A runoff prediction method and system based on statistical saliency constraint

Abstract

This invention belongs to the field of runoff prediction technology, and specifically discloses a runoff prediction method and system based on statistical significance constraints. The method includes: extracting features from hydrological and meteorological time-series data of the target prediction section and at least one upstream hydrological station to obtain candidate features; performing statistical significance testing and multiple hypothesis testing on the candidate features, combined with information theory correlation screening and feature redundancy screening, to obtain a feature subset; constructing a runoff prediction model including a variable selection subnetwork, a time lag gating subnetwork, and a main prediction network; training the runoff prediction model using the feature subset and historical runoff increments of the target prediction section; and realizing runoff prediction based on the trained runoff prediction model. This invention can improve the reliability of feature inputs and the stability of runoff prediction output.

Description

Technical Field

[0001] This invention belongs to the field of runoff prediction technology, and more specifically, relates to a runoff prediction method and system based on statistical significance constraints. Background Technology

[0002] Runoff forecasting is widely used in flood control early warning, reservoir operation and scheduling, water resource allocation, and navigation support. The accuracy and stability of the forecast results have a significant impact on engineering decisions. With the improvement of hydrological station networks, meteorological observation, and information platforms, engineering operations can obtain hydrological and meteorological time-series data from multiple stations, multiple variables, and multiple time scales, providing a richer data foundation for runoff forecasting. However, the high-dimensional redundancy and spurious correlation risks associated with multi-source data pose greater challenges to the statistical reliability of feature selection and the multi-scale representation depth of model architecture.

[0003] In existing technologies, to fully explore the evolution patterns of runoff, data-driven methods (such as recurrent neural networks and convolutional neural networks) are often used to construct high-dimensional candidate features by combining multi-scale time windows. However, while high-dimensional data brings incremental information, it also introduces high-dimensional redundancy and noise interference. Existing feature engineering methods often focus on correlation analysis or simple dimensionality reduction, which can easily introduce statistically unstable random correlation features when faced with massive candidate features, thus adversely affecting the generalization stability of the model. On the other hand, the runoff generation and confluence process in a watershed has significant multi-scale lag effects, and the response of runoff to precipitation, upstream inflow, and soil moisture exhibits lag characteristics at different scales. Existing deep learning models typically use a uniform time window and overall representation method to process lag information. Especially under different seasons and different inflow conditions, the lag contribution of upstream inflow to the target prediction section is dynamically changing, and a single time window or overall representation is insufficient to simultaneously characterize both abrupt and gradual processes. When a sudden change occurs in the watershed or a flood peak occurs, the model's ability to adaptively adjust the lag contribution is insufficient, which may limit the accuracy of characterizing key turning points, thereby affecting the degree to which the prediction requirements for key processes are met in engineering scenarios.

[0004] In summary, the existing technology has at least the following problems or needs for improvement: (1) Under the condition of multi-source high-dimensional hydrological and meteorological data, when the size of candidate features increases, statistically unstable accidental related features may be introduced, resulting in high feature subset redundancy and adverse effects on model training stability, which in turn affects the generalization stability of prediction.

[0005] (2) Existing prediction models often use fixed time windows or global attention mechanisms to represent multi-scale lag information as a whole, which makes it difficult to adapt to the dynamic laws of lag contribution under different hydrological conditions, resulting in limited accuracy in capturing key processes such as runoff mutations and flood peaks. Summary of the Invention

[0006] In view of the above-mentioned defects or improvement needs of the existing technology, the present invention provides a runoff prediction method and system based on statistical significance constraints, the purpose of which is to improve the generalization stability of runoff prediction.

[0007] To achieve the above objectives, according to one aspect of the present invention, a runoff prediction method based on statistical significance constraints is proposed, comprising the following steps: The runoff prediction model is trained by using a feature subset and the historical runoff increment of the target prediction section; the runoff increment of the target prediction section at the future prediction time is predicted based on the trained runoff prediction model, and the predicted runoff increment is superimposed with the current runoff to achieve runoff prediction. The feature subset is constructed in the following manner: Feature extraction is performed on the hydrological and meteorological time-series data of the target prediction section and at least one upstream hydrological station to obtain candidate features; Candidate features are screened as follows: Statistical significance tests and multiple hypothesis tests are performed on the candidate features and historical runoff increments to screen out the candidate features that meet the statistical significance requirements, forming a statistically significant feature set; the information theory correlation between the candidate features in the statistically significant feature set and the historical runoff increments is calculated, and candidate features that meet the information theory correlation requirements are screened out, forming a relevant feature set; based on the redundancy among the candidate features in the relevant feature set, candidate features that meet the redundancy requirements are screened out, forming a feature subset.

