Hydrological forecasting method based on physical process and interpretable deep learning dual drive

Abstract

The invention discloses a hydrological forecasting method based on a physical process and interpretable deep learning dual drive, relates to the technical field of hydrological forecasting, and is used for solving the problems that a process-driven model is difficult to summarize a dynamic hydrological process completely and a data-driven model ignores the physical process. By fusing a traditional hydrological model and interpretable deep learning, the advantages of the traditional hydrological model and the interpretable deep learning are fully utilized, so that the precision and the efficiency of real-time hydrological forecasting are remarkably improved. Parameters of the hybrid model are optimized by adopting a head specific improved aurora optimization algorithm, prediction precision can be improved, reliability and stability of the model are ensured, consumption of computing resources is reduced, the deep learning model is explained by adopting a Shapley additive explanation method, the interpretability of the model is further enhanced, and the prediction accuracy is improved. And the user can clearly know the influence of the input variable on the prediction result. The characteristic provides important support for practical application of the model, especially in the field of hydrological forecasting requiring transparency decision.

Description

Technical Field

[0001] The present invention relates to the technical field of hydrological forecasting, and more specifically, to a hydrological forecasting method based on dual drive of physical process and interpretable deep learning. Background Art

[0002] Hydrological forecasting is an extremely important non-engineering measure that plays a key role in basin water resources management and flood disaster mitigation. The accuracy and efficiency of hydrological forecasting are crucial to fields such as flood warning, flood risk analysis, and reservoir operation. However, due to the complexity of hydrological processes and the limitations of human cognition, hydrological forecasting itself contains various uncertainties, such as data observations, model structures, and model parameters. These uncertainties lead to deviations in forecast results and pose new challenges to the theories and methods of hydrological forecasting. Therefore, comprehensive analysis of uncertainty information and migration and transformation principles is of far-reaching significance for improving existing forecasting models.

[0003] Hydrological forecasting techniques are mainly divided into process-driven models and data-driven models. Process-driven models often face challenges in generalizing the complex nonlinear relationships between environmental variables and runoff. This limitation stems from the incomplete understanding and representation of dynamic hydrological processes, which introduces errors and uncertainties into flow prediction. On the other hand, the heavy reliance of data-driven models often leads to the neglect of the basic physical mechanisms that govern hydrological processes. Therefore, developing a hybrid model that combines process-driven models with data-driven models is a promising and resource-saving strategy.

[0004] In recent years, deep learning, as a specialized subset of machine learning, has gained widespread attention in hydrological research. Compared with traditional machine learning techniques, deep neural networks are distinguished by their complex architecture and larger number of neurons. However, interpretability remains an obvious limitation of deep learning, and the internal mechanisms of the model are usually difficult to directly elucidate during the forecasting process. This opacity leads to insufficient credibility of the forecast results, which limits the practical application of such models, especially in the field of real-time, hourly hydrological forecasting. In addition, deep learning models still have a clear trade-off between model accuracy and interpretability. Therefore, how to optimize the unique advantages of process-driven models and data-driven models when building hybrid models, quantitatively evaluate the uncertainty of model outputs, and confirm the credibility of these hybrid models needs to be comprehensively addressed within a unified theoretical framework.

[0005] In view of the above problems, the present invention proposes a solution. Summary of the invention

[0006] In order to overcome the above-mentioned defects of the prior art, an embodiment of the present invention provides a hydrological forecasting method based on dual drive of physical process and interpretable deep learning to solve the problems raised in the above-mentioned background technology.

[0007] To achieve the above object, the present invention provides the following technical solutions: The hydrological forecasting method based on physical processes and interpretable deep learning dual drive includes the following steps: Based on the physical model, a basin hydrological model is constructed, basin characteristics are analyzed and an appropriate rainfall-runoff model is selected. The model parameters are calibrated and verified through the head-specific improved Aurora optimization algorithm to generate initial forecast results. A deep learning model was constructed, with the forecast residuals of the basin hydrological model as the training target, and the hyperparameters of the deep learning model were tuned through the head-specific improved Aurora optimization algorithm; Based on the initial forecast results of the basin hydrological model and the measured data, a multi-dimensional multi-step forecast residual matrix and a multi-dimensional multi-step hydrological element matrix are constructed. The matrix represents the difference between the actual physical process and the simulated physical process of the basin. The forecast residuals predicted by the deep learning post-processing model are synchronously corrected with the original forecast results of the basin hydrological model for multiple forecast periods to generate a dual-drive correction model; Generate real-time hydrological forecast results through the dual-drive correction model, and obtain multi-step correction forecast results in different forecast periods; Based on the corrected forecast results, the Shapley additive interpretation method is used to perform importance analysis on the input variables of the deep learning post-processing model, quantify the contribution of each input variable to the correction results, and optimize the design and correction mechanism of the model input variables.

