Medium and long term hydrological probability forecasting method and system considering interpretable deep learning model nested combination

Abstract

The invention provides a medium and long term hydrological probability forecasting method and system considering interpretable deep learning model nested combination, and relates to the technical field of hydrological forecasting. The method comprises the following steps: collecting historical reservoir runoff data and an atmospheric circulation index of a target station; analyzing the correlation of the runoff time sequence, and determining the lag time of the medium-and-long-term runoff combined prediction model; constructing an input matrix containing the initial factor set, screening medium and long-term hydrological forecasting factors from the input matrix, and reconstructing the screened medium and long-term hydrological forecasting factors and the warehousing runoff data to form reconstructed combined data; constructing a multi-model nested structure as a medium-and-long-term runoff combined prediction model; and obtaining a deterministic prediction result and a probability prediction result of the medium-and-long-term runoff under different synchronization lengths by taking the reconstructed combined data as an input item of the medium-and-long-term runoff combined prediction model and taking the predicted future runoff volume as an output quantity. Compared with the prior art, the method has remarkable advantages in the aspect of forecasting result precision.

Description

Technical Field

[0001] The present invention relates to the technical field of hydrological forecasting, and in particular to a medium- and long-term hydrological probability forecasting method and system considering the nested combination of interpretable deep learning models. Background Art

[0002] Accurate and reliable medium- and long-term runoff forecasts are the key foundation for supporting water resources management and allocation, water conservancy project scheduling and operation, and flood and drought prevention. Since the forecast period of medium- and long-term forecasts is relatively long, future runoff information can be obtained in advance, which is conducive to the early formulation of flood prevention and benefit development plans, the promotion of efficient water resources management and scientific and reasonable scheduling of water conservancy projects. The evolution of medium- and long-term runoff in the basin is affected by the combined effects of weather systems, underlying surface conditions and ocean circulation. The causes are extremely complex, showing high-dimensional nonlinear, non-stationary, and alternating dynamic characteristics such as high-dimensional dry and high water levels. Its forecasting theory and method are significantly different from those of short-term forecasts, and the forecasting effect is not ideal. Therefore, how to accurately forecast medium- and long-term runoff has become an important research direction and a key issue that needs to be solved in the discipline of hydrology and water resources.

[0003] Traditional methods for medium- and long-term runoff forecasting can be divided into two categories: process-driven and data-driven models. Representative process-driven models include the Xin'anjiang model, the Tank water tank model, and the Sacmento model; representative data-driven methods include periodic analysis extrapolation, time series method, and historical evolution method. Studies have shown that rainfall and runoff in a basin are closely related to many teleconnected climate factors such as sea temperature and atmospheric circulation. However, in the prediction model, too few input factors may cause information loss and inability to effectively explore the internal mechanism of the forecast, resulting in inaccurate forecasts; while too many input factors may lead to low forecast accuracy due to information redundancy and the inability of key factors to play a role, and may also cause problems such as increased model structure complexity and decreased forecast speed. Therefore, selecting an appropriate number of forecast factors as independent variables to input into the prediction model is the key to improving the accuracy of runoff forecasts.

[0004] Although many deep learning models have been widely used, different models have their own unique advantages, such as processing high-dimensional nonlinear information, capturing time series data characteristics, and focusing on key factors; in addition, some studies in other fields have shown that the coupling of multiple models can better integrate the different advantages of each model, so it is possible to consider building a prediction structure that nests multiple deep learning models. At the same time, although the prediction accuracy of artificial intelligence methods is high, due to the lack of physical mechanism in modeling, it is a "black box model" and it is difficult to judge its internal structure. Therefore, there are certain inconveniences when decision makers adopt its results and apply them to real scenarios. Summary of the invention

[0005] Purpose of the invention: To propose a medium- and long-term hydrological probability forecasting method that takes into account the nested combination of interpretable deep learning models, and further propose a system for implementing the above method, so as to effectively solve the above problems existing in the prior art.

[0006] First, a medium- and long-term hydrological probabilistic forecasting method considering the nested combination of interpretable deep learning models is proposed. The method includes the following steps:

[0007] Collect and preprocess the inflow runoff data and atmospheric circulation index of the target station to be predicted for several years;

[0008] Based on the inflow runoff data, the correlation of the runoff time series is analyzed using an autocorrelation function and / or a partial autocorrelation function, thereby determining the lag time of the medium- and long-term runoff combined prediction model;

[0009] Based on the atmospheric circulation index, an input matrix including an initial factor set is constructed, and medium- and long-term hydrological forecast factors are screened out therefrom, and the screened medium- and long-term hydrological forecast factors are reconstructed with the inflow runoff data to form reconstructed combined data;

[0010] Construct a CNN-BiLSTM-Attention multi-model nested structure as a medium- and long-term runoff combination prediction model, optimize the hyperparameters of the medium- and long-term runoff combination prediction model, and train the medium- and long-term runoff combination prediction model;

[0011] The reconstructed combined data is used as the input item of the medium- and long-term runoff combined prediction model, and the predicted future runoff volume is used as the output, so as to obtain the deterministic prediction results and the probabilistic prediction results of the medium- and long-term runoff under different step lengths.

[0012] In a further embodiment of the first aspect, for the collected inflow runoff data, the integrity of the inflow runoff data is first checked, and if there are missing values, the average value of the historical runoff in the same period is used to fill in the missing values;

[0013] The atmospheric circulation index contains several monthly teleconnection factor data. For the collected teleconnection factor data, if there are missing values ​​and the number of missing values ​​is less than or equal to 10% of the sequence length, the historical mean of the same period series is used to fill the missing values; if the missing values ​​are greater than 10% of the sequence length, the teleconnection factor data is eliminated.

[0014] In a further embodiment of the first aspect, based on the teleconnection factor data, an input matrix including an initial factor set is constructed, and medium- and long-term hydrological forecast factors are screened out therefrom, and the screening process is divided into two rounds:

[0015] The first round of screening was completed through the Spearman correlation coefficient method, and the teleconnection factor data with an absolute value of the correlation coefficient greater than the threshold A were found as the preliminary factors to enter the second round of screening process.

[0016] In a further embodiment of the first aspect, the second round of screening process comprises:

[0017] The primary factors and inflow runoff data obtained from the first round of screening were combined into a table data, and the table data was converted into a form with a mean of 0 and a standard deviation of 1;

[0018] Set up a stepwise regression model and perform stepwise iteration to finally obtain the medium- and long-term hydrological forecast factors: For an equation containing m independent variables x and dependent variable y, use the least squares method to perform derivatives and obtain the regression coefficients The expression is:

[0019]

[0020] In the formula, the independent variable x is the teleconnection factor data, and the dependent variable y is the inflow runoff data; is the coefficient of the mth term in the mth regression equation; represents the regression coefficient; Represents the correlation coefficient between the mth x and y in the data set.

