GWO-BP improved neural network-based irrigation area underground water level burial depth prediction method

Abstract

The invention discloses an irrigation area underground water level burial depth prediction method based on a GWO-BP improved neural network, and the method comprises the steps: obtaining the data of the influence factors of the irrigation area underground water level burial depth, and carrying out the normalization processing; determining a BP neural network topological structure according to the number of the input and output parameters; optimizing the weight and threshold of the BP neural network based on an improved grey wolf algorithm GWO, and taking the optimized weight and threshold as the initial weight and threshold of the BP neural network; the trained improved GWO-BP model is used for underground water level burial depth prediction, and the monthly underground water level burial depth is finally obtained after an output result is subjected to reverse normalization processing; and calculating a Nash efficiency coefficient, and performing parameter optimization on the GWO-BP prediction model to obtain an irrigation area underground water level burial depth prediction model. The improved grey wolf algorithm is used for optimizing the weight and the threshold value of the BP neural network, the optimized weight and the optimized threshold value serve as the initial weight and the initial threshold value of the BP nerve, and the precision and the stability of the irrigation area underground water level burial depth prediction model can be improved.

Description

Technical Field

[0001] The present invention relates to the technical field of groundwater level depth prediction, and in particular to a method for predicting groundwater level depth in an irrigation area based on a GWO-BP improved neural network with high accuracy and good stability. Background Art

[0002] Groundwater depth in irrigation areas influences crop growth, yield, and soil water and nutrient absorption. Appropriate groundwater depth can effectively improve farmland water and soil environments, promote crop growth, and increase crop yields. Particularly in my country's arid northwest region, excessively high groundwater levels can exacerbate secondary soil salinization, while excessively low levels can adversely impact terrestrial ecosystems such as farmland crops, natural grasslands, and woodlands. Furthermore, groundwater depth provides an important reference for groundwater extraction in irrigation areas. Therefore, accurate and reliable groundwater depth prediction plays a vital role in agricultural production, ecology, and water resource management in irrigation areas, and is crucial for the sustainable development of agriculture in these areas.

[0003] Over the past few decades, scholars from various fields, both domestically and internationally, have employed a variety of methods to assess groundwater level fluctuations in various regions around the world. Commonly used methods for predicting groundwater depth include regression analysis, time series analysis, and neural networks. However, most existing methods suffer from shortcomings such as low prediction accuracy and instability. Further research is needed to identify groundwater depth prediction methods suitable for specific regions through comparison, validation, and optimization of different methods, thereby improving the accuracy and stability of groundwater depth prediction results for specific irrigation districts. Therefore, this paper proposes a groundwater depth prediction method for irrigation districts based on an improved GWO-BP neural network. Summary of the Invention

[0004] Purpose of the invention: The purpose of the present invention is to provide a method for predicting the depth of groundwater level in irrigation areas based on the improved GWO-BP neural network with high accuracy and good stability.

[0005] Technical solution: The method for predicting the depth of groundwater level in an irrigation area based on the improved GWO-BP neural network of the present invention comprises the following steps:

[0006] (1) Obtain data on factors affecting the depth of groundwater level in the irrigation area and perform normalization processing;

[0007] (2) Determine the BP neural network topology according to the number of input and output parameters;

[0008] (3) Optimize the weights and thresholds of the BP neural network based on the improved grey wolf algorithm GWO, and use the optimized weights and thresholds as the initial weights and thresholds of the BP neural network;

[0009] (4) Using the trained improved GWO-BP model to predict the groundwater depth, the output results are denormalized to obtain the monthly groundwater depth;

[0010] (5) Based on the prediction results, the Nash efficiency coefficient NSE is calculated, and the parameters of the GWO-BP prediction model are optimized to obtain a suitable irrigation area groundwater level depth prediction model.

[0011] Furthermore, the factors affecting the depth of the groundwater level in step (1) include monthly rainfall, Yellow River water diversion, evaporation, drainage, and the depth of the groundwater level in the previous month.

[0012] Furthermore, the calculation formula for data normalization in step (1) is:

[0013]

[0014] Among them, x max is the maximum value of the input sequence; x min is the minimum value of the input sequence; x and x′ are the data before and after normalization, respectively.

[0015] Furthermore, step (2) includes establishing a three-layer network topology structure of m×k×n, determining the values ​​of m, k, and n, where m is the number of input layer nodes, k is the number of hidden layer nodes, and n is the number of output layer nodes, and determining the maximum number of training times, transfer function, and training function.

