Reservoir output sand content prediction method based on multi-tree genetic programming

Abstract

The invention provides a reservoir ex-reservoir sand content prediction method based on multi-tree genetic programming, and relates to the technical field of hydraulic engineering, and the method comprises the following steps: S1, data collection and preprocessing: collecting daily scale water and sand of a reservoir and geometric feature data of the reservoir, and carrying out the normalization processing; s2, constructing a multi-tree genetic programming model, wherein the model is composed of symbol trees; s3, an objective function is defined, the objective function is a linear weighting function, and decision coefficients and complexity are comprehensively considered; s4, performing model training and evolution, training a multi-tree genetic programming population through a genetic programming algorithm and a training set, and evaluating population fitness; s5, model verification and evaluation: verifying the trained model by using a verification set; s6, outputting a prediction result; according to the method, through combination of multi-tree genetic programming and a linear weighted objective function, the model can simultaneously ensure high prediction precision and high generalization ability, and through integration of multiple symbol trees, the nonlinear relationship of the reservoir water-sediment process can be accurately captured.

Description

Technical Field

[0001] This invention relates to the field of water conservancy engineering technology, and in particular to a method for predicting reservoir outflow sediment concentration based on multi-tree genetic programming. Background Technology

[0002] The Yellow River has the highest sediment content of any river in the world, with an average annual sediment content of 35 kg / m³. Constructing reservoirs in the Yellow River basin inevitably leads to severe siltation problems. Siltation directly results in reservoir capacity loss, reducing the reservoir's efficiency in regulation, flood control, irrigation, and power generation. The deposited sediment may form "barrier sand" in front of the dam, threatening the dam's safety. Simultaneously, changes in the sediment content of the reservoir's outflow can disrupt the water-sediment balance in the downstream river channel, causing river channel shrinkage, riverbed elevation, and exacerbating the risk of flooding. The Xiaolangdi Reservoir, a key project for sediment control in the middle and lower reaches of the Yellow River, is located in northern Luoyang City, Henan Province. It is a crucial water conservancy hub connecting the upper and lower reaches of the Yellow River and constantly faces high-intensity sedimentation pressure. Therefore, conducting research on predicting the sediment content of the Xiaolangdi Reservoir's outflow is of great strategic significance for sediment control in the Yellow River basin, the safe operation of the reservoir, and downstream ecological protection.

[0003] Currently, the methods for predicting sediment content at reservoir outflow are mainly divided into three categories: measured data analysis, physical model testing, and numerical simulation. However, measured data analysis is difficult to reflect the complex nonlinear coupling mechanism of sediment movement, resulting in limited prediction accuracy and poor generalization ability. Physical model testing is difficult to simulate complex operating conditions, with high experimental costs and long cycles, making it difficult to apply efficiently to actual scheduling. Numerical simulation has high computational complexity, relies on a large number of parameters and boundary conditions, often requires the satisfaction of idealized assumptions, and has significant limitations in application.

[0004] To address the aforementioned issues, machine learning methods, due to their powerful nonlinear modeling capabilities, have been increasingly applied to the fields of hydrological and sediment prediction. However, these machine learning methods still have shortcomings in terms of interpretability, feature selection, and generalization performance control. Summary of the Invention

[0005] The purpose of this invention is to provide a method for predicting reservoir sediment concentration based on multi-tree genetic programming, thereby solving the technical problems existing in the prior art.

[0006] To achieve the above-mentioned objectives, the technical solution adopted by this invention is as follows:

[0007] A method for predicting reservoir outflow sediment concentration based on multi-tree genetic programming includes the following steps: S1: Data collection and preprocessing, collecting daily-scale water and sediment data and reservoir geometric characteristics data, and performing normalization processing; S2: Constructing a multi-tree genetic programming model, the model consisting of... Tree of symbols composition, Tree symbols are used to construct an ensemble model and function set using the averaging method. Includes addition, subtraction, multiplication, and division operations, terminal set Includes input variables and random constants; S3: Define the objective function, which is a linear weighted function, taking into account the coefficient of determination. and Complexity S4: Model Training and Evolution. A multi-tree genetic programming population is trained using a genetic programming algorithm and a training set, and the population fitness is evaluated. The population is updated using subtree crossover, subtree mutation, and selection operations to optimize the model structure and parameters. S5: Model Validation and Evaluation. The trained model is validated using a validation set, and its generalization performance is evaluated using an external validation set. S6: Output Prediction Results. The trained model is applied to actual predictions, outputting the sediment content at the time of release. .