[0021] In a further embodiment of the first aspect, in the CNN-BiLSTM-Attention multi-model nested structure:

[0022] BiLSTM consists of a forward LSTM layer and a backward LSTM layer, which are responsible for processing input data in the forward and reverse directions respectively;

[0023] The update status and final output value of the forward LSTM layer and the backward LSTM layer use the activation function of each layer , , The calculation results are:

[0024]

[0025] In the formula, represents the reconstructed combined data input at the i-th moment; represents the predicted future runoff; represents the i-th forward LSTM layer; represents the i-th backward LSTM layer; Represents the weight of each layer.

[0026] Use CNN to extract nonlinear features of runoff data, and input the processed output information as a whole into BiLSTM for prediction. The process expression is as follows:

[0027]

[0028] In the formula, is the input layer, l is the output layer, represents the feature matrix containing s input feature variables, For the input of previous runoff and filtered atmospheric circulation data, is the activation function; represents the number of input feature variables; y represents the model output information; Represents the bias term of the j-th input feature variable in the output layer.

[0029] Attention is used to calculate the weighted sum between the output of each time step and the learnable attention weight to obtain the comprehensive features of the sequence. The calculation process is as follows:

[0030]

[0031]

[0032]

[0033]

[0034] In the formula, for the degree of importance; yes The attention weight value expresses the influence of the input atmospheric circulation factors on the predicted runoff; represents the output sequence; Represents the hidden layer state value of the i-th period; Indicates the importance of the k-th period; represents the hyperbolic tangent function; represents the exponential function with the natural logarithm base e as the base; Represents the final output value obtained after weighted calculation; Represents the input sequence; F represents the weighted feature vector; W and b are the weight matrix and bias vector respectively, and V and U are the learning parameters that are continuously updated with the training iterations.

[0035] In a further embodiment of the first aspect, the process of training the medium- and long-term runoff combined prediction model specifically includes:

[0036] For a given n-dimensional training set , then when inputting the test set Give the predicted value , making it closer to the measured value , then the output Obey a joint Gaussian distribution with mean 0 and covariance kernel k:

[0037]

[0038] In the formula, represents a vector composed of n measured runoff values ​​y, which obeys Gaussian distribution, and n is the number of samples; represents the feature matrix composed of the input x of n training sets; represents the predicted value of runoff probability after Gaussian process regression; represents the joint Gaussian distribution function with a mean of 0; x represents the input of the training set; Represents the input of the test set.

[0039] In a further embodiment of the first aspect, based on the screened medium- and long-term hydrological forecast factors, the SHAP value of each medium- and long-term hydrological forecast factor is calculated in turn to quantify the respective contribution degree and find out the key factors affecting runoff;

[0040] Calculate the SHAP value according to the following expression :

[0041]

[0042] Where M is the m-dimensional set of all characteristic variables in the data set, that is, the input data matrix composed of the previous runoff data and the teleconnection factor data obtained by the second round of screening; s is the number of factors extracted from M. A subset of size ; represents all possible subsets; is the runoff prediction result obtained based on the set s; It means adding eigenvalues ​​to s The results obtained;

[0043] The larger the absolute value of SHAP value is, the greater the contribution to the runoff prediction value is;

[0044] The positive or negative value of SHAP indicates the direction of influence on runoff. If the SHAP value is positive, it means that the characteristic variable has a positive influence on the runoff prediction result, otherwise it has a negative influence.

[0045] The second aspect of the present invention discloses a medium- and long-term hydrological probability forecasting system, which is used to execute the medium- and long-term hydrological probability forecasting method considering the nested combination of interpretable deep learning models disclosed in the first aspect. The medium- and long-term hydrological probability forecasting system includes a data collection module, a first data processing module, a second data processing module, a model building module, and a result output module.

[0046] The data collection module is used to collect and preprocess the inflow runoff data and atmospheric circulation index of the target site to be predicted for several years.

[0047] The first data processing module analyzes the correlation of the runoff time series based on the inflow runoff data using an autocorrelation function and / or a partial autocorrelation function, thereby determining the lag time of the medium- and long-term runoff combination prediction model.

[0048] The second data processing module constructs an input matrix containing an initial factor set based on the atmospheric circulation index, and selects medium- and long-term hydrological forecast factors therefrom, and reconstructs the selected medium- and long-term hydrological forecast factors with the inflow runoff data to form reconstructed combined data.

[0049] The model building module is used to construct a CNN-BiLSTM-Attention multi-model nested structure as a medium- and long-term runoff combination prediction model, optimize the hyperparameters of the medium- and long-term runoff combination prediction model, and train the medium- and long-term runoff combination prediction model.

[0050] The result output module uses the reconstructed combined data as the input item of the medium- and long-term runoff combined prediction model and the predicted future runoff volume as the output, thereby obtaining the deterministic prediction results and the probabilistic prediction results of the medium- and long-term runoff under different step lengths.

[0051] Compared with the prior art, the medium- and long-term hydrological probability forecasting method considering the nested combination of interpretable deep learning models proposed in the present invention has at least the following beneficial effects:

[0052] (1) The impact of the atmospheric circulation index on runoff is fully considered, and the forecast results have physical significance and high reliability.

[0053] (2) Compared with the previous use of a single machine learning model for training and prediction, the multi-model nested structure constructed by the present invention can couple the different advantages of multiple models and have higher prediction accuracy.

[0054] (3) Taking into full account the complex spatiotemporal characteristics of medium- and long-term runoff series in different study areas and seasons, various pre-processing and post-processing operations are performed on the input and output data of the combined model, so that the combined model can truly meet the unique requirements of medium- and long-term runoff prediction.

[0055] (4) The present invention quantifies the importance of each input item, explains and describes the inherent prediction mechanism of the model, and provides a good decision-making basis for the application and promotion of the model. BRIEF DESCRIPTION OF THE DRAWINGS

[0056] Figure 1 The present invention is a flowchart of a medium- to long-term hydrological probability forecasting method considering a nested combination of interpretable deep learning models in an embodiment.

[0057] Figure 2 Schematic diagram of LSTM structure in the embodiment.

[0058] Figure 3 Schematic diagram of the BiLSTM structure in the embodiment.

[0059] Figure 4 Schematic diagram of CNN structure in the embodiment.

[0060] Figure 5 Schematic diagram of the Attention structure in the embodiment. DETAILED DESCRIPTION

[0061] In the following description, a large number of specific details are provided to provide a more thorough understanding of the present invention. However, it is apparent to those skilled in the art that the present invention can be implemented without one or more of these details. In other examples, in order to avoid confusion with the present invention, some technical features known in the art are not described.

[0062] See also Figure 1 This embodiment discloses a medium- and long-term hydrological probability forecasting method considering a nested combination of interpretable deep learning models, and the steps are as follows:

[0063] Step 1: Collect and preprocess the previous hydrological data and teleconnection factor data of the target site to be predicted. The former refers to the inflow runoff data of several years, and the latter refers to 130 atmospheric circulation indices of the same sequence length.

