LSTM daily runoff prediction method based on MFF and NRBO

Abstract

The invention relates to an LSTM daily runoff prediction method based on MFF and NRBO, and the method comprises the steps: carrying out the variational mode decomposition of an original runoff sequence, and obtaining a plurality of intrinsic mode function components; hydrometeorological characteristics highly related to the runoff are screened through correlation analysis; fusing the intrinsic mode function component with the screened hydro meteorological features, and constructing a multi-dimensional information feature matrix; using a Newton-Raphson optimization algorithm to optimize hyper-parameters of the LSTM model; and taking the multi-dimensional information feature matrix as input, and performing daily runoff prediction by adopting the optimized LSTM model. The method has the beneficial effects that the Newton-Raphson optimization algorithm is applied to hyper-parameter optimization of the runoff prediction model for the first time, and the global search capability is enhanced, so that the prediction precision is improved. Meanwhile, multi-feature fusion is carried out on the intrinsic mode function component and the screened hydro meteorological features, and the multi-feature fusion is combined with hyper-parameter optimization, so that runoff prediction is more efficient and stable.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of runoff prediction, and particularly relates to an LSTM daily runoff prediction method based on MFF and NRBO. BACKGROUND

[0002] As a core link of water resources allocation and management and ecological flow guarantee, the importance of runoff prediction is increasingly significant. However, runoff prediction is affected by multiple factors such as temperature and precipitation, and the data presents non-stationary, nonlinear and seasonal characteristics, so it is necessary to effectively extract complex runoff characteristics and fuse multiple feature data to improve the prediction accuracy.

[0003] Hydrological prediction models are divided into physical models and data-driven models. Physical models are based on hydrological process mechanisms and have strong interpretability but complex calculations; data-driven models construct mapping relationships based on historical data and do not need to understand physical processes, and perform excellently in multi-feature hydrological prediction. Data-driven models can be divided into statistical learning, shallow machine learning and deep learning. Traditional statistical models rely on the stationarity assumption and are difficult to capture nonlinear relationships. Machine learning models such as support vector machines (SVM) are still difficult to cope with the complexity and uncertainty of hydrological data.

[0004] In recent years, deep learning models have made significant progress in runoff prediction. Long short-term memory (LSTM) effectively solves the gradient problem of traditional recurrent neural networks (RNN) by introducing a gating mechanism and can capture long and short-term dependencies. However, there are stability problems in processing very long sequences. Hybrid architectures have emerged. For example, the model combining temporal convolutional network (TCN) and LSTM proposed by Wang Wanliang et al. can capture both local and long-term dependencies. Dai et al. proposed a multi-modal deep learning (MDL) model DSAMDL based on dual-stage attention (DSA) that combines the advantages of one-dimensional convolution, bidirectional long short-term memory (Bi-LSTM) and DSA, improving the reliability and interpretability of prediction.

[0005] Although existing models can handle nonlinear relationships, they are still insufficient in extracting features of non-stationary runoff sequences. Moreover, the training process requires a large amount of time to find the optimal solution. Therefore, signal decomposition methods and optimization algorithms are widely used in deep learning models. For example, variational mode decomposition (VMD) effectively improves the non-stationary problem of hydrological sequences through frequency domain decomposition, but the feature and information dimension of this method are single, which is difficult to capture complex runoff driving factors. Yu et al. proposed an AFDM-MTCN model based on adaptive fourier decomposition model (AFDM) and multi-scale temporal convolutional network (MTCN), which combines AFDM and multi-scale temporal convolution, and uses sparrow search algorithm (SSA) optimization. However, SSA has the problems of slow convergence speed and local optimum, which limits the further improvement of the prediction accuracy of the model. SUMMARY

[0006] The purpose of the present application is to overcome the deficiencies in the prior art and provide an LSTM daily runoff prediction method based on MFF and NRBO.

