Runoff prediction method based on multi-source satellite rainfall data fusion and deep learning optimization model

Abstract

The invention provides a runoff prediction method based on multi-source satellite rainfall data fusion and a deep learning optimization model. The runoff prediction method comprises the following steps: collecting rainfall data and hydro meteorological data of a multi-source satellite product in a research basin; carrying out noise reduction processing on the precipitation data of the multi-source satellite product by adopting Kalman filtering; and fusing the multi-source satellite product rainfall data after noise reduction processing by adopting a Bayesian model average algorithm. Constructing a deep learning runoff prediction model with adaptive periodic position coding, taking runoff data in hydro meteorological data as supervision, training and testing the runoff prediction model by using the fused multi-source satellite product rainfall data, and performing hyper-parameter optimization by adopting a Newton-Raphson optimization algorithm in the training process; and performing runoff prediction by using the trained runoff prediction model. According to the method, the problems that in existing runoff forecasting model fusion, static weighting cannot describe the change of model performance along with time and time-varying errors are ignored are solved, and the accuracy of input data is improved.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of hydro-meteorological modeling and artificial intelligence, and particularly relates to a runoff prediction method based on a deep learning optimized model. BACKGROUND

[0002] As a key input in hydrological models, the accuracy of precipitation data directly affects the reliability and timeliness of runoff simulation and flood prediction. Currently, observation methods such as ground rain gauges, weather radars, and satellite remote sensing are mainly relied on. Although ground stations have high accuracy, they are difficult to cover complex terrain areas comprehensively due to their sparse distribution. Radar observation is greatly affected by terrain obstruction and has limited spatial continuity. Satellite remote sensing precipitation data, which has wide-area coverage and high temporal and spatial resolution, has gradually become an important alternative means and is widely used in watershed hydrological simulation.

[0003] However, different satellite precipitation products have significant differences in inversion mechanisms, orbital characteristics, and observation frequencies, which often cause systematic bias and timing inconsistency problems. If directly used in hydrological models, it will lead to cumulative input errors and decreased prediction accuracy. Existing multi-source fusion methods such as weighted average, linear regression, and spatial interpolation treat precipitation sequences as static processes. Although they improve data consistency to some extent, they generally ignore the dynamic changes of precipitation sequences, i.e., the non-stationarity of precipitation processes in time, space, and intensity. In the time dimension, it reflects the randomness (such as alternating sudden rain and long drought), periodicity (seasonal precipitation pattern), and trend (long-term evolution under climate change) of precipitation events. In the spatial dimension, it reflects the spatial heterogeneity of precipitation within the basin caused by factors such as topography and atmospheric circulation, such as strong rainfall on the windward slope of mountains and weak rainfall on the leeward side. In terms of intensity, it reflects the nonlinear transition of precipitation intensity from weak to strong, such as rapid intensification of convective precipitation. This ignorance leads to static weights that cannot adapt to short-term heavy rainfall mutations during heavy rain periods, resulting in smoothing of the fusion results and weakening of the peak values. The precipitation pattern difference between long drought and wet periods is ignored, and the fusion sequence cannot reflect the true dry-wet alternation. In addition, the time-varying error characteristics of precipitation sequences are generally ignored, i.e., the error of satellite precipitation data dynamically changes with observation time, location, and weather conditions. Static fusion weights continue to trust high-error data sources during heavy rain periods, leading to amplification of systematic bias in input model data, fixed error models cannot represent the uncertainty of sudden precipitation events, affecting the reliability of subsequent runoff prediction, and being difficult to adapt to the changing process of strong convective rainfall or sudden floods. SUMMARY

[0004] In view of the technical problem that the existing runoff prediction method ignores the dynamic change of the precipitation sequence and the time-varying error characteristics, resulting in insufficient accuracy of the input data, the present application provides a runoff prediction method based on multi-source satellite precipitation data fusion and deep learning optimization model, which realizes a dynamic weight prediction mechanism based on meteorological-hydrological factors by fusing Kalman filtering and Bayesian model averaging method to process multi-source satellite precipitation data, overcomes the problem that the static weighting in the existing runoff prediction model fusion cannot depict the change of model performance over time and ignores the time-varying error, and improves the accuracy of the input data.