[0008] Furthermore, the input variables in step S2 are: , Prediction task: Learning mappings , making ,in, For inbound flow, For the sand content entering the reservoir, For outbound flow, For water level, For water level difference, For the amount of siltation in the reservoir area, Elevation of the deep thalweg point at section 37 The distance from the delta apex to the dam. For the elevation of the delta apex, This refers to the sand content at the outlet.

[0009] Furthermore, in step S3, the coefficient of determination is considered. ,in, To accurately determine the sand content at the point of release, For predicted values, This is the sample mean.

[0010] Furthermore, in step S3 Complexity: in, Independent and identically distributed Random variable, taking values , For the upper bound, This is the expected value.

[0011] Furthermore, the weight parameters in the objective function Then the individual fitness function is: The goal is to minimize .

[0012] Furthermore, the input to the genetic programming algorithm is: the training set. Validation set Parameter design: Population size Maximum iteration algebra The number of symbol trees in each individual Maximum tree depth Crossover probability Probability of mutation ,championship

[0013] Furthermore, the output of the genetic programming algorithm includes the following steps: T1: Population initialization, generating a population of [size missing]. The initial population, each individual consisted of The tree is composed of random symbols, and the tree depth does not exceed [number]. ;set up T2: Fitness calculation, for each individual in the population. T3: Selection operation, using tournament selection scale. T4: Select parent individuals for reproduction; T5: Genetic operation, for the selected parent individuals, use probability... Perform subtree crossing; with probability Perform mutation operation; T5: Population update, generate a new population. T6: Termination condition, if Then output the validation set The individual with the smallest value Otherwise, let Then return to step T2.

[0014] Furthermore, step T2 includes: T2.1: processing the input sample Calculate the individual output: T2.2: Calculate the coefficient of determination T2.3: Estimation The complexity; from Medium sampling ,calculate T2.4: Calculate the objective function: .

[0015] Compared with the prior art, the present invention has the following beneficial effects:

[0016] (i) This invention combines multi-tree genetic programming with a linear weighted objective function, enabling the model to simultaneously guarantee high prediction accuracy and high generalization ability. Furthermore, by integrating multiple symbolic trees, it can accurately capture the nonlinear relationship of water and sediment processes in reservoirs.

[0017] (ii) By analyzing the importance of features, this invention can enhance the interpretability of the prediction model, providing efficient and reliable intelligent prediction support for reservoir sediment discharge scheduling, flood control decision-making and extending reservoir life. Furthermore, this invention is applicable to prediction scenarios for various types of river reservoirs with high sediment content. Attached Figure Description

[0018] Figure 1 This is a flowchart of the present invention;

[0019] Figure 2 This is a comparison chart of the predictions and actual values ​​made by this invention on the training set of data prior to 2023.

[0020] Figure 3 This is a comparison chart of the predictions and actual values ​​of this invention on a test set of data prior to 2023;

[0021] Figure 4 This is a comparison chart of the predictions and actual values ​​of this invention on the 2023 dataset;

[0022] Figure 5 The importance of features in the 2023 dataset for this invention;

[0023] Figure 6 This is a comparison chart of the predictions and actual values ​​made by this invention on the training set of data prior to 2024.