[0007] In a first aspect, an LSTM daily runoff prediction method based on MFF and NRBO is provided, comprising:

[0008] S1, performing variational mode decomposition on the original runoff sequence to obtain a plurality of intrinsic mode function components (VMD);

[0009] S2, screening hydro-meteorological features highly correlated with runoff through correlation analysis;

[0010] S3, performing multi-feature fusion (Mutil-feature fusion, MFF) on the intrinsic mode function components and the screened hydro-meteorological features to construct a multi-dimensional information feature matrix;

[0011] S4, optimizing the hyperparameters of the LSTM model using a Newton-Raphson-based optimizer (NRBO);

[0012] S5, inputting the multi-dimensional information feature matrix and using the optimized LSTM model to predict daily runoff.

[0013] Preferably, in S1, the intrinsic mode function components are used to represent the characteristics of the runoff data in different frequency domains.

[0014] Preferably, in S3, the fusing of the intrinsic mode function components with the screened hydro-meteorological features comprises: horizontally splicing the intrinsic mode function components with the screened hydro-meteorological features according to time steps.

[0015] Preferably, S4 comprises:

[0016] The search and development weights are balanced by using a nonlinear dynamic attenuation weight factor balance model;

[0017] The learning rate of the LSTM model is automatically adjusted in different training stages by calculating the difference between the current position and the optimal position and combining a random number to generate a dynamic step size;

[0018] Local optimum is avoided by a double random disturbance mechanism and a trap avoidance operator;

[0019] The update operations of multiple particles are combined into a single matrix operation through vectorization and matrix operations.

[0020] Preferably, in S4, the LSTM model comprises an LSTM layer, a ReLU activation function, a fully connected layer, and a regression layer; the LSTM layer is used to capture the long-term dependence of the runoff time series data; the ReLU activation function provides a nonlinear transformation; the fully connected layer extracts high-order features through linear combination; and the regression layer maps the model output to the prediction result.

[0021] Preferably, in S4, the hyperparameters of the LSTM model include the number of hidden layer units of the LSTM layer, the number of training rounds, and the learning rate.

[0022] In a second aspect, an LSTM daily runoff prediction system based on MFF and NRBO is provided, which is used to execute the method of any one of the first aspect, and comprises:

[0023] A decomposition module is configured to perform variational mode decomposition on an original runoff sequence to obtain a plurality of intrinsic mode function components;

[0024] A screening module is configured to screen hydro-meteorological features highly correlated with runoff through correlation analysis;

[0025] A fusion module is configured to fuse the intrinsic mode function components with the screened hydro-meteorological features to construct a multi-dimensional information feature matrix;

[0026] An optimization module is configured to optimize the hyperparameters of the LSTM model by using a Newton-Raphson optimization algorithm;

[0027] A prediction module is configured to input the multi-dimensional information feature matrix and use the optimized LSTM model to perform daily runoff prediction.

[0028] In a third aspect, a computer storage medium is provided, and the computer storage medium stores a computer program; the computer program, when running on a computer, causes the computer to execute the method according to any one of the first aspect.

[0029] In a fourth aspect, an electronic device is provided, and the electronic device comprises:

[0030] a memory configured to store a computer program;

[0031] a processor configured to execute the computer program to implement the method according to any one of the first aspect.

[0032] The present application has the following beneficial effects:

[0033] 1. The present application first applies the Newton-Raphson optimization (NRBO) algorithm to the hyperparameter optimization of the runoff prediction model, enhances the global search ability, and thus improves the prediction accuracy. Meanwhile, after the intrinsic mode function component is combined with the screened hydro-meteorological features for multi-feature fusion (MFF), the hyperparameter optimization is combined, so that the runoff prediction is more efficient and robust.

[0034] 2. The present application uses the variational mode decomposition (VMD) to decompose the historical runoff sequence, extracts different frequency components and fuses them with other key features, expands the data input dimension of the model, and enables it to more deeply analyze the internal structure of the data, thereby greatly enhancing the recognition and extraction ability of complex sequence features.