[0005] In order to achieve the above purpose, the technical scheme of the present application is as follows:

[0006] A runoff prediction method based on multi-source satellite precipitation data fusion and deep learning optimization model, comprising the steps of:

[0007] S1: collecting multi-source satellite product precipitation data and hydro-meteorological data in the study basin;

[0008] S2: performing noise reduction processing on the multi-source satellite product precipitation data by using Kalman filtering;

[0009] S3: fusing the multi-source satellite product precipitation data after noise reduction processing by using Bayesian model averaging algorithm;

[0010] S4: constructing a deep learning runoff prediction model with adaptive periodic position encoding, using the runoff data in the hydro-meteorological data as supervision, training and testing the runoff prediction model using the fused multi-source satellite product precipitation data, and using Newton-Raphson optimization algorithm for hyperparameter optimization in the training process;

[0011] S5: obtaining the multi-source satellite product precipitation data to be predicted after processing by steps S2-S3, and using the trained runoff prediction model to predict the runoff.

[0012] Further, the method for performing noise reduction processing on the multi-source satellite product precipitation data by using Kalman filtering is as follows:

[0013] S2.1, constructing a state space model including a state transition equation and an observation equation by taking the state estimation of the real precipitation as the system state variable and taking the satellite product precipitation data as the observation;

[0014] S2.2, initializing the state estimation of the real precipitation and the error covariance of the state estimation of the real precipitation and the observation;

[0015] S2.4, calculating the Kalman gain according to the prior error covariance;

[0016] S2.5, performing state update according to the Kalman gain, the state transition equation and the observation equation to obtain the posterior state estimation of the real precipitation;

[0017] S2.6, updating the posterior error covariance according to the Kalman gain and the prior error covariance, and repeating S2.3-S2.5 until the posterior error covariance variation is less than a preset value.

[0018] Further, the method for calculating the prior state estimation of the real precipitation and the prior error covariance according to the state transition equation in step S2.3 is:

[0019]

[0020] P k|k-1 = AP k-1 A T + Q

[0021] wherein A is a state transition matrix, is the posterior state estimation of the real precipitation in the previous cycle, is the prior state estimation of the real precipitation in the current cycle, P k-1 is the posterior error covariance in the previous cycle, P k|k-1 is the prior error covariance in the current cycle, and Q is a process noise covariance matrix;

[0022] The method for calculating the Kalman gain in step S2.4 is:

[0023]

[0024] wherein K k is the Kalman gain, H is an observation matrix, and R is an observation noise covariance;

[0025] The method for obtaining the posterior state estimation of the real precipitation in step S2.5 is:

[0026]

[0027] wherein, is the posterior state estimation of the real precipitation in the current cycle, and z k is the current observation;

[0028] The method for updating the posterior error covariance in S2.6 is:

[0029] P k = (I-K k H) P k|k-1

[0030] wherein I is an identity matrix, and P k is the posterior error covariance in the current cycle.

[0031] Further, the implementation method of step S3 is:

[0032] S3.1, calculate the error distribution characteristics of each group of satellite product precipitation data after noise reduction processing respectively based on the real precipitation amount;

[0033] S3.2, calculate the prior probability of each group of satellite product precipitation data according to the error distribution characteristics;

[0034] S3.3, calculate the likelihood probability of the real precipitation amount with respect to each group of satellite product precipitation data according to the probability density function of Gaussian distribution;

[0035] S3.4, calculate the posterior probability of each group of satellite product precipitation data according to the prior probability of each group of satellite product precipitation data and the likelihood probability of the real precipitation amount with respect to each group of satellite product precipitation data;

[0036] S3.5, weight and fuse each group of satellite product precipitation data by taking the posterior probability of each group of satellite product precipitation data as a dynamic weight to obtain the fused satellite product precipitation data.

[0037] Further, the calculation method of the error distribution characteristics is: calculate the error standard deviation σ i of each group of satellite product precipitation data S i with respect to the absolute error ε i of the real precipitation amount G, and take the error standard deviation σ

[0038] The prior probability of each group of satellite product precipitation data in step S3.2 is calculated by using the reciprocal of the error standard deviation σ i combined with normalization:

[0039]

[0040] Wherein, m is the number of groups of satellite product precipitation data, and j represents the group number index.

[0041] Further, the method for calculating the posterior probability of each group of satellite product precipitation data in step S3.4 is:

[0042]

[0043] Wherein, P(S i |G) is the posterior probability of each group of satellite product precipitation data, and P(G|S i ) is the likelihood probability of the real precipitation amount with respect to each group of satellite product precipitation data;

[0044] The implementation method of step S3.5 is:

[0045]

[0046] wherein S fused is the fused satellite product precipitation data.