[0016] Furthermore, the step (3) includes the following steps:

[0017] (3.1) Parameter settings: population size N, current number of iterations t and maximum number of iterations T, randomly generated A, a, C parameters, initial population generation;

[0018] Among them, the update formulas of A, a, and C are:

[0019]

[0020] A=2a×r1-a

[0021] C=2r2

[0022] Among them, t is the current iteration number, T max is the maximum number of iterations, r1 and r2 obey a uniform distribution between [0, 1]. (3.2) Construct a groundwater depth prediction neural network fitness function, calculate the fitness values ​​of individual gray wolves, and select the top three best wolf records as α, β, and γ according to the fitness value ranking.

[0023] (3.3) Update the location information and control parameters A, a, C of each gray wolf;

[0024] (3.4) Determine whether the maximum number of iterations or the set error has been reached. If "yes", output the optimal weight threshold corresponding to the optimal solution. If "no", repeat steps (3.2)-(3.4).

[0025] Furthermore, in the step (3.1), the Sobol sequence is introduced to initialize the generated population when the initial population is generated. The position of the population generated by the initialization is expressed as:

[0026] X i =(b u -b l )*r+b l

[0027] Among them, b u and b l are the upper and lower bounds of the search space respectively; r is a random number in the range of [0, 1] generated by the Sobol sequence.

[0028] Furthermore, the control parameter a in step (3.3) changes nonlinearly with the number of iterations. The improved expression of a is as follows:

[0029]

[0030] Among them, aini is 2, afin is 0, t is the current iteration number, T max is the maximum number of iterations.

[0031] Furthermore, the calculation formula of the Nash efficiency coefficient NSE in step (5) is:

[0032]

[0033] Among them, O i is the measured value of the groundwater depth; O′ i is the measured average value of groundwater depth; P i is the predicted value of the GWO-BP model; n is the number of observations.

[0034] Beneficial effects: Compared with the prior art, the present invention has the following significant advantages: the present invention proposes an improved method for optimizing the combination of the initial population and the control parameter a that changes nonlinearly with the number of iterations using the Sobol sequence. The Sobol sequence makes the overall distribution of the initial population more uniform, laying the foundation for global search. The control parameter a that changes nonlinearly with the number of iterations can better balance the local search and global search capabilities, achieving a coordinated improvement in the search capabilities of the algorithm at different stages, effectively improving the convergence speed and accuracy of the gray wolf algorithm, and avoiding it from falling into a local optimal solution. The improved gray wolf algorithm is used to optimize the weights and thresholds of the BP neural network, and the optimized weights and thresholds are used as the initial weights and thresholds of the BP neural network, which can improve the accuracy and stability of the irrigation area groundwater level depth prediction model. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] Figure 1 Detailed flow chart of the method of the present invention;

[0036] Figure 2 It is a BP neural network structure;

[0037] Figure 3 Comparison chart for Sobol sequence and random population initialization;

[0038] Figure 4 Comparison chart of 10 predicted NSE values ​​for BP and improved GWO-BP;

[0039] Figure 5 Comparison chart of groundwater level depth BP, improved GWO-BP predicted value and measured value. DETAILED DESCRIPTION

[0040] The technical solution of the present invention will be further described below with reference to the accompanying drawings.

[0041] Take a certain irrigation district as an example. The designed irrigation area is 8.61 million mu, including five major irrigation areas, which are irrigation area ①, irrigation area ②, irrigation area ③, irrigation area ④ and irrigation area ⑤ from west to east. The water resources of the irrigation area are mainly composed of three parts: Yellow River water, precipitation, and groundwater. Taking irrigation area ③ of the irrigation district as an example, based on the statistical data of the irrigation district from 2000 to 2012, the main factors affecting the groundwater level depth of the irrigation district are analyzed, which are mainly rainfall, Yellow River water, evaporation, drainage, and groundwater depth of the previous month. Therefore, the input parameters of the model are monthly rainfall, Yellow River water, evaporation, drainage and groundwater depth of the previous month, and the output parameters are the actual groundwater level depth of each month. Use the following methods respectively: Figure 2 The BP neural network and the improved GWO-BP neural network are used to predict the groundwater level in irrigation area ③ in 2012, and the prediction results are compared and analyzed to provide a reference for the selection of groundwater level prediction methods in irrigation areas. Figure 1 As shown, the present invention includes the following steps:

[0042] (1) Obtain data on the main factors affecting the groundwater depth in the irrigation area, including monthly rainfall, Yellow River water diversion, evaporation, drainage, and groundwater depth in the previous month, and normalize the above data;

[0043] Based on the statistical data of irrigation area ③ from 2000 to 2012, the main factors affecting the groundwater depth were analyzed, including rainfall, Yellow River water diversion, evaporation, drainage, and the groundwater depth of the previous month. The data normalization calculation formula is:

[0044]

[0045] Among them, x max is the maximum value of the input sequence; x min is the minimum value of the input sequence; x, x′ are the data before and after normalization respectively.