[0064] Step 2: Under the appropriate confidence level, the autocorrelation function and partial autocorrelation function are used to analyze the correlation of the runoff time series, and the internal laws in the runoff history information are mined to determine the lag time of the prediction model.

[0065] Step 3: Based on the sorted teleconnection data, an input matrix containing the initial factor set is constructed, and two rounds of optimization of medium- and long-term hydrological forecast factors are performed. The first round of screening is completed by the Spearman correlation coefficient method, and the teleconnection factors with a more significant impact on runoff, that is, the absolute value of the correlation coefficient, are found to enter the second round of screening.

[0066] Step 4: Based on the first round of screening results of the Spearman correlation coefficient method, the atmospheric circulation index with a correlation coefficient greater than 0.6 is included in the screening process of the stepwise regression method to find out the key teleconnection factors that are more important for runoff prediction under different step lengths. The factors obtained after two rounds of screening are the final input factor set of the prediction model. The screened factors are reconstructed with the previous runoff data to form a multi-dimensional and multi-step forecast matrix.

[0067] Step 5: Taking the traditional long short-term memory neural network (LSTM) as the starting point, we gradually integrated and improved the model to improve its ability to capture runoff sequence characteristics, extract a large amount of information in layers, and focus on prediction key information. We constructed a CNN-BiLSTM-Attention multi-model nested structure to significantly improve the accuracy of medium- and long-term runoff prediction.

[0068] Step 6, according to the characteristics of each part of the constructed combined model, the obtained prediction factor sequence and runoff data are pre-processed, including two types of operations: time domain processing and feature engineering. The former includes the changes in different time scales of runoff and teleconnection data, and decomposes the high-dimensional nonlinear runoff data into trend terms, seasonal terms and random terms; the latter mainly constructs derived variables based on the original teleconnection data and performs feature selection through a variety of methods; the common purpose of the two types of operations is to make the data matrix more in line with the data requirements and internal mechanisms of the combined prediction model.

[0069] Step 7, based on the constructed medium- and long-term runoff combined prediction model, considering its basic principles and internal structure, the model training process is improved by using regularization methods, loss function improvement and other processes. For example, a custom loss function that meets the runoff prediction characteristics can be designed based on the distribution characteristics of the runoff prediction results and the requirements for the width of the probability prediction interval.

[0070] Step 8: Due to the complex structure and numerous parameters of the combined prediction model, and considering that the actual runoff series in different study areas, different years or seasons have extremely complex temporal and spatial characteristics, it is difficult to accurately predict medium- and long-term runoff. Therefore, it is proposed to use the Black Hawk optimization algorithm to optimize the hyperparameters of the prediction model, construct a multi-model hyperparameter combination vector with optimization, take the vector as the optimization object, and use the parameter range and constraints as the search space to find the parameter vector that makes the combined model predict the best medium- and long-term runoff, and improve the overall performance.

[0071] Step 9: For the results of the model runoff prediction, post-process the data, including the integration of prediction results and uncertainty assessment. Gaussian process regression (GPR) is used to further expand the probability prediction and uncertainty assessment based on the deterministic point prediction of the CNN-BiLSTM-Attention model, and obtain the fluctuation range of runoff within a certain confidence level, providing decision makers with richer and more reliable decision-making basis and information.

[0072] Step 10, divide the collected data set into a training set and a test set, use the historical runoff and the screened prediction factors as input, and the future runoff as output, use the coupled model for training and testing, and make deterministic and probabilistic predictions of medium- and long-term runoff at different step lengths.

[0073] Step 11, using four evaluation indicators, namely, mean absolute error MAE, mean absolute percentage error MAPE, root mean square error RMSE, and Nash efficiency coefficient NSE, to evaluate the deterministic prediction effect of the model from the perspectives of prediction error and degree of fit. A prediction error comprehensive scoring indicator PECS is proposed, which organically combines the above four indicators to comprehensively evaluate the deterministic prediction effect of the combined model.

[0074] Step 12, using four indicators including prediction interval coverage rate PICP, prediction interval average width PINAW, continuous graded probability score CRPS, and width range comprehensive index CWC, to evaluate the probability prediction effect of the model from the perspective of probability prediction accuracy and reliability.

[0075] Step 13, using the SHAP method to estimate the SHAP value of each input variable in turn to quantify their respective contributions, including the importance of each input factor and the direction of its impact on runoff, so as to explain the internal mechanism of the analysis model and provide a basis for decision makers to trust and adopt the model prediction results.

[0076] As a preferred embodiment, the specific implementation steps of the data collection and processing mentioned in step 1 are as follows:

[0077] 1-1. The collected measured runoff data should be checked and preprocessed. If the runoff data is complete and without missing values, no processing is required; if there are individual missing values ​​in the runoff data, the average value of the historical runoff in the same period can be used to fill in the missing values.

[0078] 1-2. For atmospheric circulation index, the data comes from 130 monthly teleconnection factor data released by the National Climate Center of the China Meteorological Administration, covering 88 atmospheric circulation indices, 26 sea temperature indices and 16 other indices. For the possible missing values ​​in the collected "air-sea-land" teleconnection factor data, the following inspection and preprocessing criteria are adopted: if the number of missing values ​​in the factor is less than 10% of the sequence length, it can be filled with the mean of the historical series of the same period; if the missing value is greater than 10%, the factor will be eliminated.

[0079] As a preferred embodiment, the specific implementation steps of the first round of screening of the key prediction factors mentioned in step 3 are as follows:

[0080] 3-1. Data preparation: organize the collected teleconnection factor data and runoff data to ensure that the data format is consistent, for example, they are all time series data and have the same data length.

[0081] 3-2. Calculate the correlation coefficient matrix and sort each teleconnection factor and runoff sequence, that is, rearrange the data in order of size. Calculate the correlation coefficients between the sorted sequences to obtain a matrix containing the correlation coefficients of all factors and runoff.

[0082] 3-3. Calculate the Spearman correlation coefficient of each teleconnection factor. Generally, the factor with a correlation coefficient greater than 0.6 is taken as the primary prediction factor. The specific calculation process of the Spearman correlation coefficient is as follows: for two sets of independent and identically distributed random variable data sets X and Y, namely, runoff series data and atmospheric circulation factor series data, the number of elements is N. Assume that the i-th value is and (i=1,2,…,N). Sort X and Y at the same time to get new sorted sets x and y. Assume The order in X is , similarly The sorting in Y is . Then the Spearman correlation coefficient between X and Y is:

[0083]

[0084] 3-4. Select the first round of preliminary factors and set a threshold, such as 0.6, which means that only factors with a correlation coefficient greater than 0.6 may have a significant impact on runoff prediction. According to the correlation coefficient matrix, select factors greater than the threshold as preliminary factors. Record the number, name and correlation coefficient value of each preliminary factor for subsequent analysis.