[0035] 3. The present application applies the proposed model to the runoff prediction of a basin, and proves that it performs excellently in accuracy and feasibility through comparative tests and ablation experiments, and verifies the effectiveness of the model. BRIEF DESCRIPTION OF DRAWINGS

[0036] Figure 1 is a data set division diagram provided by an embodiment of the present application;

[0037] Figure 2 is a prediction framework diagram of MFF and LSTM provided by an embodiment of the present application;

[0038] Figure 3 is a NRBO optimized LSTM flowchart provided by an embodiment of the present application;

[0039] Figure 4 is a correlation analysis diagram provided by an embodiment of the present application;

[0040] Figure 5 is a runoff prediction result diagram of different models provided by an embodiment of the present application;

[0041] Figure 6is a scatter plot of different model predicted values and measured values of a first site provided by an embodiment of the application;

[0042] Figure 7 is a scatter plot of different model predicted values and measured values of a second site provided by an embodiment of the application. DETAILED DESCRIPTION

[0043] The application will be further described below in conjunction with embodiments. The following description of the embodiments is only to help understand the application. It should be noted that for those skilled in the art, without departing from the principles of the application, the application can be modified in several ways, and these modifications and improvements also fall within the scope of the claims of the application.

[0044] Embodiment 1

[0045] To solve the problems of the prior art, the application embodiment 1 provides an LSTM daily runoff prediction method based on MFF and NRBO, which is divided into the following two stages: MFF stage (see S1-S3 later) and NRBO optimized LSTM stage (see S4 later). MFF fuses multiple source data to make the model better understand the data structure, and the NRBO optimized LSTM stage further improves the prediction accuracy of the model by optimizing the hyperparameters of the model.

[0046] Specifically, the LSTM daily runoff prediction method based on MFF and NRBO includes:

[0047] S1, the original runoff sequence is subjected to variational mode decomposition to obtain a plurality of IMF components.

[0048] VMD is a non-recursive signal decomposition method, and its core is to construct a variational optimization problem to decompose the time series into a plurality of IMFs with specific center frequency and bandwidth. The IMF is defined as follows:

[0049]

[0050] In the formula: is the envelope amplitude of the signal, is the instantaneous phase.

[0051] The method constructs a variational model through Hilbert transform and constrains the IMF bandwidth by combining Wiener filter technology. The optimization goal is to minimize the sum of the center frequency bandwidth of each IMF while satisfying the constraint that the sum of the modal components is equal to the original signal. The solving process is realized by introducing a quadratic penalty term and a Lagrange multiplier, and the mathematical model is as follows:

[0052]

[0053]

[0054] wherein: is the center frequency, represents the Daroc distribution.

[0055] In order to fully tap the influence of multi-source data on runoff trends, the present application uses VMD, specifically, the VMD technology is used to decompose the runoff time series data into multiple IMF components, wherein these IMFs sequences represent the characteristics of runoff data in different frequency domains, so that the change trend in different time scales can be captured. This process can effectively separate the high-frequency noise and low-frequency trend of runoff data, providing clearer signals for subsequent modeling.

[0056] S2, screening hydro-meteorological features highly correlated with runoff through correlation analysis.

[0057] After completing the decomposition of the runoff sequence, in order to reduce redundant features and improve the training efficiency of the model, the present application further selects features of hydro-meteorological data, and selects features that have a significant impact on runoff prediction through correlation analysis. This step not only reduces the feature dimension, but also avoids the interference of irrelevant features on the model, thereby improving the generalization ability of the model.

[0058] S3, fusing the intrinsic mode function components with the screened hydro-meteorological features to construct a multi-dimensional information feature matrix.

[0059] Sliding window construction of spatio-temporal feature matrix: in order to capture the time series dependence, the sliding window technology is used to horizontally splice the multi-feature within the historical step For each IMF component d, the input feature matrix The formula is

[0060]

[0061] wherein: : water level, : the th VMD component, : vector splicing operation.

[0062] The above process fuses runoff data and hydro-meteorological data, which are different in origin, into the same feature space to construct a multi-dimensional information feature matrix. This matrix as the input of the model not only enhances the model's ability to understand the complex structure of time series data, but also provides more complete information for subsequent prediction. By fusing multi-source data, the model can more accurately capture the complex relationship between runoff and hydro-meteorological factors, thereby significantly improving the prediction accuracy and generalization ability. In addition, the use of multi-dimensional information can enhance the interpretability of the model, making the prediction process more transparent, which helps to better understand the physical laws and data features on which the model decision is based.