[0046] (2) Determine the BP neural network topology according to the number of input and output parameters, establish a three-layer network topology of m×k×n, determine the values ​​of m, k, and n, where m is the number of input layer nodes, k is the number of hidden layer nodes, and n is the number of output layer nodes, and determine the maximum number of training times, learning rate, etc.

[0047] The input parameters are monthly rainfall, Yellow River water diversion, evaporation, drainage, and the groundwater depth of the previous month. The output parameter is the actual groundwater depth of each month. A three-layer network topology of 5×6×1 is established, where 5 is the number of input layer nodes, 6 is the number of hidden layer nodes, and 1 is the number of output layer nodes. The maximum number of training times is set to 2000, the learning rate is 0.001, and the error accuracy is 1×10 -5 .

[0048] (3) Optimize the weights and thresholds of the BP neural network based on the improved gray wolf algorithm, and use the weights and thresholds as the initial weights and thresholds of the BP neural network; the specific steps are as follows:

[0049] (3.1) Parameter setting: population size N = 20, current iteration number t and maximum iteration number T = 15, randomly generated parameters a, A, C, and initial population generation. Among them, the initial population generation improvement includes the introduction of the Sobol sequence to initialize the generated population when generating the initial population. The Sobol sequence is a common low-discrepancy sequence. Compared with the traditional pseudo-random sequence, it can generate a series of independent and relatively uniformly distributed points. These points have low variance and high-dimensional uniformity. Figure 3The figure shows the overall distribution of the populations obtained by Sobol sequence initialization and random initialization in two-dimensional space. The population size of both methods is set to 100. The search space is in the interval [0, 1] and the Sobol sequence is introduced to initialize the population. The population position formula generated by Sobol sequence initialization is:

[0050] X i =(b u -b l )*r+b l

[0051] Among them, b u and b l are the upper and lower bounds of the search space respectively; r is a random number in the range of [0, 1] generated by the Sobol sequence.

[0052] (3.2) Construct a groundwater depth prediction neural network fitness function, calculate the fitness values ​​of individual gray wolves, and select the top three best wolves as α, β, and γ according to the fitness value ranking;

[0053] (3.3) Update the location information and control parameters A, a, C of each gray wolf.

[0054] Among them, the improvement of the control parameter a includes that the control parameter a changes nonlinearly with the number of iterations. The nonlinear change of the control parameter a can more effectively balance the local search and global search capabilities. The expression of the improved a is as follows:

[0055]

[0056] Among them, aini is 2, afin is 0, t is the current iteration number, T max is the maximum number of iterations.

[0057] (3.4) Determine whether the maximum number of iterations or the set error accuracy has been reached. If so, output the optimal weight threshold corresponding to the optimal solution. Otherwise, repeat steps (3.2)-(3.4).

[0058] (4) Using the trained improved GWO-BP model to predict the groundwater depth in irrigation area ③, the output results are denormalized to obtain the monthly groundwater depth;

[0059] (5) Calculate the Nash efficiency coefficient NSE based on the prediction results, optimize the parameters of the GWO-BP prediction model, and obtain a suitable irrigation area groundwater depth prediction model;

[0060] Among them, the Nash efficiency coefficient NSE reflects the prediction accuracy and stability of the model. The closer the NSE is to 1, the better the prediction effect. In order to analyze the stability of the prediction model, the independent repeated operation is carried out 10 times to observe the change of the NSE value. The formula of the Nash efficiency coefficient NSE is:

[0061]

[0062] Among them, O i is the measured value of groundwater depth; O′ i is the measured average value of groundwater depth; P i is the predicted value of the GWO-BP model; n is the number of observations.

[0063] The improved GWO-BP model was used to predict the groundwater depth of the irrigation area. The groundwater depth of the irrigation area was predicted for 12 months in 2012 by Matlab software programming. The input variables were the five selected variables, and the output variable was the actual groundwater depth per month. The results are shown in Table 1. Figure 4 The figure shows the comparison of 10 NSE values ​​predicted by BP and improved GWO-BP; Figure 5 Shown is a comparison chart of groundwater level depth BP, improved GWO-BP predicted value and measured value.