[0047] Further, the deep learning runoff prediction model with adaptive periodic position encoding in step S4 introduces an adaptive periodic position encoding module after the input embedding layer of the Transformer model: a trainable periodic adjustment parameter is used to dynamically map the time steps to adaptively capture the daily, ten-day, monthly and seasonal multi-scale runoff precipitation periodic characteristics;

[0048] Further, the method for dynamically mapping the time steps in the adaptive periodic position encoding module using a trainable periodic adjustment parameter is:

[0049]

[0050] wherein APPE (t,2i) is the position encoding vector, t represents the time step index, p i ∈R + is the position frequency adjustment parameter of the i-th dimension, which is used for learning and updating in the model back propagation process; λ i represents the initial periodic scale.

[0051] Further, the method for training and testing the flow prediction model using the fused multi-source satellite product precipitation data is:

[0052] S4.1, the fused satellite product precipitation data, the potential evapotranspiration in the hydro-meteorological time series and the previous runoff are constructed into time series input samples in a time window sliding manner, and the later runoff is used as a supervised label to construct a labeled runoff prediction data set, and the data set is divided into a training set, a validation set and a test set;

[0053] S4.2, using the training set as input, the runoff prediction value is calculated through the forward propagation process of the Transformer model with adaptive periodic position encoding, the mean square error is used as the loss function, and the model parameters are updated through back propagation;

[0054] S4.3, after each training round, the Transformer model with adaptive periodic position encoding is verified using the validation set, the runoff prediction value is calculated through the forward propagation process of the Transformer model with adaptive periodic position encoding, the evaluation index of the validation set is calculated according to the runoff prediction value, and the learning rate is dynamically adjusted and the hyperparameter optimization adjustment based on the Newton-Raphson optimization algorithm is carried out based on the evaluation index of the validation set, until all training rounds are completed.

[0055] S4.3 After training, the Transformer model with adaptive periodic location encoding is tested using the test set, and the performance of the runoff forecasting model is evaluated using the Nash efficiency coefficient.

[0056] Furthermore, the method for hyperparameter optimization and adjustment based on the Newton-Raphson optimization algorithm is as follows:

[0057] (1) Using multiple hyperparameters in the model as variables to be optimized, construct a multidimensional search space Ω;

[0058] (2) Generate an initial solution set in the multidimensional search space Ω, and use the evaluation index of the validation set as the objective function;

[0059] (3) For the current candidate solution, the gradient ▽f(x) and Hessian matrix ▽ of the objective function are approximately estimated in its neighborhood using the finite difference method. 2 f(x);

[0060] (4) Based on the standard Newton's method update formula, construct the update direction and calculate new candidate solutions;

[0061] (5) If the value of the new candidate solution exceeds the predefined search space Ω, project the new candidate solution back into the legal value range.

[0062] (6) If the improvement of the objective function is less than the set threshold in several consecutive generations of optimization, a perturbation operator is introduced to add random perturbation to the current solution, forcing the solution to jump out of the current region;

[0063] (7) The algorithm stops when the termination condition is met.

[0064] The beneficial effects of this invention are as follows:

[0065] Compared with existing technologies, this invention processes multi-source satellite precipitation data by fusing Kalman filtering and Bayesian model averaging, and introduces the Newton-Raphson Based Optimization Algorithm (NRBO) to improve the Transformer-structured deep learning runoff prediction model. While improving data quality and model performance, it further proposes a dynamic weighting prediction mechanism based on meteorological-hydrological factors, overcoming the problems of static weighting in existing runoff forecast model fusion failing to characterize model performance changes over time and neglecting time-varying errors. Compared with traditional methods, this invention not only improves the accuracy of input data but also achieves characterization and early correction of model performance trends by constructing machine learning models or regression equations, significantly enhancing the forecast system's ability to respond to uncertainties and improving prediction accuracy and robustness under extreme events. BRIEF DESCRIPTION OF DRAWINGS

[0066] In order to more clearly illustrate the technical solutions in the embodiments of the present application or the prior art, the drawings needed to be used in the embodiments or prior art description will be briefly introduced. Obviously, the drawings in the following description are only some embodiments of the present application, and other drawings can be obtained by those skilled in the art without creative labor.

[0067] Figure 1 Flowchart of the method of the present application;

[0068] Figure 2 Structure diagram of the Transformer model with adaptive periodic position encoding of the present application. DETAILED DESCRIPTION

[0069] The technical solutions in the embodiments of the present application will be described clearly and completely in the following with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only some embodiments of the present application, not all. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative labor are within the scope of protection of the present application.