[0085] Taking the Chitan Reservoir in the Jinxi River Basin as an example, the first round of preliminary screening results of the Spearman correlation coefficient method are shown in Table 1:

[0086] Table 1 Preliminary screening calculation results of Spearman correlation coefficient method

[0087] As a preferred embodiment, the specific implementation steps of the second round of screening of the key prediction factors mentioned in step 4 are as follows:

[0088] 4-1. Data preparation: combine the primary factors and runoff data obtained in the first round into a table data for easy subsequent operations. Standardize the data, that is, convert the data into a form with a mean of 0 and a standard deviation of 1 to eliminate the impact of different dimensions of different atmospheric circulation indices.

[0089] 4-2. Set up a stepwise regression model. You can select a statistic to measure the contribution of each independent variable to the dependent variable based on data characteristics, study area characteristics or actual needs, such as F statistics, variance contribution or AIC information criterion, to evaluate the quality of the model. Set appropriate parameters such as the number of iterations and significance level, for example, a maximum of 10 iterations and a significance level of 0.05.

[0090] 4-3. Iterate step by step.

[0091] (1) Initial model: only contains constant terms, that is, does not consider the influence of any teleconnection factors. For an equation containing n independent variables x, i.e., teleconnection factors, and dependent variable runoff value y, the least squares method is used to perform differentiation, and the regression coefficient b can be obtained. i The expression is:

[0092]

[0093] The present invention can select F statistics, variance contribution or AIC information criterion as screening indicators as needed. Here, the variance contribution of x to y is used as the screening indicator to measure whether the influence of the teleconnection factor on runoff is significant. The variance contribution can be calculated by the following formula:

[0094]

[0095] In the formula, r ij The correlation coefficient between the i-th teleconnection factor x and the runoff value y in the data set representing the atmospheric circulation index can be calculated as follows:

[0096]

[0097] (2) Step-by-step forward selection, introducing factors: Calculate the statistics of each preliminarily selected teleconnection factor after it enters the model, such as variance contribution. Select the factor that makes the greatest improvement in statistics to enter the model, that is, select the factor that contributes the most to runoff prediction, and perform an F statistical test on the factor. Calculate the variance ratio based on the maximum contribution value:

[0098]

[0099] Where n is the number of samples, p is the number of teleconnection factors currently selected into the model, and maxV i is the maximum variance contribution value, It is the element value corresponding to the result of the augmented matrix elimination transformation in step l.

[0100] The rule of the F statistical test is that, at a given confidence level, if , indicating that after the introduction of the teleconnection factor, the regression equation's ability to explain the runoff value y is enhanced, that is, the factor can be introduced; otherwise, it cannot be introduced. Update the model and add the selected factor to the model.

[0101] (3) Step by step, eliminate factors backward: Calculate the statistics after eliminating each teleconnection factor in the model. Select the factor that makes the smallest improvement in statistics and eliminate it from the model, that is, select the factor that contributes the least to runoff prediction. Select the factor with the smallest variance contribution from the selected factor set, perform an F statistical test on it, and calculate the variance ratio based on the minimum variance contribution value:

[0102]

[0103] Where minV i is the minimum variance contribution value, and its other meanings are the same as above. The rule of F statistical test is that under a given confidence level, if , indicating that after the introduction of the teleconnection factor, the explanatory power of the regression equation for runoff y has not been enhanced, that is, it has no significant effect and can be eliminated; otherwise, there is no need to eliminate this factor.

[0104] Update the model and remove the removed teleconnection factors from the input factor set of the prediction model. Repeat the above steps until no factor can be introduced or deleted in the current regression equation, that is, the runoff prediction model is no longer significantly improved, stop the calculation, and the stepwise regression is completed.

[0105] 4-4. Substitute several indicators obtained by the preliminary selection of the Spearman correlation coefficient method into the re-screening of the stepwise regression method. In the stepwise regression method, consider the lag step length of 1-12 months, and explore the influence of each factor on runoff prediction under different lag steps. Iterate according to the above process 4-3, and through several independent repetitions of the stepwise regression method, select the 10 atmospheric circulation factors that have been screened the most times as the final introduced prediction factors. Obtain the characteristic name and corresponding coefficients of the final model, that is, which teleconnection factors are finally selected, and their influence on runoff prediction and lag time.

[0106] Taking Chitan Reservoir as an example, the second round of rescreening results of the stepwise regression method are shown in Table 2:

[0107] Table 2 Stepwise regression method re-screening results

[0108]

[0109] in: Indicates the order among the 88 atmospheric circulation indices, represents different lag times of the index, and P represents rainfall.

[0110] As a preferred embodiment, the specific implementation steps of the CNN-BiLSTM-Attention multi-model nested structure mentioned in step 5 are as follows:

[0111] 5-1. LSTM can effectively overcome the gradient vanishing and gradient exploding problems of traditional recurrent neural networks when processing long sequence data, significantly enhance long-term memory capabilities, and achieve accurate modeling of data sets with short-term or long-term dependencies such as runoff. Figure 2As shown, its uniqueness lies in the fact that it introduces internal control mechanisms such as input gate, forget gate, and output gate on the basis of recurrent neural network, which effectively maintains long-term storage of data and has outstanding advantages in processing long sequence data.

[0112] 5-2. BiLSTM consists of two independent LSTM units, which are responsible for processing input data from the forward and reverse directions respectively. Therefore, it can better mine bidirectional dependencies, improve the model performance of traditional LSTM, and make it more suitable for runoff time series prediction tasks. Figure 3 As shown, express The input data at each moment, namely the previous runoff data and the screened atmospheric circulation factor data, is the corresponding output data, i.e. the predicted runoff value, and Represent the LSTM layers for forward iterative processing and backward iterative processing, respectively. Represents the weight of each layer. The update status and final output value of the forward and backward LSTM layers can be obtained by using the activation function of each layer. The calculation results are:

[0113]

[0114] 5-3. Use CNN to extract nonlinear and high-dimensional features from runoff data, and input the processed stable information as a whole into the BiLSTM model for prediction. The CNN-BiLSTM coupling model is suitable for processing sequence data with spatial characteristics and bidirectional time relationships such as runoff, and can simultaneously consider past and future information on the data, effectively improving the accuracy of the prediction model. Figure 4 As shown in the figure, data enters CNN from the input layer, and then enters the pooling layer for compression after passing through the feature mapping of multiple convolutional layers. It is then passed to the fully connected layer in the form of a one-dimensional vector, and then the extracted features are integrated and the weight values ​​are updated to achieve back propagation. Among them, the convolutional layer plays a vital role, and the calculation formula is as follows:

[0115]

[0116] In the formula, is the input layer, l is the output layer, represents the feature matrix containing s input feature variables, For the input of previous runoff and filtered atmospheric circulation data, is the activation function; represents the number of input feature variables; y represents the model output information; Represents the bias term of the j-th input feature variable in the output layer.