[0063] S4. Optimize the hyperparameters of the LSTM model using the Newton-Raphson optimization algorithm.

[0064] LSTM improves RNNs by introducing gating mechanisms and memory cells, effectively capturing long-term dependencies in sequences. Its core consists of an input gate, a forget gate, and an output gate. Assuming the output at the previous time step is... ,current The input at time is The output of the forget gate and the output of the input gate It can be represented as:

[0065]

[0066]

[0067] In the formula: and For the weights and biases of the forget gate, and The weights and biases of the input gate, This is the Sigmoid activation function.

[0068] Then, based on the output of the previous time point Input of current time The formula for calculating the current memory cell is as follows:

[0069]

[0070] In the formula: and For the weights and biases of memory cells, for

[0071] Hyperbolic tangent function. Then, update the memory units. The formula is as follows:

[0072]

[0073] In the formula: It represents the memory cells from the previous moment. Similar to the calculation methods of the forget gate and input gate, the output gate... The calculation formula is as follows:

[0074]

[0075] In the formula: and The weights and biases of the output gate. Current output. From memory unit and The decision is made jointly, and the formula is as follows:

[0076]

[0077] Furthermore, NRBO is a novel metaheuristic optimization algorithm based on the Newton-Raphson method. NRBO divides the population into two roles: explorers and developers. Explorers are responsible for finding new potential solutions in the search space, while developers use these discoveries to refine the search process. The explorer update mechanism is as follows:

[0078]

[0079] In the formula: This represents the first derivative of the objective function at the current position. Represents the second derivative. This is the current location. The developer update rules are as follows:

[0080]

[0081] In the formula: NRSR is the Newton-Raphson search rule, used to guide developers to migrate towards better solutions. The trap avoidance operator (TAO) update rule is as follows:

[0082]

[0083] In the formula: Indicates the globally optimal position. It is the current position, and It is a random number that follows a normal distribution. and These are matrix elements randomly assigned with 1s and -1s. It is a fixed parameter used to control the balance between exploration and development.

[0084] S5. Using the multidimensional information feature matrix as input, the optimized LSTM model is used to predict daily runoff.

[0085] Example 2:

[0086] Building upon Example 1, Example 2 of this application provides a more specific LSTM daily runoff prediction method based on MFF and NRBO, including:

[0087] S1. Perform variational mode decomposition on the original runoff sequence to obtain several IMF components.

[0088] S2. Screen hydrological and meteorological features that are highly correlated with runoff through correlation analysis.

[0089] S3. The inherent mode function components are fused with the screened hydrological and meteorological features to construct a multidimensional information feature matrix.

[0090] S4. Optimize the hyperparameters of the LSTM model using the Newton-Raphson optimization algorithm.

[0091] Building upon MFF, this application applies NRBO to LSTM hyperparameter optimization. NRBO possesses powerful global search capabilities, effectively overcoming the problem of traditional optimization algorithms easily getting trapped in local optima, thereby improving the model's hyperparameter optimization efficiency. Meanwhile, LSTM, with its excellent time-series modeling capabilities, can fully capture the long-term dependencies and complex nonlinear characteristics of runoff time series. By combining NRBO with LSTM, the generalization ability and prediction accuracy of the runoff prediction model can be improved, enabling more accurate simulation and prediction of watershed runoff changes.

[0092] like Figure 1 As shown, for the initial population, each particle represents a set of LSTM hyperparameters. This application determines the optimal fitness in the initial population by calculating the fitness of each particle, which is the evaluation metric of the LSTM model under these hyperparameter configurations—root mean square error (RMSE). and worst fitness And the corresponding hyperparameter combinations. After introducing the overall framework, this application further explores the following applications of NRBO in LSTM.

[0093] S4 includes:

[0094] (1) Real-time optimization method for nonlinear dynamic parameters.