[0008] In a preferred embodiment, the construction of the multi-dimensional multi-step prediction residual matrix includes: The forecast values ​​are separated from the result set of the basin hydrological model, and the time series correlation of the forecast differences is analyzed in combination with the measured values; Based on the time series lag factor and the forecast period setting, a multi-dimensional multi-step forecast residual matrix is ​​generated: ; In the formula, It represents the forecast residual value at time t with a forecast period of m and a forward lag period of s. express time to time t and time t to The measured value at time, express time to time t and time t to The forecast value at time.

[0009] In a preferred embodiment, the initial forecast results of the basin hydrological model are subjected to multi-forecast period synchronous correction, specifically including: Runoff forecast results of the dual-drive correction model at time t and within the forecast period m The expression is as follows:

[0010] In the formula, is the forecast residual at time t + m obtained by the deep learning post-processing model, is the forecast flow at time t + m obtained by the rainfall-runoff model, and They represent the calculation process of the deep learning post-processing model and the rainfall-runoff model respectively. is the forecast difference of rainfall-runoff model at time t, The hydrological elements required for the rainfall-runoff model calculation at time t + m, is the initial calculation condition of the rainfall-runoff model at time t + m.

[0011] In a preferred embodiment, the construction of the physical model comprises the following steps: The soil layer was divided into three layers and evapotranspiration was calculated separately; Calculate runoff based on rainfall runoff conditions and divide runoff into surface runoff, subsoil runoff and underground runoff; The Muskingum method is used to calculate runoff and generate hourly flow forecast results for the basin.

[0012] In a preferred embodiment, the construction of the multi-dimensional and multi-step hydrological element matrix includes: Select key hydrological elements of the watershed, including rainfall, rainfall runoff, soil moisture, and evapotranspiration; Based on the time series mutual correlation and hysteresis characteristics, a multi-dimensional and multi-step hydrological element matrix is ​​generated, and the matrix is ​​expressed as: ; In the formula, It represents the hydrological element matrix value with a forecast period of m at time t and a front lag period of s2. express time to time t and time t to The value of the hydrological element at the time.

[0013] In a preferred embodiment, the specific steps of optimizing the model parameters using the head-specific improved Aurora optimization algorithm include: An initial population is generated based on a chaos mapping method, wherein the chaos mapping parameters are determined by analyzing the variation characteristics of the model parameters; In the process of population individual renewal, the rotational motion, auroral elliptical trail and particle collision mechanism are introduced to optimize the objective function; Continue to iterate and update the population position until the objective function reaches the optimal value or the maximum number of iterations is reached.

[0014] In a preferred embodiment, the uncertainty of the dual-drive correction model is quantified using Bayesian inference and Markov Monte Carlo algorithm (MCMC), specifically including: The output results of the dual-drive correction model are transformed into a normal distribution and an initial prior distribution is generated; Combined with observed data, the posterior distribution is iteratively updated based on the Bayesian inference method to quantify the uncertainty of the model prediction results; The probability forecast interval for each moment is generated through posterior distribution sampling analysis.

[0015] In a preferred embodiment, the deep learning post-processing model is analyzed for interpretability by Shapley's additive interpretation method, comprising the following steps: The Shapley values ​​of the forecast residual matrix and the hydrological element matrix for the model output are calculated based on the Shapley additive interpretation method; Quantify the contribution of each input variable to the model output; Combined with the flow generation mechanism and error sources of the basin hydrological model, the impact of input variables on the overall prediction results of the dual-drive model is explained.

[0016] In a preferred embodiment, the dual-driven fusion mechanism of the deep learning post-processing model and the watershed hydrological model is applicable to different types of watershed hydrological models, including but not limited to the Xinanjiang model, the SCS-CN model and the TOPMODEL model.

[0017] The technical effects and advantages of the hydrological forecasting method based on physical process and interpretable deep learning dual drive of the present invention are as follows: The present invention combines traditional hydrological models with interpretable deep learning, making full use of the advantages of both, thereby significantly improving the accuracy and efficiency of real-time hydrological forecasting. The use of the head-specific improved Aurora optimization algorithm to optimize the parameters of the hybrid model can not only improve the prediction accuracy, ensure the reliability and stability of the model, but also reduce the consumption of computing resources.

[0018] The present invention further enhances the interpretability of the model by using the Shapley additive interpretation method to interpret the deep learning model, allowing users to clearly understand the impact of input variables on the prediction results. This feature provides important support for the practical application of the model, especially in the field of hydrological forecasting where decision transparency is required.