[0070] A runoff prediction method based on multi-source satellite precipitation data fusion and deep learning optimization model, as shown in Figure 1 The steps are as follows:

[0071] S1: Collecting multi-source satellite product precipitation data and hydro-meteorological data in the study basin.

[0072] Collecting hydro-meteorological data in the study basin, including real precipitation, potential evapotranspiration, and runoff data, which are derived from rain stations and hydrological stations set by national or local meteorological and hydrological departments. Runoff data is used as the verification and prediction target of the model.

[0073] Preprocessing: using bilinear interpolation to unify all satellite product precipitation data and hydro-meteorological data to the target resolution, and adjusting all satellite product precipitation data and hydro-meteorological data to daily time step to improve data consistency and avoid subsequent model failure due to time and space misalignment;

[0074] Further, 3σ criterion is used to identify and eliminate abnormal points, and time series linear interpolation or spatial neighborhood weighted interpolation method is used to complete the missing values to ensure data integrity and prevent training interruption;

[0075] Further, Min-Max normalization method is used to scale each variable to the range of [0, 1] to ensure the stability of neural network training.

[0076] Finally, a plurality of sets of satellite product precipitation time series and a set of hydro-meteorological time series are obtained.

[0077] S2: Adopting Kalman filtering to carry out noise reduction processing on the multi-source satellite product precipitation data.

[0078] Introducing the Kalman filtering algorithm to independently filter each set of satellite product precipitation time series, regarding the satellite product precipitation time series as the observation output of a dynamic system, setting the system state variable as the state estimation of the real precipitation, the observation as the satellite product precipitation data, i.e., the satellite remote sensing inversion value, and the state transition function as the Markov property of precipitation in a short time, and adopting a first-order autoregressive model for description.

[0079] Specifically, the method for adopting Kalman filtering to carry out noise reduction processing on the multi-source satellite product precipitation data is as follows:

[0080] First, regarding the state estimation of the real precipitation as the system state variable and the satellite product precipitation data as the observation, a state space model including a state transition equation and an observation equation is constructed:

[0081] x k|k-1 =Ax k-1 +w k ;

[0082] z k =Hx k|k-1 +v k ;

[0083] Wherein, x k-1 is the posterior state estimation of the real precipitation in the previous cycle, x k|k-1 is the prior state estimation of the current real precipitation, A is the state transition matrix, which is set as the unit matrix, w k is the process noise, z k is the observation, H is the observation matrix, and v k is the observation noise.

[0084] Further, the state estimation of the real precipitation is initialized as x0=S1(0), and the error covariance is initialized as P0=Var(z), S1(0) is the satellite product precipitation data at the first time step, and Var(z) represents the sample variance of the satellite product precipitation data.

[0085] Further, the prior state estimation of the real precipitation and the prior error covariance are calculated according to the state transition equation:

[0086]

[0087] P k|k-1 =AP k-1 A T +Q;

[0088] in, For the prior state estimate of the actual precipitation, P k|k-1 Let be the prior error covariance, and Q be the process noise covariance matrix.

[0089] Furthermore, the Kalman gain K is calculated based on the prior error covariance. k :

[0090]

[0091] Where R is the observation noise covariance matrix.

[0092] Furthermore, based on the Kalman gain, state transition equation, and observation equation, a posterior state estimate of the actual precipitation is obtained by updating the state:

[0093]

[0094] in, This is a posterior state estimate of the current actual precipitation.

[0095] Furthermore, the posterior error covariance P is updated based on the Kalman gain and the prior error covariance. k This continues until the change in the posterior error covariance is less than the preset value.

[0096] P k =(IK k H)P k|k-1 ;

[0097] Where I is the identity matrix.

[0098] Error covariance represents the covariance between the posterior state estimate and the observed amount of precipitation, reflecting the degree of uncertainty in the current step state estimate.

[0099] Finally, after processing the precipitation data from multiple satellite products, Kalman filtering smoothing results of multiple sets of satellite product precipitation data were obtained. The process noise covariance Q and observation noise covariance R were adaptively updated, which can adapt to different precipitation intensities and significantly reduce noise.

[0100] S3: The Bayesian model averaging algorithm is used to fuse precipitation data from multiple satellite products after noise reduction. The prior and posterior probabilities of each data source are calculated, and then the data are weighted and averaged.

[0101] First, based on the actual precipitation, the error distribution characteristics of precipitation data for each group of satellite products after noise reduction were calculated.