[0008] As a further preferred method, the extraction of candidate features includes the following steps: Under a preset feature calculation window set, sliding window segmentation is performed on hydrological and meteorological time series data. For each window segment obtained from the segmentation process, feature extraction is performed using time series feature calculation operators from a preset operator set to obtain the prediction reference time. Candidate feature values :

[0009] in, Indicates the first The first hydrological station Time series data of hydrological and meteorological variables, Indicates to The result obtained after segmentation is based on the reference time. The right endpoint is, and the length is Window segmentation; Indicates the first feature calculation window in the preset feature calculation window set. The length of the feature calculation window, Represents the first in the preset operator set A time-series feature calculation operator; These represent the hydrological station index, hydrometeorological variable index, feature calculation window index, and time-series feature calculation operator index, respectively; each group A corresponding candidate feature dimension is generated, and they are numbered in a preset order. , This represents the total number of dimensions of the generated candidate features; For any i Each candidate feature dimension will be used to predict the baseline time. Candidate feature values By concatenating the sequences, candidate features can be obtained. .

[0010] As a further preferred embodiment, the runoff prediction model includes a variable selection subnetwork, a time-lag gating subnetwork, and a main trunk prediction network, wherein: The variable selection subnetwork dynamically weights the input sequence to obtain a weighted input sequence; the input sequence refers to the sequence at the prediction reference time. t The preset history playback window length is L The input sequence is the sequence of the nearest features in the feature subset. L The sequence fragment obtained by splicing the candidate feature values ​​at each time point in chronological order; The time-delay gating subnetwork weights the features in the input sequence according to the length of the history lookup window. L The lag distance is divided into three lag groups: short lag group, main lag group and long lag group; gating transformation is performed on each lag group to obtain gating score, and the gating score is normalized to obtain gating coefficient, so that the sum of the gating coefficients of the three lag groups is 1; the features of each lag group are weighted and fused according to the gating coefficient to obtain lag fusion features; The backbone prediction network, based on time-delay fusion characteristics, obtains the target prediction section relative to time at a future prediction time. The predicted runoff increment, and the predicted runoff increment with time The known runoff is superimposed to obtain the predicted runoff at the target prediction section at the future prediction time.

[0011] As a further preferred embodiment, the variable selection sub-network dynamically weights the input sequence to obtain a weighted input sequence, including: The input sequence is processed by a non-linearly activated feedforward network to compute sample-level weight vectors. :

[0012] The weighted input sequence is obtained by element-wise multiplying the sample-level weight vector with the input sequence. :

[0013] in, Given the input sequence, It is a non-linear activation function; These are the learnable parameters for the feedforward network; This represents the Hadamard element-wise product.

[0014] As a further optimization, statistical significance tests and multiple hypothesis tests are performed on the candidate features and historical runoff increments to screen out candidate features that meet the statistical significance requirements, including: For each preset prediction step size h Based on historical runoff increments, construct a system with a predicted step size. h Aligned historical runoff increment sequence ; For candidate features and historical runoff increment series Construct a statistical hypothesis test, taking the absence of statistical correlation between the two as the null hypothesis. And through statistical testing of the operator Calculate the statistic ; Under the null hypothesis Under the condition that it holds, the statistical test operator Obtain the statistical random variable ; Statistic According to the null hypothesis Random variables The distribution is mapped to a significance probability value. ; Perform multiple hypothesis testing correction based on significance probability values: when candidate features At least one prediction step h When the significance probability value meets the preset significance threshold, it is considered to meet the statistical significance requirement.

[0015] As a further optimization, the information-theoretic correlation between candidate features in the statistically significant feature set and historical runoff increments is calculated, and candidate features that meet the information-theoretic correlation requirements are selected, including: For any candidate feature in the statistically significant feature set : Calculate its relationship with each prediction step size h Corresponding historical runoff increment series The information-theoretic correlation between them is used, and the average, weighted, or maximum of these information-theoretic correlations is used as the candidate feature. The comprehensive information theory relevance; When candidate features When the overall information theory relevance is not less than the preset relevance threshold, it is considered to meet the information theory relevance requirement.

[0016] As a further optimization, based on the redundancy among candidate features in the relevant feature set, candidate features that meet the redundancy requirements are selected to form a feature subset, including: The candidate features with the highest comprehensive information theory relevance from the relevant feature set are placed into the feature subset; The remaining candidate features in the relevant feature set are traversed sequentially, and the redundancy between the current candidate feature and each candidate feature in the feature subset is calculated. If the redundancy between the current candidate feature and all candidate features in the feature subset is not greater than the preset redundancy threshold, the current candidate feature is placed into the feature subset. After the traversal is completed, the final feature subset is obtained.