[0095] Traditional optimization algorithms typically employ fixed parameters or linear decay methods to balance model search and development. This approach can lead to the model easily getting trapped in local optima or experiencing slow convergence, thus affecting generalization ability. To address these issues, this study introduces a nonlinear dynamic decay weight factor based on NRBO. The formula is as follows:

[0096]

[0097] In the formula: It is the current iteration number. It represents the maximum number of iterations. When its value is large, the algorithm tends to perform a global search; otherwise, the algorithm switches to local fine-tuning.

[0098] Its core objective is to balance the search and development weights of the model by adaptively adjusting the search range during iteration, thereby finding the optimal parameters for the LSTM model. This method can meet the needs of different stages during training, allowing the model to fully utilize global search capabilities in the early stages of iteration to avoid local optima, and to focus on local fine-tuning in the later stages to avoid premature convergence, thus improving the model's convergence speed and generalization ability.

[0099] (2) Adaptive learning rate dynamic programming method.

[0100] Traditional LSTM models typically use a fixed learning rate during training, making it difficult to adapt to the needs of different training stages and resulting in low training efficiency. To address this issue, this study introduces an adaptive learning rate dynamic programming method based on NRSR. This method calculates the difference between the current position and the optimal position and combines this with random numbers to generate a dynamic step size, enabling the LSTM model to automatically adjust the learning rate at different training stages.

[0101] (3) Double random perturbation mechanism.

[0102] Traditional optimization algorithms are prone to getting trapped in local optima during iteration, lacking effective mechanisms to help particles escape these local optima. To address this, this study introduces a double-random perturbation mechanism based on NRBO, introducing randomness in both direction and intensity, and combining it with... This mechanism provides significant perturbations in early iterations, helping particles escape local optima. The perturbations are gradually reduced in later iterations, enhancing the algorithm's ability to evolve. This study also employs a triggering mechanism to activate the TAO only in certain iterations, avoiding complex random perturbation calculations in every iteration and thus balancing computational overhead and algorithm performance. This probabilistic triggering mechanism effectively prevents premature convergence while maintaining algorithm efficiency.

[0103] (4) Vectorization and matrix operations.

[0104] In high-dimensional search spaces, traditional particle position update methods typically rely on element-wise operations, resulting in low computational efficiency. This study introduces vectorized operations and matrix operations into the NRBO algorithm, significantly improving computational efficiency. By merging the update operations for multiple particles into a single matrix operation, the overhead of loops and conditional checks is reduced. In LSTM applications, this efficient computational approach can shorten training time.

[0105] After optimizing the hyperparameters of the LSTM model using NRBO, a deep learning model is constructed using these hyperparameters. This model consists of LSTM, ReLU activation function, fully connected layers, and regression layers. The LSTM layer is used to capture long-term dependencies in runoff time-series data, and its number of hidden layer units, number of training epochs, and learning rate are optimized using NRBO. The ReLU activation function provides a non-linear transformation to enhance the model's expressive power. The fully connected layers extract higher-order features through linear combination. The regression layers map the model output to the prediction results.

[0106] S5. Using the multidimensional information feature matrix as input, the optimized LSTM model is used to predict daily runoff.

[0107] Furthermore, this application conducts experiments using the methods described above. Stations A and B in a certain watershed are selected as research cases and target stations for predicting runoff. Simultaneously, meteorological stations closest to the target stations with relatively complete meteorological data are selected as the meteorological data source for each monitoring station. The selected dataset covers annual hydrological and meteorological data for a certain period, and also includes the geographical coordinates of each station, totaling 5478 data points. The watershed's hydrological data mainly includes water level, flow rate, and sediment concentration, collected daily; the attribute information of the hydrological data is shown in Table 1. The watershed's meteorological data includes six meteorological characteristics: temperature, dew point temperature, air pressure, wind speed, visibility, and precipitation, collected daily; the attribute information of the meteorological data is also shown in Table 1.