[0102] Specifically, calculate the precipitation data S for each set of satellite products. i The absolute error ε between the actual precipitation G and the actual precipitation Gi , for quantifying the deviation of each group of satellite data from the true value, providing the basis for subsequent error distribution statistics:

[0103] ε i = |S i -G|;

[0104] Statistics of the error distribution of each group of satellite precipitation data, the error standard deviation σ i , reflecting the dispersion degree of satellite precipitation data error, the smaller the standard deviation, the more stable and concentrated the satellite precipitation data error, the higher the natural reliability of the data:

[0105]

[0106] Where n is the total number of time steps in each group of satellite precipitation data, ε i (t) is the absolute error of satellite precipitation data S i tthtime step and the true precipitation G, δ is the regularization term, to prevent the error sum of squares from being too small, causing the standard deviation to approach 0.

[0107] Further, according to the error distribution characteristics, the prior probability of each group of satellite precipitation data is calculated, which gives each satellite an initial weight, reflecting the reliability of its historical error performance.

[0108] The prior probability describes the reliability of satellite precipitation data itself without relying on the true precipitation of current ground observation. Since the smaller the error standard deviation, the more reliable the data, the reliability is measured by the reciprocal of the error standard deviation, and the prior probability is obtained by normalization:

[0109]

[0110] Where m is the number of groups of satellite precipitation data, and j represents the group number index.

[0111] Further, according to the probability density function of Gaussian distribution, the likelihood probability of true precipitation about each group of satellite precipitation data is calculated. The likelihood probability quantifies the explanatory ability of satellite precipitation data for current ground observation, the more matched the satellite precipitation data and the true precipitation of ground observation, the higher the likelihood probability. Here we assume that the deviation of ground observation relative to satellite data follows Gaussian distribution, so we use the probability density function of Gaussian distribution to represent the likelihood:

[0112]

[0113] Further, the posterior probability of each set of satellite product precipitation data is calculated according to the prior probability of each set of satellite product precipitation data and the likelihood probability of the true precipitation with respect to each set of satellite product precipitation data. The posterior probability considers the reliability of the historical error of the satellite product precipitation data (prior) and the matching degree of the current and the ground observation (likelihood) at the same time, so that the fusion result is more biased to the final reliable degree of the satellite product precipitation data. The posterior probability of each set of satellite product precipitation data is derived by Bayes theorem:

[0114]

[0115] Further, each set of satellite product precipitation data is weighted and fused with the posterior probability of each set of satellite product precipitation data as a dynamic weight to obtain the fused satellite product precipitation data.

[0116]

[0117] S4: A deep learning runoff prediction model with adaptive periodic position coding is constructed, the runoff data in hydro-meteorological data are supervised, the fused multi-source satellite product precipitation data are used for training and testing the flow prediction model, and the Newton-Raphson optimization algorithm is used for hyperparameter optimization in the training process.

[0118] A Transformer model with adaptive periodic position coding is constructed, the adaptive periodic position coding module is introduced on the basis of the original Transformer model, the time step is dynamically periodical mapping by using the trainable period adjustment parameter, so that the model can adaptively capture the multi-scale runoff precipitation period characteristics of day, ten, month, season and the like. As shown in the following formula, the specific structure includes an input embedding layer, an adaptive periodic position coding module, a multi-layer encoder, a multi-layer decoder and an output layer connected in sequence. Figure 2

[0119] The traditional Transformer model encodes the input time step t by using the following fixed position coding formula:

[0120]

[0121] Wherein, PE (t,2i) is a position encoding vector, d is an encoding dimension, and i is a dimension index.

[0122] The adaptive periodic position coding mechanism proposed in the application introduces a trainable period adjustment parameter matrix P on this basis: P∈R d .

[0123] By defining the following encoding method:

[0124] ​

[0125] where, APPE (t,2i) is the position encoding vector, t represents the time step index, i.e., the position index, p i ∈R + is the position frequency adjustment parameter of the i-th dimension, which is learned and updated together with the rest of the weights during the backpropagation of the model; λ i represents the initial periodic scale, which can be a fixed constant or a preset variable (an initial value adjusted flexibly according to the task).

[0126] The trainable periodic adjustment parameter is used to dynamically map the time steps, so that the model can adaptively capture the multi-scale runoff and precipitation periodic characteristics of days, weeks, months, seasons, etc., thereby improving the perception and modeling ability of complex hydrological periodic laws.