[0019] The present invention feeds back the predicted forecast residuals to the original forecast results to obtain the corrected forecast results, and conducts comprehensive evaluation and comparison through the established evaluation index system, thereby ensuring the accuracy and practicality of the forecast results. BRIEF DESCRIPTION OF THE DRAWINGS

[0020] Figure 1 This is a dual-drive hydrological forecasting flow chart of the present invention; Figure 2 It is a schematic diagram of the head-specific improved Aurora optimization algorithm flow of the present invention; Figure 3 The figure is a schematic diagram of the calculation flow of the Markov Monte Carlo algorithm based on the non-reentry sampler of the present invention. DETAILED DESCRIPTION

[0021] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0022] The present invention combines traditional hydrological models with emerging interpretable deep learning, giving full play to the advantages of both, and using the insights of interpretable deep learning to improve the accuracy and efficiency of real-time hydrological forecasts. The present invention calibrates the parameters of the Xinanjiang model through a head-specific improved Aurora optimization algorithm, outputs the original forecast results and forecast residuals; then, the hyperparameters of the deep learning model are optimized using the head-specific improved Aurora optimization algorithm to predict the forecast residuals, and the Shapley additive interpretation method is used to interpret the deep learning model. Finally, the predicted forecast residuals are fed back to the original forecast results to obtain the corrected forecast results, and the Bayesian inference method is used to obtain the forecast interval. The accuracy and practicality of the forecast results are ensured through comprehensive evaluation and comparison through the established evaluation index system.

[0023] Embodiment, the present invention provides a hydrological forecasting method based on physical process and interpretable deep learning dual drive, such as Figure 1 As shown in the figure, taking the Chitan Reservoir Basin as a research case, the following steps are included: S1: Systematically collect hydrological data of the target basin, perform data cleaning and preprocessing operations on the data set, obtain the hourly flood data set of the target basin, and divide the data set into three sections: training set, validation set and test set; S2: According to the characteristics of the watershed, a qualified rainfall-runoff model is constructed, including a lumped rainfall-runoff model, a distributed rainfall-runoff model and a semi-distributed rainfall-runoff model. Based on S1, the Aurora optimization algorithm with head-specific improvements is used, and the model parameter group range constraint conditions are used as the search space. The initial population is generated by initializing the objective function with head-specific improvements. The objective function is used to describe the optimization goal of the hydrological forecasting system, and the constraint conditions are used to describe the constraints of the physical watershed on the rainfall-runoff model. The individuals in the population are used to describe the different parameter expressions of the rainfall-runoff model on the physical watershed. The parameters of the constructed rainfall-runoff model are finely calibrated and strictly verified. The runoff forecast results of each model run are recorded in detail, and the runoff forecast results of the rainfall-runoff model on the test set are obtained based on the calibrated parameters. S3: Separate the forecast values ​​from the result set, analyze the temporal autocorrelation of the forecast differences, and construct a multidimensional multi-step forecast residual matrix based on the measured values ​​and the physical process model. The matrix represents the difference between the actual hydrological process and the simulated hydrological process, including the difference in different step lengths, the difference in different residual variables, and the difference in time sequence. Analyze the average temporal cross-correlation of each hydrological element, and reorganize the S1 data set into a multidimensional multi-step hydrological element matrix based on the node with the largest average cross-correlation. The matrix represents the actual physical process of the basin and is normalized separately from the forecast residual matrix. S4: Input the hydrological element matrix and the forecast residual matrix into the deep learning prediction model and deep learning post-processing model respectively, and use the Aurora optimization algorithm with specific head improvements to carefully optimize and strictly verify the hyperparameters of the models. The individuals in the former population are used to describe the nonlinear expression of the prediction model for the basin elements, and the individuals in the latter population are used to describe the nonlinear expression of the post-processing model for the forecast differences. Record the runoff forecast results and residual forecast results of each model run in detail, and obtain the prediction results of the two types of deep learning models on the test set based on the optimized hyperparameters. S5: The deep learning post-processing model trained by S4 and the rainfall-runoff model calibrated by S2 are integrated to obtain a dual-driven correction model, that is, the deep learning post-processing model is driven by the rainfall-runoff model, and the model is responded to by feedback. The deep learning post-processing model is used to predict the forecast residuals in different forecast periods, and the original forecast results of the rainfall-runoff model are respectively screened to match the forecast residuals in different forecast periods. Then, for each forecast period, the forecast residuals and the original forecast results are simultaneously integrated in the form of feedback to obtain the runoff forecast results of the dual-driven correction model in different forecast periods. S6: Based on the deterministic forecast, the output result matrix is ​​split into single-dimensional arrays according to the forecast period, and the normal distribution transformation that conforms to the hydrological data is performed respectively to obtain the parameters from the artificially assumed initial prior distribution. Initial values ​​are obtained, and then a probabilistic forecast model is further established to quantify the forecast uncertainty of the rainfall-runoff model and the dual-drive correction model in S5; the Bayesian inference method is iteratively applied in multiple single-dimensional arrays, and the posterior probability distribution sampling analysis of normal distributions with different parameters is performed in combination with the Markov Monte Carlo algorithm based on the non-reentrant sampler; a large number of sampling results are averaged to obtain the parameters of each normal distribution , and then take the deterministic forecast as the mean to construct the probability forecast distribution at each moment; according to the specific needs of hydrological forecast applications, calculate and determine the forecast interval at each moment at a specified confidence level to provide more comprehensive and reliable forecast information; S7: In view of the complexity and black box nature of the internal operating mechanism of deep learning, a detailed interpretability analysis is conducted on the deep learning post-processing model in the dual-drive correction model. The constructed forecast residual matrix is ​​re-input into the deep learning post-processing model, and the Shapley values ​​of the input variables at each moment in different forecast periods are recorded. In combination with the runoff generation mechanism and possible error sources of the rainfall-runoff model, the influence of the errors generated by the rainfall-runoff model at different moments on the overall prediction of the dual-drive correction model is explained, and the actual runoff generation process of the rainfall-runoff model under the calibrated parameters is further understood, thereby improving the transparency and credibility of the model. S8: An index system consisting of 7 quantitative evaluation indicators is used to evaluate the deterministic forecast results and the probabilistic forecast results respectively; from multiple dimensions such as forecast interval bandwidth, forecast interval coverage, probabilistic forecast comprehensive score, probabilistic forecast reliability, forecast accuracy and forecast error, a comprehensive comparative analysis and evaluation is conducted on the proposed dual-driven hydrological forecasting method to improve the comprehensiveness and reliability of the forecast results.