[0108] Table 1. Attribute Information of Multi-Source Data

[0109]

[0110] The completeness of runoff data affects prediction accuracy; therefore, the KNNImputer method in Python is used to fill in missing values. Some outliers also exist in the data, but these values ​​may reflect extreme weather events or special hydrological phenomena, containing important hydro-meteorological information. Therefore, these outliers are retained as normal values ​​to ensure the model can capture more comprehensive features. After data preprocessing, the dataset is divided into training and test sets. 75% of the data constitutes the training set, 10% serves as the validation set, and the remaining 10% is used as the test set.

[0111] Furthermore, the Spearman rank correlation coefficient is a nonparametric statistical method used to measure the monotonic relationship between two variables. Spearman does not require a linear relationship between the variables, but rather focuses on their monotonicity. This method calculates correlation by converting the data into ranks, thus avoiding the influence of outliers on the results. The calculation steps are as follows:

[0112] (1) Ranking: Sort the data of the two variables separately and assign a rank to each data point. If there are duplicate values ​​in the data, assign the same average rank to these duplicate values.

[0113] (2) Calculate the rank difference: For each pair of data points, calculate the difference in their rank between the two variables:

[0114]

[0115] (3) Calculate the correlation coefficient:

[0116]

[0117] In the formula: rank difference of each pair of data It represents the number of data points.

[0118] The Spearman correlation coefficient ranges from -1 to 1; the closer the value is to 1, the stronger the positive correlation between the variables. To further analyze the influencing factors of runoff, this application uses the Spearman method to conduct correlation analysis on the hydrological and meteorological data of stations A and B. For example... Figure 4 As shown, correlation coefficient analysis of the influencing factors of runoff reveals a certain correlation between water level and sediment concentration, among hydrological factors, and the predicted target. Based on this, this application uses preprocessed runoff and water level as input feature data for subsequent research.

[0119] Assume the input feature sequence is It can be expressed using the formula for the Spearman rank correlation coefficient, and the ideal output sequence predicted by the model is: In order to predict the future For the output at a given time, the model should appropriately utilize the data sequence preceding that time period. The formula for this process is:

[0120]

[0121]

[0122] In the formula: express One feature in The value at time. The goal of runoff prediction is to establish a mathematical function that fits the value... and the true value The closest match is generally determined using a loss function.

[0123] In addition, the evaluation indicators and experimental parameter settings for the experiment include:

[0124] The following four commonly used evaluation indicators are selected as evaluation indicators for runoff prediction: RMSE, mean absolute percentage error (MAPE), mean absolute error (MAE), and Nash-Sutcliffe efficiency coefficient (NSE), with the following expressions:

[0125]

[0126]

[0127]

[0128]

[0129] In the formula: Indicates the first Measured values ​​of runoff. Indicates the first Predicted runoff values, This represents the average measured runoff. is the length of the runoff time series.

[0130] The hardware environment for model training is as follows: an Intel Core i9-10900K CPU and an NVIDIA GeForce RTX 1660 Laptop GPU, with 64GB of memory. The initial parameters of the model are as follows: the CNN model uses convolutional kernels of size 2 with 16 output channels; the TCN model contains two one-dimensional convolutional layers, each using a convolutional kernel of size 2 with 16 output channels; the CNN, TCN, and LSTM models have 70 hidden layers; the initial learning rate is 0.01; the maximum number of training epochs is 70; the L2 regularization parameter is 0.0000001; the gradient threshold is set to 1; the learning rate adjustment strategy is a piecewise constant; and the learning rate reduction cycle is 60. The optimization algorithm uses a population size of 100, a maximum number of iterations of 6, and the variables are the optimal number of hidden units, the optimal maximum training epoch, and the optimal initial learning rate, with upper limits of 500, 500, and 0.01, and lower limits of 15, 50, and 0.0001, respectively.

[0131] Furthermore, this application designed comparative experiments to verify the superiority of the proposed MFF-NRBO-LSTM model. By comparing it with eight other models, including Random Forest (RF), Convolutional Neural Network (CNN), TCN, TCN-LSTM, LSTM, MFF-LSTM, MFF-SSA-LSTM, and MFF-Black Kite Algorithm (BKA)-LSTM, the performance of each model in predicting runoff change trends can be comprehensively evaluated.