[0127] The forward propagation process of the Transformer model with adaptive periodic position encoding is as follows:

[0128] The input layer embedding layer receives the input sequence, introduces the time feature, and embeds and maps the input sequence into a high-dimensional vector to obtain an input embedding vector, forming a complete time series representation. The adaptive periodic position encoding module learns the periodicity in the input sequence, dynamically adjusts the periodicity, replaces the fixed trigonometric function encoding, adds the position encoding result to the input embedding vector or takes the encoder input sequence, the multi-layer encoder extracts the time series dependency feature according to the encoder input sequence, and the multi-layer decoder recursively predicts the future runoff according to the encoder output and the historical prediction value. The output layer maps the decoder output to a runoff prediction value through linear transformation.

[0129] The method for training and testing the runoff prediction model using the fused multi-source satellite product precipitation data is as follows:

[0130] First, the KF-BMA fused satellite product precipitation data is used as the main driving factor, and the potential evapotranspiration in the preprocessed hydro-meteorological time series and the previous runoff in the runoff data are introduced. The fused satellite product precipitation data, potential evapotranspiration, and previous runoff are constructed into time series input samples in a time window sliding manner, and the later runoff is used as the supervision label to construct a labeled runoff prediction data set.

[0131] Further, the labeled runoff prediction data set is divided into a training set, a validation set, and a test set according to the ratio of 8:1:1.

[0132] Further, the training set is used as the input, and the runoff prediction value is calculated through the forward propagation process of the Transformer model with adaptive periodic position encoding. The mean square error is used as the loss function, and the model parameters are updated through backpropagation.

[0133] Further, after each round of training, the Transformer model with adaptive periodic position encoding is verified by using the validation set, the runoff prediction value is calculated through the forward propagation process of the Transformer model with adaptive periodic position encoding, and the mean square error is calculated as an evaluation index of the validation set.

[0134] Further, based on the evaluation index of the validation set, the learning rate is dynamically adjusted and the hyperparameter optimization adjustment based on the Newton-Raphson optimization algorithm (NRBO) is performed respectively until all training rounds are completed.

[0135] Wherein the dynamic adjustment of the learning rate adopts the ReduceLROnPlateau learning rate scheduler, the initial learning rate is set to 3x10 -4 , parameters, mode='max', factor=0.5, patience=5, threshold=1e-4.

[0136] The method of hyperparameter optimization adjustment based on the Newton-Raphson optimization algorithm (NRBO) is:

[0137] First, the number of encoder layers, the number of decoder layers, the number of attention heads, the model dimension, and the feedforward dimension are set as the hyperparameters to be optimized; a discrete value space is set to construct a 5-dimensional search space Ω;

[0138] Further, in the search space Ω, an initial solution set P0={x1,x2,...,x b} is generated, each x i represents a set of hyperparameter combinations, which is used as a candidate solution for hyperparameter optimization; the evaluation index of the validation set is used as the objective function, and in this embodiment, the minimum mean square error function f(x) is used as the objective;

[0139] Further, for the current candidate solution, the finite difference method is used to approximate the first-order and second-order partial derivatives of the objective function in its neighborhood, that is, the gradient and the Hessian matrix

[0140] Further, based on the standard Newton method update formula, the update direction is constructed, and the new candidate solution is calculated, and the core advantage of the Newton method is to combine the second-order information (Hessian), which can more efficiently approximate the optimal solution compared with the gradient descent using only the first-order information:

[0141]

[0142] Wherein, x new is the new candidate solution, x is the current solution, and α is the step size coefficient.

[0143] Further, since there are predefined upper and lower limit constraints on hyperparameters, such as the number of encoder layers cannot be negative, the number of attention heads must be a positive integer, etc. If the new candidate solution x new values beyond the predefined search space Ω, project the new candidate solution back into the value interval of the legal value;

[0144] Further, if the improvement of the objective function in the continuous several generations of optimization is less than the set threshold β, it is determined that the current search may fall into local optimum, a disturbance operator δ is introduced, and a random disturbance δx ~ U(-γ, γ) is added to the current solution x, U(-γ, γ) represents a uniform distribution, and γ is the disturbance amplitude, that is, the disturbance δx is randomly taken in the interval (-γ, γ) with equal probability, forcing the solution to jump out of the current region and enhancing the global search ability.

[0145] Further, until any of the following termination conditions is met, the algorithm stops, and the solution at this time is the optimal hyperparameter configuration after the current training round, which is used for the next round of model training:

[0146] The maximum number of iterations is reached;

[0147] The objective function is less than the preset accuracy requirement;

[0148] The improvement of the objective function in the continuous multiple generations is less than the threshold β, and there is still no effective improvement after introducing disturbance.