[0017] As a further optimization, the runoff prediction model is trained and validated several times, including: After training the runoff prediction model once, calculate the error evaluation index. If the error evaluation index does not meet the preset verification threshold, update at least one parameter in the parameter set and train the runoff prediction model again until the error evaluation index meets the preset verification threshold, and obtain the final trained runoff prediction model. The parameter set includes network structure parameters, training parameters, and feature engineering configuration parameters of the runoff prediction model. The feature engineering configuration parameters include candidate feature generation parameters and candidate feature selection parameters. When updating parameters, network structure parameters or training parameters are adjusted and updated first. If the preset verification threshold is still not met after a preset number of adjustments, the feature engineering configuration parameters are then updated.

[0018] As a further preferred embodiment, the error evaluation index includes a full-sample error evaluation index and a flood peak section error evaluation index; the full-sample error evaluation index includes normalized root mean square error, mean absolute error, Nash efficiency coefficient, and mean absolute percentage error; the flood peak section error evaluation index includes flood peak qualification rate, flood peak mean relative error, and flood peak underestimation rate. The flood peak section error evaluation index is calculated on the flood peak sample set, which refers to the sample set where the measured runoff at the target prediction section is not less than the flood peak threshold.

[0019] According to another aspect of the present invention, a runoff prediction system based on statistical significance constraints is provided, including a processor for executing the above-described runoff prediction method based on statistical significance constraints.

[0020] In summary, compared with the prior art, the above-described technical solutions conceived by this invention mainly possess the following technical advantages: 1. When screening candidate features, statistical significance constraints and multiple hypothesis testing corrections are introduced. Then, based on the candidate features retained after correction, information theory correlation screening and redundancy thresholding are combined to suppress the accumulation of statistically unstable correlations and redundant features into the feature subset under multi-source hydrological and meteorological data conditions. This improves the reliability of feature input and helps to improve the training stability of the prediction model and the generalization stability of runoff prediction.

[0021] 2. By jointly modeling variable selection and time-delay grouping gating, short, main, and long time delay groups are dynamically weighted and inter-group competitively fused, which can adaptively adjust the contribution of information at different time delay scales. Combined with the prediction method of outputting prediction increments from the backbone prediction network and superimposing the increments, the ability to express multi-scale lag responses and key processes such as abrupt changes and flood peaks can be enhanced, which helps to improve the prediction accuracy and engineering applicability of key processes. Attached Figure Description

[0022] Figure 1 This is a flowchart of the runoff prediction method based on statistical significance constraints according to an embodiment of the present invention.

[0023] Figure 2 This is a bar chart showing the feature weight distribution output by the variable selection subnetwork in an embodiment of the present invention.

[0024] Figure 3 This is a box plot comparing the time-delay grouping gate coefficients for peak and non-peak flood periods in an embodiment of the present invention.

[0025] Figure 4 This is a comparison chart of the predicted results and the measured results of an embodiment of the present invention. Detailed Implementation

[0026] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention. Furthermore, the technical features involved in the various embodiments of this invention described below can be combined with each other as long as they do not conflict with each other.

[0027] For runoff prediction tasks under multi-source hydrological and meteorological data conditions, this invention addresses the problems of candidate feature expansion easily introducing statistical instability and correlation, leading to feature redundancy, and the difficulty in characterizing the multi-scale lag response of runoff to external drivers during abrupt changes and peak flood periods. This invention provides a runoff prediction method based on statistical significance constraints. In the feature generation stage, this method obtains a stable feature subset through statistical significance testing, multiple hypothesis testing correction, information theory correlation screening, and redundancy removal. In the model stage, it combines variable selection, lag gating, and incremental superposition prediction to improve generalization stability and the accuracy of key process predictions. Figure 1As shown, the specific steps include the following: Step S1: Data acquisition and structured preprocessing.

[0028] Acquire multi-source hydrological and meteorological time-series data of the target prediction section and at least one upstream hydrological station, as well as historical runoff time-series data of the target prediction section; and perform structured preprocessing on the multi-source hydrological and meteorological time-series data and historical runoff time-series data.

[0029] Specifically, the upstream section of the target prediction section contains a total of S There are 10 hydrological stations, and each station collects data. K Hydro-meteorological variables, with a time length of T The preprocessed multi-source hydrological and meteorological time series data can be expressed as:

[0030] in, Indicates the first s Hydrological stations at time t The first moment k Hydrometeorological variables observation values; historical runoff time series data for the target prediction section are represented as follows:

[0031] Missing data can be processed using a combination of forward and backward imputation; outlier data can be processed using threshold pruning or quantile replacement. Subsequently, using the timestamp of the target prediction section as a unified time index, the multi-source hydrological and meteorological time-series data of each station are time-aligned with the historical runoff time-series data of the target prediction section to form a structured time-series dataset. In the structured time-series dataset, each time-series sample contains the observed values ​​of each hydrological and meteorological variable of each hydrological station, as well as the historical runoff observation values ​​of the target prediction section at the corresponding time.

[0032] Step S2: Candidate feature generation and feature subset construction.