[0024] Furthermore, the specific steps of step S1 are: S11: Based on the actual geographical distribution, operation time and control area of ​​the hydrological stations in the target basin, systematically collect hydrological station data with the longest possible time series, the most uniform spatial distribution or representativeness; standardize and time-periodize the collected hydrological data according to hydrological specifications to obtain hourly hydrological data sets that meet the standards; S12: Based on the drainage characteristics of surface runoff, subsurface flow and underground runoff and the relationship between hydrological data, the hydrological data set is smoothly segmented according to the conditions of flood rise and fall to obtain hourly flood data sets; S13: Considering the requirements of hydrological forecasting for hydrological data, the secondary flood data set is divided into a training set (rate set), a validation set, and a test set in a ratio of 7:2:2. In the case study, the data of the first 14 floods in the Chitan Reservoir Basin are used as the training set, the data of the middle 4 floods are used as the validation set 1, and the data of the last 4 floods are used as the test set.

[0025] Furthermore, the specific steps of step S2 are: S21: Analyze the characteristics of watershed runoff, select and construct a rainfall-runoff model that meets the hydrological conditions of the watershed: the lumped rainfall-runoff model does not consider the spatial heterogeneity of hydrological elements, the distributed rainfall-runoff model fully considers the spatial heterogeneity of hydrological elements, and the semi-distributed rainfall-runoff model is between the two. In the case study, the Chitan Reservoir Basin belongs to a humid and semi-humid area. According to hydrological conditions such as annual precipitation, the Xin'anjiang model is suitable for the rainfall-runoff model; S22: Using the model parameter group range constraint as the search space, the initial population is generated by initializing the objective function with a head-specific improvement, where the objective function is used to describe the optimization goal of the hydrological forecasting system, the constraint is used to describe the constraints of the physical basin on the rainfall-runoff model, and the individuals in the population are used to describe the different parameter expressions of the rainfall-runoff model on the physical basin; S23: Specifically, the objective function takes minimizing the hydrological forecast error as the optimization goal, and the constraint conditions are composed of the basin underlying surface conditions, basin runoff conditions, and basin confluence conditions. For N floods, the calculation expression of the objective function is as follows:

[0026] In the formula, t0 is the initial time series of hydrological data, T is the total time series length of hydrological data, is the measured value of the nth flood at time series t, is the forecast value of the rainfall-runoff model at the nth flood and time series t. For the multidimensional parameter group, is the upper limit of the model parameter group, is the lower limit of the model parameter group, and the constraint conditions are expressed as follows:

[0027] In the case study, the range of values ​​of the rainfall-runoff model parameter group is shown in Table 1: Table 1 Range of parameters for rainfall-runoff model

[0028] Different from random generation, the population is initialized through head-specific improvements to make individuals more consistent with the nature of hydrological data. The calculation expression is as follows:

[0029] Where D is the number of multidimensional parameter groups, is a chaotic mapping parameter ranging from 0 to 1. By analyzing the relationship between model parameters, the parameter variation coefficient can be determined as the chaotic mapping parameter. In the case study, the Logistic method is used to determine the chaotic mapping parameter, and the formula is: , r is 0.8, initial Use random numbers.

[0030] S24: Based on the individual fitness value in the initial population, i.e., the objective function value, the position of the individuals in the population is continuously iterated and updated through the head-specific improved Aurora optimization algorithm (the head-specific improvement is reflected in S23). The calculation process is as follows: Figure 2 As shown in the figure, the rainfall-runoff model is updated to express different parameters of the physical basin, and the population after updating the individual position is obtained until the forecast requirement is met or the maximum number of iterations is reached; specifically, the individual position is updated through rotation, auroral ellipse trail and particle collision, and the individual position after each update is and The calculation expression is as follows:

[0031]

[0032] In the formula, are four independent random numbers between 0 and 1, and It is a constant that controls the degree of individual position update, which is determined by the number of iterations and the fitness value. Is the impact The coefficient of Is the impact The coefficient of is any individual in the population. In the study case, the population size of the head-specific improved Aurora optimization algorithm is 50, and the maximum number of iterations is 10.