[0117] 5-4. Attention can calculate the weighted sum between the output of each time step and the learnable attention weight to obtain the comprehensive features of the sequence, thereby improving the prediction accuracy of the model. Figure 5 As shown, is the input sequence, is the corresponding hidden layer state value, yes The attention weight value expresses the influence of the input atmospheric circulation factors on the predicted runoff; represents the output sequence, is the output feature vector. The calculation process is as follows:

[0118]

[0119]

[0120]

[0121]

[0122] In the formula, for the degree of importance; yes The attention weight value expresses the influence of the input atmospheric circulation factors on the predicted runoff; represents the output sequence; Represents the hidden layer state value of the i-th period; Indicates the importance of the k-th period; represents the hyperbolic tangent function; represents the exponential function with the natural logarithm base e as the base; Represents the final output value obtained after weighted calculation; Represents the input sequence; F represents the weighted feature vector; W and b are the weight matrix and bias vector respectively, and V and U are the learning parameters that are continuously updated with the training iterations.

[0123] Taking Chitan Reservoir as an example, the accuracy of runoff prediction is compared between the LSTM basic model and the integrated models with different nested structures. The results are shown in Table 3:

[0124] Table 3 Prediction results of basic model and different ensemble models

[0125]

[0126] As a preferred embodiment, the specific implementation structure of the prediction model data pre-processing mentioned in step 6 is as follows:

[0127] 6-1. Time domain processing:

[0128] (1) Time scale transformation: For the initial matrix of runoff and atmospheric circulation factors, converting the monthly scale data to the ten-day scale or weekly scale can better learn to capture the runoff variation pattern in the short term, which matches the characteristics of the CNN model that is good at extracting local features and is also the basis for accurately capturing the medium- and long-term runoff change process.

[0129] (2) Time series decomposition: Decomposing high-dimensional, complex and nonlinear runoff series into trend terms, seasonal terms and random terms, modeling and predicting different components separately, and then merging the prediction results can improve the accuracy of medium- and long-term runoff prediction, which matches the characteristics of the BiLSTM model that is good at processing long sequence data.

[0130] (3) Sliding window averaging: Sliding window averaging is performed on the input runoff and atmospheric circulation index data matrix to smooth the data, reduce the impact of noise, and improve the stability of the medium- and long-term runoff combination prediction model, which matches the characteristics of the Attention model that focuses on key information.

[0131] 6-2. Feature Engineering:

[0132] (1) Constructing derived teleconnection variables: Constructing derived variables based on the original atmospheric circulation data, such as the difference between rainfall and evaporation, cumulative rainfall, etc., can better reflect the key factors affecting medium- and long-term runoff and provide richer feature information for the CNN model.

[0133] (2) Prediction feature selection: Adopt more advanced feature selection methods for medium- and long-term runoff prediction, such as model selection or information entropy-based methods, to select the features that contribute most to the prediction results, reduce redundant information, improve the efficiency of the combined model, and make the model more focused on key information.

[0134] (3) Data standardization: Standardizing the input runoff and filtered teleconnection factor data matrix can eliminate the impact of different dimensions between data, improve the convergence speed and prediction accuracy of the model, and make the model pay more attention to the importance of the feature itself rather than the magnitude of the dimension.

[0135] As a preferred embodiment, the specific implementation steps of the improved prediction model training process mentioned in step 7 are as follows:

[0136] (1) Regularization method: Add regularization terms during model training, such as L1 / L2 regularization or Dropout. L1 regularization tends to produce sparse weight vectors, while L2 regularization tends to produce smooth weight vectors. This can prevent model overfitting, improve the generalization ability of the model, and make the model pay more attention to the key information that affects medium- and long-term runoff prediction.

[0137] (2) Improvement of loss function: Use a custom loss function, for example, consider the distribution characteristics of runoff prediction results or the width of the prediction interval. Since the medium- and long-term runoff prediction results may show the probability distribution characteristics of normal distribution or log-normal distribution, a loss function based on probability distribution can be used, such as the log-likelihood loss function; in addition to paying attention to the accuracy of the runoff prediction value, it is also necessary to control the width of the prediction interval. A loss function based on the width of the prediction interval can be used, such as a prediction interval width penalty term. Both loss functions can better evaluate the medium- and long-term runoff prediction effect of the combined model and guide the model to learn runoff prediction values ​​that are more in line with the actual situation.

[0138] As a preferred embodiment, the specific implementation steps of optimizing the model hyperparameters using the intelligent algorithm mentioned in step 8 are as follows:

[0139] It is proposed to use the Black Hawk optimization algorithm to optimize the hyperparameters of the prediction model, to optimize the hyperparameters within the combined prediction model, to construct a multi-model hyperparameter combination vector with optimization, to use this vector as the optimization object, and to use the hyperparameter range constraint as the search space, to find the parameter vector that makes the combined model mid- and long-term runoff prediction effect the best, and to improve the model prediction performance. The algorithm combines the biological laws of the Black Hawk and mathematical transformations to guide the search behavior of particles. The specific calculation process is as follows:

[0140] (1) Population initialization: As in most algorithms, the initial search agent is generated by the following formula:

[0141]

[0142] Where lb and ub are the lower and upper boundaries of the search space, i.e., the constraints of different parameter ranges in the combined model; rand is a column vector of dimension d, whose elements are random values ​​between 0 and 1.

[0143] (2) Hunting behavior: The tracking strategy proposed by simulating the hunting behavior of black hawks is a high-density search method. It increases the search density by adaptively distributing the group positions and increasing the population size, thereby improving the global optimization ability of the algorithm.

[0144]

[0145]

[0146]

[0147]

[0148] Where, X r is a random position in the search space, X k is the random black hawk position, X bestis the current best position, indicating the position of the prey; D is X best The farthest distance to the search boundary; r1 is a random number between 0 and 1, and t1 is a random number from 0 to 1 formed by the tent mapping. Simulate a random black hawk standing on high ground looking for potential directions for prey; It is an adversarial-based learning strategy suitable for exploring the search space that is not explored at this time; It means selecting n individuals with the smallest fitness as the update positions; the fitness function of the algorithm is the goal that long-term runoff prediction in the combined model expects to achieve, such as minimizing the error between the predicted runoff value and the measured value.

[0149] (3) Hovering behavior: The hovering operation is used to perform a rotation search to further refine the range of the global optimal position. The hovering of the Black Hawk is simulated by using the rotation method of high-dimensional space points.

[0150]

[0151]

[0152]

[0153] Where m is a d-dimensional hovering matrix, a is the hovering angle, and r2 is a random number between 0 and 1. The hovering strategy performs a rotation search within the global optimal position initially determined by the tracking strategy.