[0149] The Newton-Raphson optimization algorithm (NRBO) automatically realizes the exploration, performance evaluation and dynamic update of the combination of hyperparameters, greatly improving the modeling efficiency and prediction accuracy.

[0150] Further, after training is completed, the Nash efficiency coefficient (Nash-Sutcliffe Efficiency coefficient, NSE) is used to evaluate the performance of the runoff prediction model.

[0151] Wherein, the Nash efficiency coefficient NSE:

[0152]

[0153] Wherein, is the measured flow at a certain time step, and n is the total number of time steps; is the runoff prediction value at a certain time step; is the total average of the measured flow.

[0154] S5: After the multi-source satellite product precipitation data to be predicted is processed through steps S2-S3, the trained runoff prediction model is used to predict runoff.

[0155] The above merely provides the preferred embodiment of the present application, and is not used to limit the present application. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present application should be included in the protection scope of the present application.

Claims

1. A runoff prediction method based on multi-source satellite precipitation data fusion and deep learning optimization model, characterized in that, The method comprises the steps of: S1: collecting multi-source satellite product precipitation data and hydro-meteorological data in a study basin; S2: performing noise reduction processing on the multi-source satellite product precipitation data by using Kalman filtering; S3: fusing the multi-source satellite product precipitation data after noise reduction processing by using a Bayesian model averaging algorithm; S4: constructing a deep learning runoff prediction model with adaptive periodic position coding, taking runoff data in the hydro-meteorological data as supervision, training and testing the runoff prediction model by using the fused multi-source satellite product precipitation data, and performing hyperparameter optimization on the runoff prediction model in the training process by using a Newton-Raphson optimization algorithm; S5: obtaining multi-source satellite product precipitation data to be predicted, performing noise reduction processing on the multi-source satellite product precipitation data by using steps S2-S3, and performing runoff prediction on the trained runoff prediction model.

2. The runoff prediction method based on multi-source satellite precipitation data fusion and deep learning optimization model according to claim 1, characterized in that, The method for performing noise reduction processing on the multi-source satellite product precipitation data by using Kalman filtering comprises the following steps: S2.1: taking state estimation of real precipitation as a system state variable, and taking satellite product precipitation data as an observation quantity to construct a state space model including a state transition equation and an observation equation; S2.2: initializing state estimation of real precipitation, and error covariance of state estimation of real precipitation and observation quantity; S2.3: calculating prior state estimation and prior error covariance of real precipitation according to the state transition equation; S2.4: calculating a Kalman gain according to the prior error covariance; S2.5: performing state updating to obtain posterior state estimation of real precipitation according to the Kalman gain, the state transition equation and the observation equation; S2.6: updating the posterior error covariance according to the Kalman gain and the prior error covariance, and repeating S2.3-S2.5 until a change in the posterior error covariance is less than a preset value.

3. The runoff prediction method based on multi-source satellite precipitation data fusion and deep learning optimization model according to claim 2, characterized in that, The method for calculating the prior state estimation and the prior error covariance of real precipitation according to the state transition equation in step S2.3 comprises the following steps: P k|k-1 = AP k-1 A T + Q where A is the state transition matrix, is the posterior state estimate of the true precipitation amount of the previous cycle, is the prior state estimate of the current true precipitation amount, P k-1 is the posterior error covariance of the previous cycle, k|k-1 is the current prior error covariance, Q is the process noise covariance matrix; The method for calculating the Kalman gain in step S2.4 comprises the following steps: Among them, K k Let H be the Kalman gain, H be the observation matrix, and R be the observation noise covariance. The method for obtaining the posterior state estimation of real precipitation in step S2.5 comprises the following steps: wherein, z is the current observation; k is the current observation; The method for updating the posterior error covariance in step S2.6 comprises the following steps: P k = (I - K k H)P k|k-1 where I is the identity matrix, P k is the current posterior error covariance.

4. The runoff prediction method based on multi-source satellite precipitation data fusion and deep learning optimization model according to claim 3, characterized in that, The implementation method of step S3 comprises the following steps: S3.1: taking real precipitation as a benchmark, and calculating error distribution characteristics of each set of satellite product precipitation data after noise reduction processing; S3.2: calculating a prior probability of each set of satellite product precipitation data according to the error distribution characteristics; S3.3: calculating a likelihood probability of real precipitation with respect to each set of satellite product precipitation data according to a probability density function of a Gaussian distribution; S3.4: calculating a posterior probability of each set of satellite product precipitation data according to the prior probability of each set of satellite product precipitation data and the likelihood probability of real precipitation with respect to each set of satellite product precipitation data; S3.5: performing weighted fusion on each set of satellite product precipitation data by taking the posterior probability of each set of satellite product precipitation data as a dynamic weight, and obtaining fused satellite product precipitation data.