[0033] S25: Take the best parameter combination for the objective function in the iterative process, that is, let the rainfall-runoff model best describe the physical basin, and conduct hydrological forecast experiments in the validation set based on the physical phenomena that actually occur in the basin; record the runoff forecast results of each model run in detail, and further obtain the runoff forecast results of the model on the test set after the experiment.

[0034] Furthermore, the specific steps of step S3 are: S31: The result set of the rainfall-runoff model contains forecast values, measured values, and model details. The forecast values ​​are separated from the result set, and the time series correlation of the forecast differences is analyzed. The time lag of the forecast differences is determined by combining the measured values ​​and the physical process model, and the forecast period is set according to the requirements of the hydrological forecast. In this way, a multi-dimensional and multi-step forecast residual matrix is ​​constructed. The calculation expression is as follows:

[0035] In the formula, It represents the forecast residual value at time t with a forecast period of m and a forward lag period of s. express time to time t and time t to The measured value at time, express time to time t and time t to The multi-dimensional and multi-step forecast residual matrix represents the difference between the actual hydrological process and the simulated hydrological process, including the difference of different step lengths, the difference of different residual variables and the difference of time sequence; in the case study, the lag term of the forecast difference determined by the autocorrelation coefficient is s = 15, and the forecast period is m = 4.

[0036] S32: Before deep learning prediction, it is necessary to calculate the correlation between the multidimensional hydrological element independent variables and the single-dimensional or multidimensional dependent variables, analyze the average time series correlation, and then determine the time lag of the hydrological element based on the node with the largest average correlation. The forecast period is set the same as S31, so as to reorganize the S1 data set into a multidimensional and multi-step hydrological element matrix. The calculation expression is as follows:

[0037] In the formula, It represents the hydrological element matrix value with a forecast period of m at time t and a front lag period of s2. express time to time t and time t to The hydrological element value at the moment. The multi-dimensional and multi-step hydrological element matrix represents the actual physical process of the basin; in the case study, the mutual correlation coefficient is used to determine the lag term of the hydrological element s2 = 10, and the forecast period m = 4.

[0038] S33: Normalize the forecast residual matrix S31 and the hydrological element matrix S32 according to the following expression to avoid the influence of magnitude:

[0039] In the formula, x t is the matrix data at time t, min(·) and max(·) represent the minimum and maximum functions respectively, and x represents the entire matrix data.

[0040] Furthermore, the specific steps of step S4 are: S41: A deep learning prediction model and a deep learning post-processing model were constructed respectively, and the range constraints of the two model hyperparameter groups were used as the search space. The initial population was generated by initializing the objective function with a head-specific improvement. The individuals in the former population were used to describe the nonlinear expression of the prediction model on the watershed elements, and the individuals in the latter population were used to describe the nonlinear expression of the post-processing model on the forecast differences. In the research case, the long short-term memory network was selected as the deep learning model, and the range of the deep learning model hyperparameter group is shown in Table 2.

[0041] Table 2. Hyperparameter search space of deep learning models

[0042] S42: Specifically, the objective function of the deep learning prediction model is to optimize the actual runoff of the basin, and the objective function of the deep learning post-processing model is to optimize the change law of the forecast difference of the physical process model. The calculation formulas of the two objective functions can be expressed as follows:

[0043] In the formula, It is expressed as the forecast residual or the true value of the hydrological element at time t. It is expressed as the forecast residual or the predicted value of the hydrological element at time t; S43: Input the hydrological element matrix and the forecast residual matrix into the constructed deep learning prediction model and deep learning post-processing model respectively, and continuously iterate and update the positions of individuals in the population through the head-specific improved Aurora optimization algorithm (the detailed steps are the same as S2), that is, update the different parameter expressions of the deep learning model for the basin runoff process or the law of change of model prediction differences, and obtain the population after updating the individual positions until the forecast requirements are met or the maximum number of iterations is reached; in the research case, the population size of the head-specific improved Aurora optimization algorithm is 50, and the maximum number of iterations is 10.

[0044] S44: Take the best parameter combination for the objective function in the iteration process of each of the two models, that is, let the model best describe the basin elements or forecast differences, and conduct prediction tests in the validation set under the condition of being close to the changing rules of basin elements or forecast differences; record the runoff forecast results and residual prediction results of each operation of the two models in detail, and further obtain the prediction results of the two models on the test set after the experiment.