[0033] Candidate features are generated based on multi-source hydrological and meteorological time series data under a preset feature calculation window set and a preset operator set; the candidate features are then screened to obtain a subset of features that meet the requirements of statistical significance, information theory relevance, and redundancy.

[0034] Specifically, within the preset feature calculation window set and preset operator set The following steps involve performing sliding window segmentation on multi-source hydrological and meteorological time-series data according to a preset feature calculation window set, and calling a set of operators for calculation and summarization on each window segment to generate candidate features. To preset the number of feature calculation windows, Calculate the number of operators for the temporal features in the preset operator set.

[0035] The preset set of operators includes at least one of the following: statistical, trend, periodic, mutation, nonlinear dynamics, multivariate interaction, and hydrological mechanism characteristics. Table 1 provides some examples of operators and their hydrological and physical meanings, which are for illustration and do not constitute a limitation of the present invention.

[0036] Table 1. Examples of Preset Time-Series Feature Calculation Operator Sets

[0037] For any time scale window With any operator At the historical sample baseline time The candidate feature values ​​at a given location can be represented as:

[0038] in Indicates the first The first hydrological station Time series data of hydrological and meteorological variables; Indicates the reference time based on historical samples The right endpoint is, and the length is A sliding window fragment; These represent the hydrological station index, hydrological variable index, time scale window index, and preset time-series feature calculation operator index, respectively. Each group... The generated candidate feature dimensions are uniquely numbered according to a preset order. This yields the set of candidate feature dimensions:

[0039] in, The number of candidate feature dimensions. Indicates the first Temporal mappings corresponding to each candidate feature dimension Indicates the first Each candidate feature dimension at the historical sample baseline time The feature value at that location. For any historical sample reference time... , consisting of the candidate feature dimension set The values ​​of each candidate feature dimension at this moment constitute the candidate feature vector:

[0040] Multiple historical sample reference times The corresponding candidate feature vectors are arranged in chronological order to form a candidate feature sample matrix:

[0041] Among them, the The sequence of values ​​for each candidate feature dimension at each historical sample baseline time is denoted as:

[0042] For ease of description, this value sequence These are the candidate features, which are then used to perform statistical significance tests, information-theoretic correlation calculations, and redundancy assessments on the historical runoff increment sample sequences of the target prediction section. To control the size of the candidate features, disabled or restricted conditions can be set for the combined explosion-type operators.

[0043] For ease of understanding, for example, a preset feature calculation window set. At a certain hydrological station Hydrological variables and computation operators Below, for any Obtaining multi-source hydrological and meteorological time-series data from time intervals At that time Corresponding sequence fragments Then, the computation operator is invoked. Candidate features at the corresponding scale are calculated; that is, the interval can be obtained here. , The corresponding candidate features are all based on the baseline time. Candidate features are generated. Under different combinations of hydrological stations, hydrological variables, feature calculation windows, and calculation operators, multiple candidate feature dimensions and their values ​​at each historical sample baseline time are generated in the same manner.

[0044] Furthermore, after generating candidate features, the candidate features are screened, including: performing statistical significance tests and multiple hypothesis testing corrections based on the feature sample sequences formed by the candidate features at each historical sample baseline time and the historical runoff increment sample sequences of the target prediction section aligned with the prediction step size; on this basis, a feature subset is obtained by combining information theory relevance screening and feature redundancy removal processing; specifically including: (1) Statistical significance test: For candidate feature dimension set Each candidate feature dimension The characteristic sample sequence formed at each historical sample reference time is taken. For the prediction step size set Each prediction step size Construct a historical runoff increment sample sequence for the target prediction section aligned with the prediction step size. Based on this, construct and The statistical hypothesis testing model between the two assumes that there is no statistical correlation between them as the null hypothesis. The hypothesis that the two are statistically correlated is used as the alternative hypothesis. .

[0045] Statistical tests were performed on the operators. Calculate the statistic :

[0046] Based on the distribution characteristics and data type of the candidate features, the statistics are... According to the null hypothesis Random variables The distribution is mapped to a significance probability value. :

[0047] in, These are statistical test operators, which may include statistical hypothesis testing methods based on relevance measures or information theory measures; where... S Null hypothesis Under the condition that it holds, the statistical test operator The resulting statistical random variable.

[0048] (2) Multiple hypothesis test correction: the set of significance probability values ​​obtained for each candidate feature and each prediction step size. Perform multiple hypothesis testing correction to reduce the risk of false significance due to a large number of candidate features. For example, to control the false discovery rate, the significance probability values ​​are arranged in ascending order:

[0049] And determine the largest index that satisfies the following conditions ,

[0050] in Ntest This represents the total number of significance probability values ​​involved in the correction of multiple hypothesis tests. To preset the false discovery rate threshold; when the number of candidate feature dimensions is And the set of prediction step sizes for multi-step prediction is Sometimes, Ntest = m × H ; The test combinations that satisfy the multiple hypothesis testing correction requirements are denoted as the significant test combination set, and a statistically significant feature set is formed based on this set:

[0051] In other words, when candidate features At least one prediction step If the candidate feature meets the corrected statistical significance requirement, retain the candidate feature; if the candidate feature does not meet the requirement, retain the candidate feature. If the statistical significance requirement is not met at any prediction step size, the candidate feature is eliminated.