5. The runoff prediction method based on multi-source satellite precipitation data fusion and deep learning optimization model according to claim 4, characterized in that, The calculation method of the error distribution characteristics is: calculating the absolute error ε of each group of satellite product precipitation data S i with the true precipitation G i , and calculating the error standard deviation σ of each group of satellite product precipitation data i as the error distribution characteristics; and using the reciprocal of the error standard deviation σ i to combine the prior probability of each group of satellite product precipitation data calculated in step S3.2 of the normalization calculation: Wherein, m is the number of sets of satellite product precipitation data, and j represents a set number index.

6. The runoff prediction method based on multi-source satellite precipitation data fusion and deep learning optimization model according to claim 5, characterized in that, The method for calculating the posterior probability of each set of satellite product precipitation data in step S3.4 comprises the following steps: Wherein, P(S) i |G) represents the posterior probability of precipitation data for each set of satellite products, P(G|S) i The probability of the actual precipitation is given by the precipitation data for each set of satellite products. The implementation method of step S3.5 comprises the following steps: where S fused is the fused satellite product precipitation data.

7. The method of claim 1 to 6, wherein the method is characterized in that, The deep learning runoff prediction model with adaptive periodic position encoding of step S4 introduces an adaptive periodic position encoding module after the input embedding layer of the Transformer model: the time steps are dynamically periodized mapped by using a trainable period adjustment parameter to adaptively capture the daily, ten-day, monthly, and seasonal multi-scale runoff precipitation period characteristics.

8. The runoff prediction method based on multi-source satellite precipitation data fusion and deep learning optimization model according to claim 7, characterized in that, The method for dynamically periodizing mapping the time steps in the adaptive periodic position encoding module by using a trainable period adjustment parameter is: where APPE (t,2i) is the position encoding vector, t denotes the time step index, p i ∈ R + is the i-th dimensional position frequency adjustment parameter, which is used for learning update during model backpropagation; λ i denotes the initial periodic scale.

9. The runoff prediction method based on multi-source satellite precipitation data fusion and deep learning optimization model according to any one of claims 4 to 6, characterized in that, The method for training and testing the convection prediction model using the fused multi-source satellite product precipitation data is: S4.1, the fused satellite product precipitation data, potential evapotranspiration in the hydro-meteorological time series, and previous runoff are constructed into time series input samples in a time window sliding manner, and the later runoff is used as a supervised label to construct a labeled runoff prediction data set, and the data set is divided into a training set, a validation set, and a test set; S4.2, using the training set as input, the runoff prediction value is calculated through the forward propagation process of the Transformer model with adaptive periodic position encoding, the mean square error is used as the loss function, and the model parameters are updated through back propagation; S4.3, after each training round, the Transformer model with adaptive periodic position encoding is verified using the validation set, the runoff prediction value is calculated through the forward propagation process of the Transformer model with adaptive periodic position encoding, the evaluation index of the validation set is calculated according to the runoff prediction value, and the learning rate is dynamically adjusted and the hyperparameter optimization adjustment based on the Newton-Raphson optimization algorithm is performed based on the evaluation index of the validation set, until all training rounds are completed; S4.3, after training is completed, the Transformer model with adaptive periodic position encoding is tested using the test set, and the Nash efficiency coefficient is used to evaluate the performance of the runoff prediction model.

10. The runoff prediction method based on multi-source satellite precipitation data fusion and deep learning optimization model according to claim 9, characterized in that, The method for hyperparameter optimization adjustment based on the Newton-Raphson optimization algorithm is: (1) taking multiple hyperparameters in the model as optimization variables to construct a multi-dimensional search space Ω; (2) generating an initial solution set in the multi-dimensional search space Ω, and taking the evaluation index of the validation set as the objective function; (3) For the current candidate solution, the gradient of the objective function, ∇f(x), and the Hessian matrix, ∇ 2 f(x); (4) based on the standard Newton method update formula, an update direction is constructed to calculate a new candidate solution; (5) if the value of the new candidate solution exceeds the predefined search space Ω, the new candidate solution is projected back into the value interval of the standard Newton method; (6) if the improvement of the objective function is less than the set threshold in continuous several generations of optimization, a perturbation operator is introduced to add random perturbation to the current solution to force the solution to jump out of the current region; (7) until the termination condition is met, the algorithm stops.

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