[0132] As shown in Table 2, the MFF-NRBO-LSTM model performed best in RMSE, MAE, MAPE, and NSE evaluation metrics, indicating that it has the highest prediction accuracy and the smallest error. Among several individual models, the LSTM model exhibits a clear advantage, highlighting its ability to handle complex time series data.

[0133] Table 2 Model performance evaluation results

[0134]

[0135] In the composite model, MFF-LSTM significantly improves prediction accuracy through MFF. In particular, compared with LSTM alone, MFF-NRBO-LSTM reduces RMSE, MAE and MAPE by 74.68%, 74.59% and 70.98% respectively, and improves NSE by 5.56%.

[0136] The MFF-LSTM model, by incorporating MFF (Mean Factor Selection), enhances the model's temporal decomposition capability and effectively extracts multi-scale temporal features of runoff sequences. Compared to the original LSTM, the average RMSE, MAE, and MAPE decreased by 45.70%, 44.68%, and 37.51%, respectively, while the NSE improved by 4.09%. This validates the effectiveness of MFF in feature extraction and noise suppression. Furthermore, the average RMSE, MAE, and MAPE of the MFF-LSTM model are reduced by 29.12%, 17.37%, and 4.63% compared to the MFF-SSA-LSTM and MFF-BKA-LSTM models, respectively. This indicates that NRBO outperforms the SSA and BKA algorithms in runoff prediction, further validating the effectiveness of NRBO in improving prediction accuracy.

[0137] like Figure 5 As shown, among the five single models, LSTM has the best fitting effect, while among the latter mixed models, MFF-LSTM has the best fitting effect for both the trend and the peak value. Figure 6 andFigure 7 The scatter plot further shows that the prediction points of LSTM in the single model and MFF-LSTM in the mixed model are most densely distributed near the fitted line, indicating that they have stronger predictive consistency and correlation.

[0138] Table 3. Model Ablation Evaluation Indicators

[0139]

[0140] Furthermore, this application also conducted ablation experiments, and through performance evaluation of LSTM, MFF-LSTM, NRBO-LSTM, and MFF-NRBO-LSTM models, explored the impact of MFF and NRBO on model performance. As shown in Table 3, the results show that compared with the LSTM model, NRBO-LSTM reduced the average RMSE, MAE, and MAPE by 9.81%, 6.37%, and 3.21%, respectively, while improving NSE, indicating that NRBO-LSTM has strong parameter optimization capabilities. After MFF, the STNR-LSTM model reduced the average RMSE, MAE, and MAPE by 71.91%, 72.81%, and 70.12%, respectively, compared with NRBO-LSTM, while improving NSE by 4.04%, highlighting the importance of the MFF method in focusing on key information of multi-feature data and improving the model's predictive performance, significantly improving prediction accuracy.

[0141] It should be noted that the parts in this embodiment that are the same as or similar to those in Embodiment 1 can be referred to each other, and will not be repeated in this application.

[0142] Example 3:

[0143] Based on Example 2, Example 3 of this application provides an LSTM daily runoff prediction system based on MFF and NRBO, including:

[0144] The decomposition module is used to perform variational mode decomposition on the original runoff sequence to obtain several IMF components;

[0145] The screening module is used to screen hydrological and meteorological features that are highly correlated with runoff through correlation analysis.

[0146] The fusion module is used to fuse the inherent mode function components with the screened hydrological and meteorological features to construct a multi-dimensional information feature matrix;

[0147] The optimization module is used to optimize the hyperparameters of the LSTM model using the Newton-Raphson optimization algorithm;

[0148] The prediction module is used to predict daily runoff using the multidimensional information feature matrix as input and an optimized LSTM model.

[0149] It should be noted that the system provided in this embodiment is the system corresponding to the method provided in embodiment 2. Therefore, the parts in this embodiment that are the same as or similar to those in embodiment 2 can be referred to each other, and will not be described again in this application.