[0045] Furthermore, the specific steps of step S5 are: S51: The rainfall-runoff model determined by S2 drives the deep learning post-processing model trained by S4, and responds to the rainfall-runoff model in the form of feedback to form a hydrological forecasting model based on physical process and deep learning dual drive; S52: Specifically, the deep learning post-processing model is used to predict the length of time periods in different forecast periods. According to the specific time of the forecast residual in each forecast period, the original forecast results of the rainfall runoff model are screened to match the time of the forecast residual in different forecast periods. Then, for each forecast period, the forecast residual and the original forecast result are fused at the same time in the form of feedback to obtain the runoff forecast results of the dual-drive correction model in different forecast periods. The runoff forecast results of the dual-drive correction model at time t and forecast period m are The expression is as follows:

[0046] In the formula, is the forecast residual at time t + m obtained by the deep learning post-processing model, is the forecast flow at time t + m obtained by the rainfall-runoff model, and They represent the calculation process of the deep learning post-processing model and the rainfall-runoff model respectively. is the forecast difference of rainfall-runoff model at time t, The hydrological elements required for the rainfall-runoff model calculation at time t + m, is the initial calculation condition of the rainfall-runoff model at time t + m.

[0047] Furthermore, the specific steps of step S6 are: S61: Split the runoff forecast result matrix output by the rainfall-runoff model and the dual-drive correction model according to the forecast period to obtain multiple single-dimensional arrays, each array representing a forecast period; select a suitable normal distribution according to the characteristics of the hydrological data, perform normal distribution transformation on the multiple single-dimensional arrays respectively, and obtain the parameters from the artificially assumed initial prior distribution The initial value of is used to further establish the probability forecast model; in the research case, it is assumed that the initial prior distribution is a semi-Cauchy distribution.

[0048] S62: Specifically, the Bayesian inference method is iteratively applied to multiple single-dimensional arrays, that is, the expression is , where After the hydrological element sample information DS is given, the parameter The posterior probability density of For a given parameter The likelihood function of the hydrological element sample information DS is as follows: For parameters The prior probability distribution of ; S63: Based on S62, combined with the Markov Monte Carlo algorithm based on the non-reentry sampler, the algorithm calculation process is as follows Figure 3 As shown, the posterior probability distribution sampling analysis is performed on the normal distribution with different parameters, and the calculation expression is as follows:

[0049] In the formula, It is a logical function that determines the truth or falsehood of an expression and assigns a value. When it is True, it is assigned a value of 1, and when it is False, it is assigned a value of 0. and are the direction vectors of left and right parameter sampling, respectively. and They are the left and right candidate parameters generated according to the current state. , It is the algorithm identifier before the update, which is used to determine whether the current sampling is finished; S64: Repeat S63 and take the average of a large number of sampling results as a reasonable parameter for each normal distribution , and then use the deterministic forecast as the mean , construct the probability forecast normal distribution at each time t, and each forecast period has a unique normal distribution; according to the specific needs of hydrological forecast applications, calculate and determine the forecast interval at each time t at a specified confidence level, and obtain the probability forecast results of the rainfall runoff model and the dual-drive correction model in different forecast periods. In the study case, the maximum number of samplings is set to 5000 times, the number of samplings used to adjust the benchmark is set to 2500 times, and 4 are run in parallel.

[0050] Furthermore, the specific steps of step S7 are: S71: Reorganize the measured data into a multi-dimensional multi-step measured matrix with a forecast period of m and a front lag period of s (consistent with step S32), and input it into the deep learning post-processing model together with the forecast residual matrix of S31, and record the Shapley value of the input variable at each moment in different forecast periods. The calculation expression of the Shapley value is as follows:

[0051] In the formula, is the contribution of the i-th dimension prediction residual matrix to the output of the dual-drive correction model; k is the dimension of the prediction residual matrix; K is the prediction residual matrix; S is the prediction residual matrix before the i-th dimension in the sequence, which is a subset of K; is the value generated collaboratively by the prediction residual matrices included in the subset S; S72: Considering the different hydrological forecast periods, and combining the runoff generation mechanism and possible error sources of the rainfall-runoff model (including model parameter errors, model structure errors, measurement data errors, etc.), explain the impact of the errors generated by the rainfall-runoff model at different times on the overall prediction of the dual-drive correction model, and further understand the actual runoff generation process of the rainfall-runoff model under the calibration parameters. In the case study, special attention should be paid to the forecast errors of the rainfall-runoff model at the current moment and the last three moments. The forecast errors of the constructed rainfall-runoff model are highly transferable in a short time.