[0024] Figure 7 This is a comparison chart of the predictions and actual values ​​of this invention on a test set of data prior to 2024;

[0025] Figure 8 This is a comparison chart of the predictions and actual values ​​on the 2024 dataset of this invention;

[0026] Figure 9 The importance of features in the 2024 dataset for this invention. Detailed Implementation

[0027] To make the content of this invention easier to understand, the technical solutions of the embodiments of this invention will be clearly and completely described below with reference to the accompanying drawings. Identical components are represented by the same reference numerals. It should be noted that the terms "front," "rear," "left," "right," "up," and "down" used in the following description refer to directions in the accompanying drawings, while the terms "inner" and "outer" refer to directions toward or away from the geometric center of a specific component, respectively.

[0028] like Figure 1 As shown, this embodiment provides a method for predicting reservoir outflow sediment concentration based on multi-tree genetic programming, including the following steps:

[0029] S1: Data collection and preprocessing, collecting daily-scale water and sediment data and reservoir geometric characteristics data, and performing normalization processing; data collection sources include core water and sediment movement data and reservoir geometry and topography data; the core water and sediment movement data includes inflow discharge. Sand content entering the reservoir Outbound flow Sand content at the outlet The reservoir geometry and topography data include water level. Water level difference Siltation in the reservoir area Elevation of the deep thalweg point at section 37 Distance from the delta apex to the dam Delta apex elevation .

[0030] S2: Construct a multi-tree genetic programming model, the model consisting of... Tree of symbols composition, Tree symbols are used to construct an ensemble model and function set using the averaging method. Includes addition, subtraction, multiplication, and division operations, terminal set Including input variables and random constants; the input variables in step S2 are: , Prediction task: Learning mappings , making ,in, For inbound flow, For the sand content entering the reservoir, For outbound flow, For water level, For water level difference, For the amount of siltation in the reservoir area, Elevation of the deep thalweg point at section 37 The distance from the delta apex to the dam. For the elevation of the delta apex, This refers to the sediment content at the outlet; for the input sample Individual output is defined as: By ensembling multiple trees, the robustness and generalization ability of predictions are improved; the function set When the divisor is 0, the result is returned as 1, avoiding calculation errors caused by a divisor of 0 in traditional division and ensuring stable model operation; terminal set ,in For output variables, It is a random function.

[0031] S3: Define the objective function, which is a linear weighted function, taking into account the coefficients of determination. and Complexity The determination coefficient is considered. ,in, To accurately determine the sand content at the point of release, For predicted values, For sample mean, For the sample size; for the total number of samples; This is transformed into a minimization objective, consistent with subsequent complexity metrics, and adopts... As a term of accuracy loss The smaller the value, the higher the precision.

[0032] The Complexity: in, Independent and identically distributed Random variable, taking values , For the upper bound, This is the expected value;

[0033] The weight parameters in the objective function By linearly combining the accuracy loss term and the complexity term, the individual fitness function becomes: The goal is to minimize The smaller the value, the better the balance between the model's accuracy and complexity.

[0034] S4: Model Training and Evolution. A multi-tree genetic programming population is trained using a genetic programming algorithm and a training set, and the population fitness is evaluated. The population is updated through operations such as subtree crossover, subtree mutation, and selection to optimize the model structure and parameters. This allows individual population members to gradually reduce prediction errors on the training set, accurately capturing the mapping pattern between reservoir outflow sediment concentration and input features. Additionally, through… Complexity constraints and validation set feedback are used to avoid model overfitting and ensure that the best individual in the population still has stable predictive performance under unknown working conditions. The final output is a simplified, parameter-optimized, and highly generalizable prediction model for outbound sediment content.

[0035] The input to the genetic programming algorithm is: training set. Validation set Parameter design: Population size Maximum iteration algebra The number of symbol trees in each individual Maximum tree depth Crossover probability Probability of mutation ,championship The training set The preprocessed daily-scale feature matrix Compared with the actual value of sand content in the corresponding outflow Composition; the said Consistent with the structure of the training set, Given the feature vector of the input year, The actual sediment content of the reservoir in the corresponding year is used. This step uses the controlled variable method to calibrate the parameters. Other parameters are fixed and only the target parameter is adjusted. The quality of the parameters is evaluated by three indicators: the convergence speed of the training set, the validation set, and the model complexity. The optimal parameter combination is subjected to perturbation test. If the fluctuation range of the validation set is <5%, it indicates that the parameter combination is robust and adaptable to different reservoir data.