[0052] In some implementations, a threshold correction rule can be used to correct the significance probability value, that is, to shrink the preset significance threshold according to the number of candidate features, and to determine whether the candidate features meet the statistical significance condition.

[0053] (3) Information theory relevance screening: in the statistically significant feature set corrected by multiple hypothesis testing Above, calculate candidate features With each prediction step size Corresponding historical runoff increment sample sequence Information-theoretic correlation between them: ; For information theory relevance measurement, mutual information, maximum information coefficient, or normalized information relevance can be used as the measurement methods.

[0054] Based on candidate features Determine the overall information-theoretic correlation based on the information-theoretic correlation at each prediction step size:

[0055] Alternatively, in some implementations, the overall information-theoretic relevance can also be the average or weighted value of the information-theoretic relevance at each prediction step.

[0056] Based on the preset relevance threshold The candidate features are filtered to obtain the relevant feature set:

[0057] in, This is a preset information theory relevance threshold.

[0058] (4) Redundancy removal: First, retain the candidate features with the highest comprehensive information theory relevance in the relevant feature set and place them into the feature subset; Then, the remaining candidate features in the relevant feature set are traversed sequentially, and the redundancy between the current candidate feature and the retained candidate features in the feature subset is calculated; if the redundancy between the current candidate feature and any retained candidate feature is greater than a preset redundancy threshold... If the redundancy between the current candidate feature and all retained candidate features is not greater than a preset redundancy threshold, then the current candidate feature dimension will be eliminated. If the current candidate feature is selected, it is retained and added to the feature subset; after traversal, the final feature subset is obtained.

[0059] Step S3: Runoff prediction model construction and training.

[0060] Based on feature subsets and historical runoff time-series data, a model input sequence and corresponding runoff increment supervision labels are constructed to form a training sample set. The runoff prediction model is then trained based on this training sample set. After constructing the training sample set, the model input features formed by the feature subset are subjected to standard normalization, and the runoff increment supervision labels constructed from the historical runoff time-series data of the target prediction section are subjected to robust scaling. The standard normalization parameters and robust scaling parameters are both obtained by fitting the training data and remain consistent throughout the training, validation, and prediction phases.

[0061] Let the length of the history playback window be... The maximum prediction step size is In single-step prediction In multi-step prediction, the prediction step size is Supervision samples are constructed using a sliding method at any historical sample reference time. The model is based on length Multivariable sequence fragments As input, with the future The historical runoff increment corresponding to each prediction step size is used as a supervision label.

[0062] Specifically, regarding time The model input is from the most recent The input sequence obtained by concatenating the feature vectors at each time step in chronological order:

[0063] in, For each candidate feature dimension in the feature subset at time... The eigenvectors are formed by the values ​​of . Correspondingly, the future is constructed. Historical runoff increment labels at each prediction step :

[0064] in:

[0065] For the target section at the historical sample reference time The measured runoff, For the target prediction section at the target time The measured runoff. To start from the historical sample reference time up to the predicted target time The measured increase in runoff, This is the monitoring label for the historical runoff increment corresponding to this sample.

[0066] Furthermore, the runoff prediction model based on time-lag gating networks includes a variable selection subnetwork, a time-lag gating subnetwork, and a main prediction network: (1) The variable selection subnetwork is a lightweight variable selection network. It dynamically generates sample-level weight vectors based on the current input feature vector (input sequence) through the feedforward network, and performs element-wise multiplication with the input features to achieve dynamic feature weighting, thus obtaining a weighted input sequence.

[0067] The sample-level weight vector is output by a feedforward network containing non-linear activation; the input feature vector for any sample is denoted as... Then the sample-level weight vector satisfy:

[0068] Sample-level weight vector It can be derived for feature contribution analysis, and then the dynamically weighted features can be obtained by element-wise multiplication. , represented as:

[0069] in, for d 3D real vector space; It is a non-linear activation function; These are the learnable parameters for the feedforward network; This represents the Hadamard element-wise product. The input feature vector is the aforementioned input sequence. ; The weighted feature vector of the subnetwork output is selected for the variable selection, i.e., the weighted input sequence. .

[0070] (2) The time-delay gated subnetwork will weight the input sequence Based on the length of the history playback window L The time lags are divided into three groups: short time lag group, main time lag group, and long time lag group. For ease of understanding, let the dividing point be... Its satisfaction Then the weighted input sequence can be... Divided into: Short delay group (most recent segment) The main time delay group (middle section) The long time delay group (an earlier segment) .