[0154] (4) Capture behavior: The capture strategy is an adaptive center search method, which aims to adjust the position distribution of all individuals to a position distribution centered on the current optimal position, in preparation for subsequent effective local development.

[0155]

[0156]

[0157]

[0158]

[0159] Where D1 and D2 are two position adjustment factors, is a column vector of dimension d, with elements ranging from 0.5 to 1. and The simulation shows that the black hawk constantly adjusts its posture to ensure successful capture when catching prey. The capture process is divided into two stages: first, the distance between all individuals and the current optimal position is expanded through D1, and then the distance between all individuals and the current optimal position is reduced to the level before the change through D2 to reduce the deviation of the group position from the current optimal position.

[0160] (5) Grabbing behavior: The grabbing strategy is a jump search method, which aims to perform a jump search on the position adjusted by the previous strategy to increase the chance of finding the global optimal position.

[0161]

[0162] In the formula, r3 is a random vector with dimension d, and the values ​​of the elements in each dimension follow a normal distribution. The above formula simplifies the snatching behavior of the Black Hawk when it flies from one point to another in a curve. Then the jumping motion of the point is used to simulate the snatching behavior of the Black Hawk.

[0163] (6) Warning behavior: Poisson distribution is used to guide particle movement, simulating the early warning mechanism between black hawks to prevent particles from escaping from the search space in each dimension.

[0164]

[0165]

[0166]

[0167]

[0168]

[0169] Where, d si is the i-th dimension The distance to the center of the search space, d s min and d s max They are d si The minimum and maximum values ​​of for According to The position matrix after rearrangement of the proximity.

[0170] (7) Migration behavior: The migration mechanism aims to move individuals with lower fitness away from the current optimal position to reduce the possibility of falling into the local optimum.

[0171]

[0172]

[0173] In the formula, f bestis the current best fitness value, f(j) is the fitness value of the jth individual, s1 is a d-dimensional column vector with elements between -1 and 1, and t2 is a random number between 0.4 and 1 formed by the Tent mixed mapping. The first formula uses the fitness function value to represent the black hawk's adaptability to the environment, and constructs a migration function z(f) to further fully simulate the migration law of the black hawk: the lower the adaptability to the environment, the longer the migration distance.

[0174] (8) Courtship behavior: The interaction between male and female black hawks during courtship was simulated by using fluctuations similar to sine-cosine functions and an odd-even alternating pattern. The advantage of this new alternating sine-cosine strategy is that it increases the diversity of individuals in the local search process and improves developability.

[0175]

[0176]

[0177] Where k is the step factor, and its function expression comes from the deformation of the Sigmoid function; r4 and r6 are random numbers between 0 and 1, and r5 and r7 are d-dimensional column vectors whose elements obey the normal distribution.

[0178] (9) Incubation behavior: According to the normal distribution, the male black eagle is more active near the nest during the incubation period and less active in farther places, because the male black eagle will protect the female incubating eggs. The incubation strategy is a diffusion search method that allows some individuals to continue to approach the current optimum while other individuals spread outward, thus preventing them from falling into the local optimum.

[0179]

[0180] In the formula, R is an array of normally distributed data, X d For group position X from nest X best The group position matrix after rearranging from nearest to farthest.

[0181] As a preferred embodiment, the specific implementation steps of post-processing the prediction results mentioned in step 9 are as follows:

[0182] 9-1. Integration of forecast results:

[0183] Integrating the prediction results of CNN, BiLSTM and Attention models, for example by adopting weighted average or empowerment mechanism, can make full use of the advantages of each model, improve the prediction accuracy, and obtain more comprehensive medium- and long-term runoff prediction results.

[0184] 9-2. Prediction interval generation and uncertainty assessment: Generate prediction intervals using model prediction results, such as using Gaussian process regression or Monte Carlo simulation, to assess the uncertainty of the prediction results and provide decision makers with a more reliable basis for decision making. The present invention is explained using the Gaussian process regression method GPR as an example.

[0185] GPR can fit nonlinear data such as runoff, realize uncertainty prediction of the model, and predict the runoff prediction point data using the characteristics of probability distribution. The main calculation process is as follows: For a given n-dimensional training set , then when inputting the test set Give the predicted value , making it closer to the measured value , then the output Obey a joint Gaussian distribution with mean 0 and covariance kernel k:

[0186]

[0187] In the formula, represents a vector composed of n measured runoff values ​​y, which obeys Gaussian distribution, and n is the number of samples; represents the feature matrix composed of the input x of n training sets; represents the predicted value of runoff probability after Gaussian process regression; represents the joint Gaussian distribution function with a mean of 0; x represents the input of the training set; Represents the input of the test set.

[0188] Taking Chitan Reservoir as an example, the specific results of the medium- and long-term runoff prediction under different step lengths mentioned in step 10 are shown in Table 4:

[0189] Table 4 Summary of prediction results for each step length (unit: m 3 / s)

[0190] As a preferred embodiment, the specific implementation steps of evaluating the deterministic prediction effect mentioned in step 11 are as follows:

[0191] The following four commonly used prediction error evaluation indicators and a comprehensive indicator proposed by the present invention are used to jointly evaluate the prediction effect of the model from a deterministic perspective. The connotation and calculation formula are as follows:

[0192] 11-1. Mean Absolute Error (MAE) represents the absolute value of the deviation between the predicted value and the measured value:

[0193]

[0194] 11-2. Mean Absolute Percentage Error (MAPE) is an improvement on MAE, which effectively avoids the interference of data magnitude and thus more intuitively reflects the degree to which the prediction results deviate from the measured values:

[0195]

[0196] 11-3. Root Mean Square Error (RMSE) takes the average of the squares of the differences between the predicted value and the measured value, and finally takes the square root to obtain the result, ensuring that the dimension remains unchanged:

[0197]

[0198] 11-4. Nash-Sutcliffe Efficiency (NSE) evaluates the model fit by comparing the difference between the measured value and the predicted value:

[0199]

[0200] Where n is the number of samples; and are the predicted and measured values ​​of the i-th runoff, respectively; is the average of all measured values.

[0201] 11-5. This invention proposes a new evaluation index, Prediction Error Composite Score (PECS), which organically combines the calculation results of the first four commonly used indicators to more intuitively judge the quality of deterministic prediction. The calculation formula is as follows:

[0202]

[0203] In the formula, w1, w2, w3, and w4 are the weight coefficients of MAPE, MAE, RMSE, and NSE, respectively, and w1+w2+w3+w4=1. max 、MAPE min 、MAE max 、MAE min 、RMSE max 、RMSE min 、NSE max 、NSE min They are the maximum and minimum values ​​of MAPE, MAE, RMSE and NSE respectively. The smaller the PECS value, the better the prediction effect of the model.