[0150] In summary, this invention innovatively proposes the STNR-LSTM model, which integrates two major optimization stages: MFF and NRBO. This overcomes the limitations of existing prediction models in extracting features from multi-source data and improves the accuracy of daily runoff prediction. In the MFF stage, the MFF method enriches the model's information sources, enabling the MFF-NRBO-LSTM to more comprehensively understand the data structure, thus significantly enhancing its ability to capture sequence features. Simultaneously, NRBO fine-tunes the hyperparameters of the LSTM model, enhancing not only its global search capability but also significantly improving prediction performance. Furthermore, experimental verification shows that the MFF-NRBO-LSTM model achieves the highest prediction accuracy, lowest error, and best stability compared to other comparative models, effectively validating the model's practical application value.

Claims

1. A daily runoff prediction method based on MFF and NRBO using LSTM, characterized in that, include: S1. Perform variational mode decomposition on the original runoff sequence to obtain several intrinsic mode function components; S2. Screen hydro-meteorological features that are highly correlated with runoff height through correlation analysis; S3. Perform multi-feature fusion between the inherent mode function components and the screened hydrological and meteorological features to construct a multi-dimensional information feature matrix; S4. Optimize the hyperparameters of the LSTM model using the Newton-Raphson optimization algorithm; S5. Using the multidimensional information feature matrix as input, the optimized LSTM model is used to predict daily runoff.

2. The LSTM daily runoff prediction method based on MFF and NRBO according to claim 1, characterized in that, In S1, the intrinsic mode function components are used to represent the characteristics of runoff data in different frequency domains.

3. The LSTM daily runoff prediction method based on MFF and NRBO according to claim 2, characterized in that, In S3, the fusion of the intrinsic mode function components with the selected hydrological and meteorological features includes: horizontally splicing the intrinsic mode function components and the selected hydrological and meteorological features according to the time step.

4. The LSTM daily runoff prediction method based on MFF and NRBO according to claim 3, characterized in that, S4 include: Weights were searched and developed using a nonlinear dynamic decay weight factor balancing model. By calculating the difference between the current position and the optimal position, and combining it with random numbers to generate a dynamic step size, the LSTM model can automatically adjust the learning rate at different training stages. Local optima are avoided through a double random perturbation mechanism and a trap avoidance operator; By using vectorization and matrix operations, the update operations of multiple particles are combined into a single matrix operation.

5. The LSTM daily runoff prediction method based on MFF and NRBO according to claim 4, characterized in that, In S4, the LSTM model includes an LSTM layer, a ReLU activation function, a fully connected layer, and a regression layer; the LSTM layer is used to capture the long-term dependencies of runoff time series data; the ReLU activation function provides nonlinear transformation; and the fully connected layer extracts higher-order features through linear combination. The regression layer maps the model output to the prediction results.

6. The LSTM daily runoff prediction method based on MFF and NRBO according to claim 4, characterized in that, In S4, the hyperparameters of the LSTM model include: the number of hidden layer units in the LSTM layer and the learning rate.

7. An LSTM daily runoff prediction system based on MFF and NRBO, characterized in that, For performing the method according to any one of claims 1 to 6, comprising: The decomposition module is used to perform variational mode decomposition on the original runoff sequence to obtain several intrinsic mode function components. The screening module is used to screen hydrological and meteorological features that are highly correlated with runoff through correlation analysis. The fusion module is used to perform multi-feature fusion of inherent mode function components and screened hydrological and meteorological features to construct a multi-dimensional information feature matrix. The optimization module is used to optimize the hyperparameters of the LSTM model using the Newton-Raphson optimization algorithm; The prediction module is used to predict daily runoff using the multidimensional information feature matrix as input and an optimized LSTM model.

8. A computer storage medium, characterized in that, The computer storage medium stores a computer program; when the computer program is run on the computer, it causes the computer to perform the method described in any one of claims 1 to 6.

9. An electronic device, characterized in that, include: Memory, used to store computer programs; A processor for executing the computer program to implement the method as described in any one of claims 1 to 6.

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