[0071] Each time delay group is represented at the group level, and a gating transformation is performed to generate a gating score. The gating score is normalized to obtain inter-group competitive gating coefficients, so that the sum of the three gating coefficients is 1. The features of each time delay group are weighted and fused according to the gating coefficients to obtain the time delay fused feature representation.

[0072] The group-level representation of each time delay group is obtained by aggregating features within the group, satisfying the following:

[0073] Each group's gating score satisfies:

[0074] The normalized gating coefficients for inter-group competition are:

[0075] Final Delay Fusion Feature Representation satisfy:

[0076] in, These represent the short delay group, the main delay group, and the long delay group, respectively. For the weighted input sequence The first, divided according to the lag distance. Group input sequence; For the first Group-level feature vectors obtained by aggregating the input sequence within a group; For the first The group's original gating score; The inter-group competitive gating coefficients obtained after normalizing the gating scores are used to perform weighted fusion of the representations of each group. This is an in-group aggregation operator, which can be mean pooling, max pooling, or attention pooling. This is the gating scoring function.

[0077] (3) The backbone prediction network is a feedforward stacked dense coding backbone (including an input projection layer and a multi-layer feedforward network stacked structure); the backbone prediction network is represented by the fused lag features. As input, output the future The predicted runoff increments for each prediction step size are then compared with the historical sample baseline time. Target runoff observation value Incremental stacking is performed to obtain the final predicted runoff value at each prediction time.

[0078] At the reference time The runoff prediction increment vector output by the backbone prediction network satisfies:

[0079] in,

[0080] For any prediction step size The corresponding predicted time is obtained by incremental superposition. Final predicted runoff values:

[0081] in, The most recent time in the input sequence, i.e., the baseline time of the historical samples. The target runoff observation value.

[0082] in, To maximize the prediction step size, during single-step prediction... Multi-step prediction ; For predicting the step size index; The incremental runoff forecast output by the backbone forecasting network; For the target cross section at the prediction time Relative to the historical sample baseline time The increase in predicted runoff; The most recent time in the input sequence, also known as the reference time. The target runoff observation value; For the target cross section at the prediction time The predicted runoff value.

[0083] Step S4: Model validation and parameter update.

[0084] The trained runoff prediction model is validated by evaluating its prediction accuracy using an error evaluation index to determine whether it meets the preset verification threshold and triggering parameter updates. Specifically, if the error evaluation index does not meet the preset verification threshold, at least one parameter in the parameter set is updated and an iterative update process is executed. The runoff prediction model is then trained and evaluated again until the error evaluation index meets the preset verification threshold, resulting in the final trained runoff prediction model.

[0085] Specifically, the error evaluation indicators include full-sample error evaluation indicators and peak-section error evaluation indicators. Full-sample error evaluation indicators include Normalized Root Mean Square Error (NRMSE), Mean Absolute Error (MAE), Nash Efficiency Coefficient (NSE), and Mean Absolute Percentage Error (MAPE). Peak-section error evaluation indicators are calculated on a peak-section sample set, which is a set of samples where the measured runoff at the target prediction section is not less than the peak-section threshold. The peak-section threshold is determined according to a preset quantile of the measured runoff sample distribution at the target prediction section; it includes the Peak Passrate, Peak MAPE, and Underestimate rate.

[0086] The preset verification threshold can be determined with reference to the provisions of GB / T 22482-2008 "Specifications for Hydrological Information Forecasting" regarding the evaluation of operational forecast accuracy, and the pass rate of forecasts within the permissible error range should be used as the basis for verification judgment. Permissible error Values ​​can be taken according to the operational provisions of the corresponding elements and forecast period in the hydrological information forecasting specifications; when The sample was judged as qualified at that time, and the predicted pass rate was the percentage of qualified samples.

[0087] Furthermore, the parameter set includes network structure parameters, training parameters, and feature engineering configuration parameters for the runoff prediction model. The feature engineering configuration parameters include candidate feature generation parameters and candidate feature selection parameters. The candidate feature generation parameters include a preset feature calculation window and a time-series feature calculation operator activation strategy. The candidate feature selection parameters include multiple hypothesis testing correction parameters, information theory relevance selection threshold parameters, and redundancy threshold parameters.

[0088] When updating network structure parameters or training parameters, return to step S3 to retrain the model based on the current feature subset; when updating feature engineering configuration parameters, return to step S2 to regenerate and filter candidate features, and then execute step S3 to train the model based on the newly obtained feature subset. Preferably, when the error evaluation index does not meet the preset verification threshold, the network structure parameters or training parameters are adjusted and updated first. If the requirements are still not met after a preset number of adjustments, the feature engineering configuration parameters are then updated.

[0089] Step S5: Application of runoff prediction model.

[0090] Call the trained runoff prediction model and output the runoff prediction results for one or more future time steps at the target prediction section.