[0052] Furthermore, the specific steps of step S8 are: S81: Construct an index system consisting of 7 quantitative evaluation indicators. The 3 deterministic evaluation indicators include Nash coefficient (NSE), root mean square error (RMSE), and mean absolute percentage error (MAPE). The expressions are as follows:

[0053]

[0054]

[0055] In the formula, is the measured value of the hydrological element, is the predicted value of the hydrological model; The four probability evaluation indicators include interval coverage (CR), interval average bandwidth (B), continuous graded probability score (CRPS), and probability integral transform (PIT), and the expressions are as follows:

[0056]

[0057]

[0058]

[0059] In the formula, is a conditional function. It takes 1 when the formula in the brackets is true, otherwise it takes 0. and are the lower and upper bounds of the forecast interval at time t, and The predicted values The probability density function and cumulative distribution function of ; The closer the NSE value is to 1, the higher the prediction accuracy of the model. The smaller the RMSE and MAPE values ​​are, the smaller the prediction error of the model is. CR and B are used to evaluate the prediction interval of the probability forecast. The larger the CR value is, the more real information the forecast result contains. The larger the B value is, the larger the bandwidth of the interval is, that is, the greater the uncertainty of the forecast. The confidence level of the interval forecast is 95%. CRPS is used to evaluate the overall performance of the probabilistic hydrological forecast. The smaller the CRPS value is, the better the comprehensive performance of the probabilistic forecast is. PIT is used to evaluate the reliability of the probabilistic forecast and to test whether the normal distribution assumption of the model is reasonable. If the PIT value obeys U (0, 1), it means that the probabilistic forecast result is reliable.

[0060] S82: Based on the forecast values ​​and measured values ​​of the dual-driven correction model, the proposed dual-driven hydrological forecast method is comprehensively compared, analyzed and evaluated from multiple dimensions, including forecast interval bandwidth, forecast interval coverage, probability forecast comprehensive score, probability forecast reliability, forecast accuracy and forecast error. In the case study, the evaluation results are shown in Table 3. The forecast effect of the dual-driven correction model is better than that of the single rainfall-runoff model at different forecast periods, and the uncertainty it brings is much smaller than that of the rainfall-runoff model, and the forecast results are more reliable.

[0061] Table 3 Evaluation index results of the dual-drive correction model and rainfall-runoff model in the test set flood

[0062] According to the above examples, in view of the complexity and uncertainty of hydrological processes in traditional hydrological forecasting methods, and the neglect of physical mechanisms by data-driven models, the present invention proposes a hydrological forecasting method based on physical processes and interpretable deep learning dual drive. The present invention uses the head-specific optimized aurora optimization algorithm to optimize the parameters of the dual-driven correction model, which can not only improve the prediction accuracy, ensure the reliability and stability of the model, but also reduce the consumption of computing resources. The present invention uses the deterministic forecast as the mean to construct the probability forecast interval at each moment, supplement the uncertainty information of the model forecast, and increase the reliability of the dual-driven correction model. The present invention combines the Shapley value and hydrological forecast knowledge to perform an interpretable analysis of the deep learning model, so that the importance of the input variables to the prediction results can be clearly presented. This feature provides users with better decision support, especially in the field of hydrological forecasting that requires transparency. The present invention combines the established evaluation index system for comprehensive evaluation and comparison, ensuring the accuracy and practicality of the forecast results, thereby providing effective technical support for flood forecasting and flood risk analysis.

[0063] The above formulas are all dimensionless and numerical calculations. The formula is a formula for the most recent real situation obtained by collecting a large amount of data and performing software simulation. The preset parameters in the formula are set by technicians in this field according to actual conditions.

[0064] The above embodiments may be implemented in whole or in part by software, hardware, firmware or any other combination. When implemented by software, the above embodiments may be implemented in whole or in part in the form of a computer program product.

[0065] Those of ordinary skill in the art will appreciate that the modules and algorithm steps of each example described in conjunction with the embodiments disclosed herein can be implemented in electronic hardware, or a combination of computer software and electronic hardware. Whether these functions are performed in hardware or software depends on the specific application of the technical solution and the invention constraints. Professional and technical personnel can use different methods to implement the described functions for each specific application, but such implementation should not be considered to be beyond the scope of this application.

[0066] In addition, each functional module in each embodiment of the present application may be integrated into one processing module, or each module may exist physically separately, or two or more modules may be integrated into one module.

[0067] The above is only a specific implementation of the present application, but the protection scope of the present application is not limited thereto. Any person skilled in the art who is familiar with the present technical field can easily think of changes or substitutions within the technical scope disclosed in the present application, which should be included in the protection scope of the present application. Therefore, the protection scope of the present application should be based on the protection scope of the claims.

[0068] Finally: The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the protection scope of the present invention.

Claims

1. A hydrological forecasting method based on physical processes and interpretable deep learning, characterized in that: The steps include: Based on the physical model, a basin hydrological model is constructed, basin characteristics are analyzed and an appropriate rainfall-runoff model is selected. The model parameters are calibrated and verified through the head-specific improved Aurora optimization algorithm to generate initial forecast results. A deep learning model was constructed, with the forecast residuals of the basin hydrological model as the training target, and the hyperparameters of the deep learning model were tuned through the head-specific improved Aurora optimization algorithm; Based on the initial forecast results of the basin hydrological model and the measured data, a multi-dimensional multi-step forecast residual matrix and a multi-dimensional multi-step hydrological element matrix are constructed. The matrix represents the difference between the actual physical process and the simulated physical process of the basin. The forecast residuals predicted by the deep learning post-processing model are synchronously corrected with the original forecast results of the basin hydrological model for multiple forecast periods to generate a dual-drive correction model; Generate real-time hydrological forecast results through the dual-drive correction model, and obtain multi-step correction forecast results in different forecast periods; Based on the corrected forecast results, the Shapley additive interpretation method is used to perform importance analysis on the input variables of the deep learning post-processing model, quantify the contribution of each input variable to the correction results, and optimize the design and correction mechanism of the model input variables.