[0204] The PECS index can effectively eliminate the influence of the order of magnitude of the original four indicators, making the indicators of different dimensions comparable; the weight of each indicator can be adjusted according to the actual needs of runoff prediction in different study areas, and more flexibly reflect the model's medium- and long-term deterministic runoff prediction effect.

[0205] The following three methods can be used to determine the weight coefficient:

[0206] ① Experience judgment: You can use subjective experience to assign values ​​or use expert consultation to score. The former refers to judging the importance of MAPE and NSE to the prediction effect based on the understanding and experience of the hydrological runoff prediction model, and determining the appropriate weight coefficient. For example, if you value the prediction accuracy more than the absolute value of the prediction error, you can set the weight of MAPE higher. The latter is to consult experts in the field of hydrological prediction, understand their views on the importance of each indicator, and determine the weight coefficient based on expert opinions.

[0207] ② Experimental analysis: Sensitivity analysis or cross-validation can be used. The former is to perform sensitivity analysis on different weight coefficients, observe the changes in PECS values, and select the weight coefficient combination that minimizes the PECS value. Or use the cross-validation method to evaluate the prediction effect of the model under different weight coefficients and select the weight coefficient combination that gives the best prediction effect of the model.

[0208] ③Statistical method: determined by principal component analysis or hierarchical analysis method. Principal component analysis is to analyze the principal components of each indicator and determine the weight coefficient according to the variance contribution rate of the principal component. Hierarchical analysis method mainly determines the weight coefficient by establishing a hierarchical structure model and determining the relative importance of each indicator through expert scoring.

[0209] The default parameters set in the present invention are w1=0.35, w2=0.15, w3=0.15 and w4=0.35. When promoting and applying the present invention, the parameter values ​​can be modified according to the above method and the actual situation of the study area. The reasons for selecting the default parameters are:

[0210] As absolute value indicators, MAE and RMSE will be affected by the magnitude of the basic runoff data. MAPE is an improvement on MAE, which can avoid the interference of magnitude and is more accurate and objective. NSE evaluates the degree of fit of the prediction model and is also more effective. Therefore, it is necessary to reduce the weight of MAE and RMSE to avoid their excessive impact on the PECS value; increase the weight of MAPE and NSE to highlight their importance to the prediction effect.

[0211] Taking Chitan Reservoir as an example, the deterministic prediction effect of the multi-model nested structure under different prediction step sizes is calculated, and the results are as follows:

[0212] Table 5 Calculation results of certainty evaluation index

[0213]

[0214] As a preferred embodiment, the specific implementation steps of evaluating the probability prediction effect mentioned in step 12 are as follows:

[0215] The following four indicators are used to evaluate the prediction effect of the model from a deterministic perspective. Their connotations and calculation formulas are as follows:

[0216] 12-1. Prediction Interval Coverage Probability (PICP) indicates the probability that the observed value falls within the prediction interval. The higher the coverage, the better the prediction effect:

[0217]

[0218] In the formula, n is the number of prediction samples; is the Boolean value of the ith sample. If the measured value of runoff falls within the prediction interval, The value is 1, otherwise the value is 0.

[0219] 12-2. Prediction Interval Normalized Average Width (PINAW) refers to the average distance between the upper and lower bounds of the prediction interval. The smaller the value, the narrower the interval range and the higher the accuracy:

[0220]

[0221] In the formula, and are the upper and lower limits of the runoff probability prediction interval, is the input variable.

[0222] 12-3. Continuous Ranked Probability Score (CRPS) characterizes the overall effect of probability forecast by measuring the average consistency between the predicted and measured runoff values. The smaller the value, the higher the prediction reliability and the better the concentration:

[0223]

[0224] In the formula, x and is the probability prediction value and measured value of period i; is the posterior probability distribution function; H is the indicator function, The value is 0 when , otherwise it is 1.

[0225] 12-4. Coverage Width-based Criterion (CWC) is a comprehensive index that can take into account the two conflicting goals of high coverage and narrow interval. The smaller the value, the better the prediction effect. Its expression is:

[0226]

[0227] In the formula, is the confidence level; is the penalty term, When it is 0, otherwise it is 1; is the penalty coefficient.

[0228] Taking Chitan Reservoir as an example, the medium- and long-term runoff probability prediction effect of the multi-model nested structure under different prediction step sizes is calculated, and the results are as follows:

[0229] Table 6 Calculation results of certainty evaluation index

[0230]

[0231] The specific implementation steps of the interpretability analysis mentioned in step 13 are as follows:

[0232] The SHAP method approximates complex machine learning models by constructing multiple linear models, and then estimates the SHAP value of each feature variable in turn to quantify their respective contributions. The calculation formula of the SHAP value is:

[0233]

[0234] Where M is the m-dimensional set of all characteristic variables in the data set, that is, the input data matrix composed of the previous runoff data and the teleconnection factor data obtained by the second round of screening; s is the number of factors extracted from M. A subset of size ; represents all possible subsets; is the runoff prediction result obtained based on the set s; It means adding eigenvalues ​​to s The results obtained;

[0235] The larger the absolute value of SHAP value is, the greater the contribution to the runoff prediction value is;

[0236] The positive or negative value of SHAP indicates the direction of influence on runoff. If the SHAP value is positive, it means that the characteristic variable has a positive influence on the runoff prediction result, otherwise it has a negative influence.

[0237] As described above, although the present invention has been shown and described with reference to specific preferred embodiments, it should not be construed as limiting the present invention itself. Various changes may be made to it in form and detail without departing from the spirit and scope of the present invention as defined in the appended claims.

Claims

1. A medium- and long-term hydrological probability forecasting method considering the nested combination of interpretable deep learning models, characterized in that: The steps include: Collect and preprocess the inflow runoff data and atmospheric circulation index of the target station to be predicted for several years; Based on the inflow runoff data, the correlation of the runoff time series is analyzed using an autocorrelation function and / or a partial autocorrelation function, thereby determining the lag time of the medium- and long-term runoff combined prediction model; Based on the atmospheric circulation index, an input matrix including an initial factor set is constructed, and medium- and long-term hydrological forecast factors are screened out therefrom, and the screened medium- and long-term hydrological forecast factors are reconstructed with the inflow runoff data to form reconstructed combined data; Construct a CNN-BiLSTM-Attention multi-model nested structure as a medium- and long-term runoff combination prediction model, optimize the hyperparameters of the medium- and long-term runoff combination prediction model, and train the medium- and long-term runoff combination prediction model; The reconstructed combined data is used as the input item of the medium- and long-term runoff combined prediction model, and the predicted future runoff volume is used as the output, so as to obtain the deterministic prediction results and the probabilistic prediction results of the medium- and long-term runoff under different step lengths.