[0091] The model prediction specifically includes: performing data preprocessing on the prediction data in the same way as in the training phase; extracting corresponding features according to the feature subset determined in the training phase under the same preset feature calculation window set as in the training phase, and organizing them into model input; calling the trained runoff prediction model to output the runoff increment of one or more prediction steps in the future at the target prediction section, and superimposing the predicted runoff increment with the current runoff to achieve runoff prediction.

[0092] The present invention will be further described below with reference to a specific embodiment.

[0093] This embodiment uses daily runoff data from multiple stations as an example. Five stations are anonymized and designated as YC, ZC, SS, JL, and CLJ, where CLJ is the target prediction section, and the upstream stations YC, ZC, SS, and JL are the input stations. Daily hydrological and meteorological observation data for multiple consecutive hydrological years of the target river section are acquired, cleaned, and missing values ​​are processed to form a structured dataset. The data is divided into training and testing data in chronological order. Within the training data, validation data is further divided for error evaluation index verification during the training process; the testing data is used only for independent testing and performance evaluation after the model is finalized.

[0094] In this embodiment, an example of a preset feature calculation window is as follows: Candidate features are generated under each preset feature calculation window. To control the feature size and reduce the impact of high-frequency noise, feature terms corresponding to the Fast Fourier Transform coefficients and Continuous Wavelet Transform coefficients are disabled. For example, the initial candidate feature set is 1252-dimensional, which is reduced to 726-dimensional after removing constant features and equivalent redundancy. Further statistical significance tests are performed on the candidate feature sample sequence and the historical runoff increment sample sequence of the target prediction section aligned with the prediction step size. After multiple hypothesis testing correction, information theory correlation screening, and redundancy removal processing using a redundancy threshold (0.95), a 23-dimensional feature subset is finally obtained. The above feature dimension statistical results are only example results under the dataset of this embodiment and do not constitute a limitation on the scope of protection of this invention. Therefore, the method of this invention can suppress statistically unstable correlation and redundancy accumulation when the candidate feature expansion scale is large, forming a controllable feature subset, providing more stable input support for subsequent model training.

[0095] Table 2 shows an example of the runoff prediction model structure and training configuration parameters in this embodiment. The sample-level weight vectors of the variable selection sub-network can be derived, and a schematic diagram of the feature weights can be drawn, as shown below. Figure 2 As shown, it is used to demonstrate the relative weight differences of different input features under dynamic weighting at the sample level, thereby reflecting the model's selective emphasis on key driving factors. This helps verify the suppression effect of the variable selection subnetwork on redundant inputs and provides a basis for feature contribution analysis. Simultaneously, three types of gating coefficients—short-delay, main-delay, and long-delay groups—can be derived. Box plots were drawn separately for peak flood periods and non-peak flood periods, as shown below. Figure 3 As shown, to compare the differences in the model's emphasis on different lag information during key stages, when there are differences in the distribution of gating coefficients corresponding to the peak flood period and non-peak flood period, it indicates that the lag grouping gating can adaptively adjust the contributions of short, main, and long lag information, and form a staged response through inter-group competitive fusion. The peak flood period sample set consists of samples whose measured runoff at the target prediction section is not less than the peak flood threshold determined according to a preset quantile (0.95 in this embodiment).

[0096] Table 2 Model Structure and Training Configuration Parameters

[0097] A runoff prediction model is trained on training data, and error evaluation metrics are validated based on validation data. Once the error evaluation metrics on the validation data meet a preset validation threshold, the model is finalized. Subsequently, the test data undergoes the same data preprocessing, candidate feature generation, feature subset construction, and model input organization as the training phase, and the runoff prediction result for the target prediction section for the next prediction step is output. This embodiment uses runoff prediction for the next day as an example, i.e., the maximum prediction step size. The corresponding historical runoff increment monitoring label is After the model outputs the runoff prediction increment, it is compared with the historical sample baseline time. Target predicted cross-sectional measured runoff Incremental summaries are performed to obtain the predicted runoff value for the next day.

[0098] The statistical results of the prediction performance evaluation indicators are shown in Table 3. Among them, the training data indicators are the back-substitution statistics on the training data after the model is trained, and the test data indicators are the statistics on the independent test data after the model is trained. In this embodiment, the determination of the preset verification threshold is based on the calculation results of the verification data. Figure 4 A comparison of the predicted and measured results is presented to illustrate the overall trend and the tracking of the flood peak. The comparison shows that the model maintains a good trend fit and provides a response to the flood peak process. These results demonstrate that the method of this invention, under this dataset and parameter configuration, has good fitting and error control effects on overall runoff changes and key samples of the flood peak, exhibiting a certain degree of stability and providing a reference for engineering applications.

