial derivatives with respect to the parameter sub-surface pipe spacing, the pipe diameter, the irrigation water quantity, respectively, wherein is the cost function are absolute values of partial derivatives with respect to the parameter sub-surface pipe spacing, the pipe diameter, the irrigation water quantity, respectively, wherein is a parameter set , ={sub-surface pipe spacing, pipe diameter, irrigation water quantity}, =1,2,3.
8. A multi-objective optimization and cost prediction system for a buried pipe salt drainage project, characterized in that, The system comprises: a physical constraint modeling module for determining soil hydraulic parameters, water-salt transport parameters and a first predicted total cost; a feature engineering module for constructing spatial topological features, water-salt dynamic features and economic cross features according to the soil hydraulic parameters, the water-salt transport parameters and the linear predicted cost; a prediction module for inputting the spatial topological features, the water-salt dynamic features and the economic cross features into a prediction model to obtain the buried pipe spacing, the pipe diameter, the irrigation water volume and the predicted cost.
9. A computer readable storage medium having stored thereon a computer program, characterized in that, The program is executed by the processor to realize the steps of the buried pipe salt drainage engineering multi-objective optimization and cost prediction method according to any one of claims 1-7.
10. An electronic device comprising a memory, a processor, and a computer program stored on the memory and executable on the processor, characterized in that, The processor executes the program to realize the steps of the buried pipe salt drainage engineering multi-objective optimization and cost prediction method according to any one of claims 1-7.