2. According to claim 1, a medium- and long-term hydrological probability forecasting method considering the nested combination of interpretable deep learning models is characterized in that: For the collected inflow runoff data, the completeness of the inflow runoff data is first checked. If there are missing values, the average value of the historical runoff in the same period is used to fill them; The atmospheric circulation index contains several monthly teleconnection factor data. For the collected teleconnection factor data, if there are missing values ​​and the number of missing values ​​is less than or equal to 10% of the sequence length, the historical mean of the same period series is used to fill the missing values; if the missing values ​​are greater than 10% of the sequence length, the teleconnection factor data is eliminated.

3. According to claim 2, a medium- and long-term hydrological probability forecasting method considering the nested combination of interpretable deep learning models is characterized in that: Based on the teleconnection factor data, an input matrix containing the initial factor set is constructed, and medium- and long-term hydrological forecast factors are screened out from it. The screening process is divided into two rounds: The first round of screening was completed through the Spearman correlation coefficient method, and the teleconnection factor data with an absolute value of the correlation coefficient greater than the threshold A were found as the preliminary factors to enter the second round of screening process.

4. According to claim 3, a medium- and long-term hydrological probability forecasting method considering the nested combination of interpretable deep learning models is characterized in that: The second round of screening process includes: The primary factors and inflow runoff data obtained from the first round of screening were combined into a table data, and the table data was converted into a form with a mean of 0 and a standard deviation of 1; Set up a stepwise regression model and perform stepwise iteration to finally obtain the medium- and long-term hydrological forecast factors: For an equation containing m independent variables x and dependent variable y, use the least squares method to perform differentiation and obtain the regression coefficients The expression is: ； In the formula, the independent variable x is the teleconnection factor data, and the dependent variable y is the inflow runoff data; is the coefficient of the mth term in the mth regression equation; represents the regression coefficient; Represents the correlation coefficient between the mth x and y in the data set.

5. According to claim 4, a medium- and long-term hydrological probability forecasting method considering the nested combination of interpretable deep learning models is characterized in that: In the CNN-BiLSTM-Attention multi-model nested structure: BiLSTM consists of a forward LSTM layer and a backward LSTM layer, which are responsible for processing input data in the forward and reverse directions respectively; The update status and final output value of the forward LSTM layer and the backward LSTM layer use the activation function of each layer , , The calculation results are: ； In the formula, represents the reconstructed combined data input at the i-th moment; represents the predicted future runoff; represents the i-th forward LSTM layer; represents the i-th backward LSTM layer; Represents the weight of each layer.

6. A medium- and long-term hydrological probability forecasting method considering nested combination of interpretable deep learning models according to claim 5, characterized in that: In the CNN-BiLSTM-Attention multi-model nested structure: Use CNN to extract nonlinear features of runoff data, and input the processed output information as a whole into BiLSTM for prediction. The process expression is as follows: ； In the formula, is the input layer, l is the output layer, represents the feature matrix containing s input feature variables, For the input of previous runoff and filtered atmospheric circulation data, is the activation function; represents the number of input feature variables; y represents the model output information; Represents the bias term of the j-th input feature variable in the output layer.

7. The method for medium- and long-term hydrological probability forecasting considering nested combinations of interpretable deep learning models according to claim 5, characterized in that: In the CNN-BiLSTM-Attention multi-model nested structure: Attention is used to calculate the weighted sum between the output of each time step and the learnable attention weight to obtain the comprehensive features of the sequence. The calculation process is as follows: ； ； ； ； In the formula, for the degree of importance; yes The attention weight value expresses the influence of the input atmospheric circulation factors on the predicted runoff; represents the output sequence; Represents the hidden layer state value of the i-th period; Indicates the importance of the k-th period; represents the hyperbolic tangent function; represents the exponential function with the natural logarithm base e as the base; Represents the final output value obtained after weighted calculation; Represents the input sequence; F represents the weighted feature vector; W and b are the weight matrix and bias vector respectively, and V and U are the learning parameters that are continuously updated with the training iterations.

8. The method for medium- and long-term hydrological probability forecasting considering nested combination of interpretable deep learning models according to claim 1, characterized in that: The training of the medium- and long-term runoff combined prediction model specifically includes: For a given n-dimensional training set , then when inputting the test set Give the predicted value , making it closer to the measured value , then the output Obey a joint Gaussian distribution with mean 0 and covariance kernel k: ； In the formula, represents a vector composed of n measured runoff values ​​y, which obeys Gaussian distribution, and n is the number of samples; represents the feature matrix composed of the input x of n training sets; represents the predicted value of runoff probability after Gaussian process regression; represents the joint Gaussian distribution function with a mean of 0; x represents the input of the training set; Represents the input of the test set.

9. The method for medium- and long-term hydrological probability forecasting considering nested combinations of interpretable deep learning models according to claim 4, characterized in that: Also includes: Based on the screened medium- and long-term hydrological forecast factors, the SHAP value of each medium- and long-term hydrological forecast factor is calculated in turn to quantify their respective contributions and find out the key factors affecting runoff. Calculate the SHAP value according to the following expression : ； Where M is the m-dimensional set of all characteristic variables in the data set, that is, the input data matrix composed of the previous runoff data and the teleconnection factor data obtained by the second round of screening; s is the number of factors extracted from M. A subset of size ; represents all possible subsets; is the runoff prediction result obtained based on the set s; It means adding eigenvalues ​​to s The results obtained; The larger the absolute value of SHAP value is, the greater the contribution to the runoff prediction value is; The positive or negative value of SHAP indicates the direction of influence on runoff. If the SHAP value is positive, it means that the characteristic variable has a positive influence on the runoff prediction result, otherwise it has a negative influence.

10. A medium- and long-term hydrological probability forecasting system, used to implement the medium- and long-term hydrological probability forecasting method considering the nested combination of interpretable deep learning models as described in any one of claims 1 to 9; characterized in that: The medium- and long-term hydrological probabilistic forecast system includes: Data collection module; the data collection module is used to collect and pre-process the inflow runoff data and atmospheric circulation index of the target site to be predicted for several years; The first data processing module: The first data processing module analyzes the correlation of the runoff time series based on the inflow runoff data using an autocorrelation function and / or a partial autocorrelation function, thereby determining the lag time of the medium- and long-term runoff combination prediction model; The second data processing module: the second data processing module constructs an input matrix including an initial factor set based on the atmospheric circulation index, and selects medium- and long-term hydrological forecast factors therefrom, and reconstructs the selected medium- and long-term hydrological forecast factors with the inflow runoff data to form reconstructed combined data; Model building module; the model building module is used to build a CNN-BiLSTM-Attention multi-model nested structure as a medium- and long-term runoff combination prediction model, optimize the hyperparameters of the medium- and long-term runoff combination prediction model, and train the medium- and long-term runoff combination prediction model; Result output module: The result output module uses the reconstructed combined data as the input item of the medium- and long-term runoff combined prediction model and the predicted future runoff volume as the output to obtain the deterministic prediction results and probabilistic prediction results of the medium- and long-term runoff under different step lengths.

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