[0036] The output of the genetic programming algorithm includes the following steps:

[0037] T1: Population initialization, generation size is... The initial population, each individual consisted of The tree is composed of random symbols, and the tree depth does not exceed [number]. ;set up ;

[0038] T2: Fitness calculation, for each individual in the population. Specifically, this includes:

[0039] T2.1: For the input sample Calculate the individual output: ;

[0040] T2.2: Calculate the coefficient of determination ;

[0041] T2.3: Estimation The complexity; from Medium sampling ,calculate ;

[0042] T2.4: Calculate the objective function: ;

[0043] T3: Select operation, using tournament selection scale. Selecting parent individuals for reproduction;

[0044] T4: Genetic operations, for the selected parent individuals, using probability... Perform subtree crossing by randomly selecting a subtree from the two trees and swapping them; with probability... Perform mutation operations, including subtree replacement, node replacement, and constant perturbation;

[0045] T5: Population update, generating a new population. If an elitist strategy is adopted, the best individuals from the previous generation are retained; the population is then updated. ;

[0046] T6: Termination condition, if Then output the validation set The individual with the smallest value Otherwise, let Then return to step T2.

[0047] S5: Model Validation and Evaluation. The trained model is validated using a validation set, and its generalization performance is evaluated using an external validation set. Evaluation metrics include the coefficient of determination. And the results of feature importance analysis.

[0048] S6: Output the prediction results. Apply the trained model to the actual prediction and output the sediment content of the reservoir on the current day. .

[0049] Experimental data:

[0050] Experimental setup:

[0051] Dataset:

[0052] (1) Data prior to 2024 (2000 to 2023); (2) Data in 2024;

[0053] Experiment 1:

[0054] Use data prior to 2023 (2000 to 2022) as the training and testing dataset;

[0055] Use data from 2023 as an additional test dataset to evaluate predictive performance on unknown data;

[0056] Dataset partitioning for Experiment 1:

[0057] (1) Training with data prior to 2023 (excluding 2023): The split ratio for testing is 0.9:0.1;

[0058] (2) All data from 2023 are from the test set;

[0059] Experiment 2:

[0060] Use data from before 2024 as the training and testing datasets, and use data from 2024 as an additional test dataset to evaluate the predictive performance on unknown data;

[0061] Dataset partitioning for Experiment 1:

[0062] (1) Training data before 2024: The test split ratio is 0.9:0.1;

[0063] (2) All data from 2024 are from the test set;

[0064] Model: A regression algorithm based on genetic programming feature learning;

[0065] Algorithm parameter settings: population size is 100, number of iterations is 100, crossover probability is 0.9, mutation probability is 0.1, elite number is 1, and complexity control weight is 10.

[0066] Experimental results:

[0067] Results of Experiment 1: Table (1) shows the experimental results using data prior to 2023 as the training set and the original test set in 2023:

[0068] Table (1)

[0069] train test test (2023) mean 1 0.6333 0.6895 Standard deviation 0 0.1144 0.0196 Maximum value 1 0.7142 0.7063

[0070] Table (1) shows the statistical values ​​of the experimental results from 20 independent runs on the original test set and the 2023 test set, using data prior to 2023 as the training set. A value of 1 indicates that the model fits the training set well and has no underfitting problem; the value on the test set... The average value is 0.6333, which is small compared to the training set, indicating a low risk of overfitting. The test on the 2023 dataset... The average value is 0.6895, indicating that the model has stable generalization ability on unknown data and can meet engineering requirements.