[0064] Table 1: Comparison of groundwater depth predictions

[0065]

[0066] Comparative analysis of the results shows that the NSE values ​​of the GWO-BP predictions are more stable and accurate than those of the BP predictions. NSE values ​​exceeding 0.8 are more frequent, and the average NSE values ​​for individual independent runs (10 predictions per run) are also higher, with NSE values ​​consistently exceeding 0.7. Furthermore, a comparison of the monthly GWO-BP predictions with the actual groundwater levels shows consistent trends, indicating relatively accurate predictions. This demonstrates that the improved GWO-BP neural network model can be used as an effective method for predicting groundwater depth in irrigation areas.

Claims

1. A method for predicting groundwater depth in irrigation areas based on GWO-BP improved neural network, characterized in that: The steps include: (1) Obtain data on factors affecting the depth of groundwater level in the irrigation area and perform normalization processing; (2) Determine the BP neural network topology according to the number of input and output parameters; (3) Optimize the weights and thresholds of the BP neural network based on the improved grey wolf algorithm GWO, and use the optimized weights and thresholds as the initial weights and thresholds of the BP neural network; (4) Using the trained improved GWO-BP model to predict the groundwater depth, the output results are denormalized to obtain the monthly groundwater depth; (5) Based on the prediction results, the Nash efficiency coefficient NSE is calculated, and the parameters of the GWO-BP prediction model are optimized to obtain the irrigation area groundwater level depth prediction model.

2. The method for predicting groundwater depth in irrigation areas based on the GWO-BP improved neural network according to claim 1 is characterized in that: The factors affecting the groundwater level depth in step (1) include the monthly rainfall, Yellow River water diversion, evaporation, drainage, and the groundwater level depth of the previous month.

3. The method for predicting groundwater depth in irrigation areas based on the GWO-BP improved neural network according to claim 1, characterized in that: The calculation formula for data normalization in step (1) is: Among them, x max is the maximum value of the input sequence; x min is the minimum value of the input sequence; x and x′ are the data before and after normalization, respectively.

4. The method for predicting groundwater depth in irrigation areas based on the GWO-BP improved neural network according to claim 1, characterized in that: The step (2) includes establishing an m×k×n three-layer network topology structure, determining the values ​​of m, k, and n, where m is the number of input layer nodes, k is the number of hidden layer nodes, and n is the number of output layer nodes, and determining the maximum number of training times, transfer function, and training function.

5. The method for predicting groundwater depth in irrigation areas based on the GWO-BP improved neural network according to claim 1, characterized in that: The step (3) comprises the following steps: (3.1) Parameter settings: population size N, current number of iterations t and maximum number of iterations T, randomly generated A, a, C parameters, initial population generation; Among them, the update formulas of A, a, and C are: A=2a×r1-a C＝2r2 Among them, t is the current iteration number, T max is the maximum number of iterations, r1 and r2 obey the uniform distribution between [0, 1]; (3.2) Construct a groundwater depth prediction neural network fitness function, calculate the fitness values ​​of individual gray wolves, and select the top three best wolves as α, β, and γ according to the fitness value ranking; (3.3) Update the location information and control parameters A, a, C of each gray wolf; (3.4) Determine whether the maximum number of iterations or the set error has been reached. If yes, output the optimal weight threshold corresponding to the optimal solution. If no, repeat steps (3.2)-(3.4).

6. The method for predicting groundwater depth in irrigation areas based on the GWO-BP improved neural network according to claim 5, characterized in that: When generating the initial population in step (3.1), the Sobol sequence is introduced to initialize the generated population. The position of the population generated by the initialization is expressed as: X i =(b u -b l )*r+b l Among them, b u and b l are the upper and lower bounds of the search space respectively; r is a random number in the range of [0, 1] generated by the Sobol sequence.

7. The method for predicting groundwater depth in irrigation areas based on the GWO-BP improved neural network according to claim 5, characterized in that: In step (3.3), the control parameter a changes nonlinearly with the number of iterations. The improved expression of a is as follows: Among them, aini is 2, afin is 0, t is the current iteration number, T max is the maximum number of iterations.

8. The method for predicting groundwater depth in irrigation areas based on the GWO-BP improved neural network according to claim 1, characterized in that: The calculation formula of the Nash efficiency coefficient NSE in step (5) is: Among them, O i is the measured value of the groundwater depth; O′ i is the measured average value of groundwater depth; P i is the predicted value of the GWO-BP model; n is the number of observations.

Images