2. The hydrological forecasting method based on physical process and interpretable deep learning dual drive according to claim 1 is characterized in that: The construction of the multi-dimensional multi-step prediction residual matrix includes: The forecast values ​​are separated from the result set of the basin hydrological model, and the time series correlation of the forecast differences is analyzed in combination with the measured values; Based on the time series lag factor and the forecast period setting, a multi-dimensional multi-step forecast residual matrix is ​​generated: ； In the formula, It represents the forecast residual value at time t with a forecast period of m and a forward lag period of s. express time to time t and time t to The measured value at time, express time to time t and time t to The forecast value at time.

3. The hydrological forecasting method based on physical process and interpretable deep learning dual drive according to claim 1 is characterized by: The initial forecast results of the basin hydrological model are calibrated synchronously for multiple forecast periods, including: Runoff forecast results of the dual-drive correction model at time t and within the forecast period m The expression is as follows: ； In the formula, is the forecast residual at time t + m obtained by the deep learning post-processing model, is the forecast flow at time t + m obtained by the rainfall-runoff model, and They represent the calculation process of the deep learning post-processing model and the rainfall-runoff model respectively. is the forecast difference of rainfall-runoff model at time t, The hydrological elements required for the rainfall-runoff model calculation at time t + m, is the initial calculation condition of the rainfall-runoff model at time t + m.

4. The hydrological forecasting method based on physical process and interpretable deep learning dual drive according to claim 1 is characterized in that: The construction of the physical model includes the following steps: The soil layer was divided into three layers and evapotranspiration was calculated separately; Calculate runoff based on rainfall runoff conditions and divide runoff into surface runoff, subsoil runoff and underground runoff; The Muskingum method is used to calculate runoff and generate hourly flow forecast results for the basin.

5. The hydrological forecasting method based on physical process and interpretable deep learning dual drive according to claim 4 is characterized in that: The construction of the multi-dimensional and multi-step hydrological element matrix includes: Select key hydrological elements of the watershed, including rainfall, rainfall runoff, soil moisture, and evapotranspiration; Based on the time series mutual correlation and hysteresis characteristics, a multi-dimensional and multi-step hydrological element matrix is ​​generated, and the matrix is ​​expressed as: ; In the formula, It represents the hydrological element matrix value with a forecast period of m at time t and a front lag period of s2. express time to time t and time t to The value of the hydrological element at the time.

6. The hydrological forecasting method based on physical process and interpretable deep learning dual drive according to claim 5 is characterized in that: The specific steps of optimizing model parameters using the head-specific improved Aurora optimization algorithm include: An initial population is generated based on a chaos mapping method, wherein the chaos mapping parameters are determined by analyzing the variation characteristics of the model parameters; In the process of population individual renewal, the rotational motion, auroral elliptical trail and particle collision mechanism are introduced to optimize the objective function; Continue to iterate and update the population position until the objective function reaches the optimal value or the maximum number of iterations is reached.

7. The hydrological forecasting method based on physical process and interpretable deep learning dual drive according to claim 1 is characterized in that: The uncertainty of the dual-drive correction model is quantified using Bayesian inference and Markov Monte Carlo algorithms, including: The output results of the dual-drive correction model are transformed into a normal distribution and an initial prior distribution is generated; Combined with observed data, the posterior distribution is iteratively updated based on the Bayesian inference method to quantify the uncertainty of the model prediction results; The probability forecast interval for each moment is generated through posterior distribution sampling analysis.

8. The hydrological forecasting method based on physical process and interpretable deep learning dual drive according to claim 7 is characterized in that: The interpretability analysis of the deep learning post-processing model is performed using the Shapley additive interpretation method, which includes the following steps: The Shapley values ​​of the forecast residual matrix and the hydrological element matrix for the model output are calculated based on the Shapley additive interpretation method; Quantify the contribution of each input variable to the model output; Combined with the flow generation mechanism and error sources of the basin hydrological model, the impact of input variables on the overall prediction results of the dual-drive model is explained.

9. The hydrological forecasting method based on physical process and interpretable deep learning dual drive according to any one of claims 1 to 8, characterized in that: The dual-driven fusion mechanism of deep learning post-processing model and watershed hydrological model is applicable to different types of watershed hydrological models, including but not limited to Xinanjiang model, SCS-CN model and TOPMODEL model.

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