[0071] Results of Experiment 2: Table (2) shows the experimental results using data prior to 2024 as the training set and the original test set in 2024:

[0072] Table (2)

[0073] train test test (2024) mean 1 0.6634 0.2842 Standard deviation 0 0.0298 0.0408 Maximum value 1 0.6829 0.4012

[0074] Table (2) shows the statistical values ​​of the experimental results from 20 independent runs on the original test set and the 2024 test set, using data prior to 2024 as the training set. The value is 1, and the test is performed on the test set. The average value is 0.6634, tested on the 2024 dataset. The value is 0.2842; training and testing The high values ​​indicate that the model fits the historical data well.

[0075] In summary, this invention significantly outperforms traditional methods in terms of prediction accuracy, generalization ability, and interpretability, and can meet the real-time requirements of engineering projects.

[0076] The above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A reservoir outflow sediment concentration prediction method based on multi-tree genetic programming, characterized in that: Comprising the following steps: S1: Data collection and preprocessing, collecting daily scale water and sediment data of reservoir and reservoir geometric characteristic data, and performing normalization processing; S2: Constructing the multi-tree genetic programming model, which is composed of a symbol tree , The symbol tree is composed of an ensemble model by averaging method, and the function set includes addition, subtraction, multiplication and division operations, and the terminal set includes input variables and random constants; S3: define the objective function, the objective function is a linear weighted function, considering the determination coefficient and complexity ; S4: Model training and evolution, training the multi-tree genetic programming population through the genetic programming algorithm and the training set, evaluating the population fitness, updating the population through sub-tree crossover, sub-tree mutation, selection and other operation operators, and optimizing the model structure and parameters; S5: Model verification and evaluation, verifying the trained model using the verification set, and evaluating the generalization performance of the model using the external test set; S6: output the prediction result, apply the trained model to actual prediction, and output the daily outflow sediment concentration .

2. The multi-tree genetic programming based reservoir outflow sediment concentration prediction method according to claim 1, characterized in that: The input variables in the S2 step are: , The prediction task: learning mapping So that Where, is the inflow, is the inflow sediment concentration, is the outflow, is the water level, is the water level difference, is the reservoir sedimentation, is the 37 section thalweg elevation, is the delta vertex distance from the dam, is the delta vertex elevation, is the outflow sediment concentration.

3. The multi-tree genetic programming based reservoir outflow sediment concentration prediction method according to claim 1, characterized in that: The step S3 considers the coefficient of determination wherein, is the true outflow sediment concentration, is the predicted value, is the sample mean.

4. The multi-tree genetic programming based reservoir outflow sediment concentration prediction method according to claim 3, characterized in that: The step S3 Complexity: wherein, are independent and identically distributed random variables taking values , is the supremum, is the expectation value.

5. The multi-tree genetic programming based reservoir outflow sediment concentration prediction method according to claim 4, characterized in that: the weight parameter in the objective function The individual fitness function is then: The objective is to minimize .

6. The multi-tree genetic programming based reservoir outflow sediment concentration prediction method according to claim 1, characterized in that: The input of the genetic programming algorithm is: training set , validation set ; parameter design: population size , maximum iteration number , number of symbol trees in each individual , maximum tree depth ; cross probability , mutation probability , tournament .

7. The multi-tree genetic programming based reservoir outflow sediment concentration prediction method according to claim 1, characterized in that: The output of the genetic programming algorithm comprises the following steps: T1: population initialization, generating an initial population with size , each individual consisting of random symbols of a tree with depth not exceeding ; setting ; T2: Fitness calculation, for each individual in the population ; T3: Select operation, tournament selection scale is used , select parent individuals for breeding; T4: Genetic manipulation, with probability p for selected parent individuals to be mutated Perform subtree crossover; with probability p Perform mutation operation; T5: population update, generating a new population ; T6: Termination condition, if Then output the validation set The individual with the smallest value Otherwise, let Then return to step T2.

8. The multi-tree genetic programming based reservoir outflow sediment concentration prediction method according to claim 7, characterized in that: The T2 step comprises: T2.1: Compute individual outputs for input samples ;​ T2.2: Calculate the coefficient of determination ; T2.3: estimate the complexity; sample from , compute ;​ T2.4: Compute objective function: .

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