[0099] Table 3 Statistical Table of Predictive Performance Evaluation Indicators

[0100] Those skilled in the art will readily understand that the above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A runoff prediction method based on statistical significance constraints, characterized in that, Includes the following steps: The runoff prediction model is trained by using a feature subset and the historical runoff increment of the target prediction section; the runoff increment of the target prediction section at the future prediction time is predicted based on the trained runoff prediction model, and the predicted runoff increment is superimposed with the current runoff to achieve runoff prediction. The feature subset is constructed in the following manner: Feature extraction is performed on the hydrological and meteorological time-series data of the target prediction section and at least one upstream hydrological station to obtain candidate features; Candidate features are screened: statistical significance tests and multiple hypothesis tests are performed on candidate features and historical runoff increments to screen out candidate features that meet the statistical significance requirements and form a statistically significant feature set; The information theory correlation between candidate features in the statistical salient feature set and historical runoff increments is calculated, and candidate features that meet the information theory correlation requirements are selected to form a relevant feature set. Based on the redundancy among the candidate features in the relevant feature set, candidate features that meet the redundancy requirements are selected to form a feature subset.

2. The runoff prediction method based on statistical significance constraints as described in claim 1, characterized in that, The extraction of candidate features includes the following steps: Under a preset feature calculation window set, sliding window segmentation is performed on hydrological and meteorological time series data. For each window segment obtained from the segmentation process, feature extraction is performed using time series feature calculation operators from a preset operator set to obtain the prediction reference time. Candidate feature values : in, Indicates the first The first hydrological station Time series data of hydrological and meteorological variables, Indicates to The result obtained after segmentation is based on the reference time. The right endpoint is, and the length is Window segmentation; Indicates the first feature calculation window in the preset feature calculation window set. The length of the feature calculation window, Represents the first in the preset operator set A time-series feature calculation operator; These represent the hydrological station index, hydrometeorological variable index, feature calculation window index, and time-series feature calculation operator index, respectively; each group A corresponding candidate feature dimension is generated, and they are numbered in a preset order. , This represents the total number of dimensions of the generated candidate features; For any i Each candidate feature dimension will be used to predict the baseline time. Candidate feature values By concatenating the sequences, candidate features can be obtained. .

3. The runoff prediction method based on statistical significance constraints as described in claim 2, characterized in that, The runoff prediction model includes a variable selection subnetwork, a time-lag gating subnetwork, and a main prediction network, wherein: The variable selection subnetwork dynamically weights the input sequence to obtain a weighted input sequence; the input sequence refers to the sequence at the prediction reference time. t The preset history playback window length is L The input sequence is the sequence of the nearest features in the feature subset. L The sequence fragment obtained by splicing the candidate feature values ​​at each time point in chronological order; The time-delay gating subnetwork weights the features in the input sequence according to the length of the history lookup window. L The lag distance is divided into three lag groups: short lag group, main lag group and long lag group; gating transformation is performed on each lag group to obtain gating score, and the gating score is normalized to obtain gating coefficient, so that the sum of the gating coefficients of the three lag groups is 1; the features of each lag group are weighted and fused according to the gating coefficient to obtain lag fusion features; The backbone prediction network, based on time-delay fusion characteristics, obtains the target prediction section relative to time at a future prediction time. The predicted runoff increment, and the predicted runoff increment with time The known runoff is superimposed to obtain the predicted runoff at the target prediction section at the future prediction time.

4. The runoff prediction method based on statistical significance constraints as described in claim 3, characterized in that, The variable selection subnetwork dynamically weights the input sequence to obtain a weighted input sequence, including: The input sequence is processed by a non-linearly activated feedforward network to compute sample-level weight vectors. : The weighted input sequence is obtained by element-wise multiplying the sample-level weight vector with the input sequence. : in, Given the input sequence, It is a non-linear activation function; These are the learnable parameters for the feedforward network; This represents the Hadamard element-wise product.

5. The runoff prediction method based on statistical significance constraints as described in claim 2, characterized in that, Statistical significance tests and multiple hypothesis tests were performed on candidate features and historical runoff increments to screen out candidate features that meet the statistical significance requirements, including: For each preset prediction step size h Based on historical runoff increments, construct a system with a predicted step size. h Aligned historical runoff increment sequence ; For candidate features and historical runoff increment series Construct a statistical hypothesis test, taking the absence of statistical correlation between the two as the null hypothesis. And through statistical testing of the operator Calculate the statistic ; Under the null hypothesis Under the condition that it holds, the statistical test operator Obtain the statistical random variable ; Statistic According to the null hypothesis Random variables The distribution is mapped to a significance probability value. ; Perform multiple hypothesis testing correction based on significance probability values: when candidate features At least one prediction step h When the significance probability value meets the preset significance threshold, it is considered to meet the statistical significance requirement.

6. The runoff prediction method based on statistical significance constraints as described in claim 5, characterized in that, The information-theoretic correlation between candidate features in the statistically significant feature set and historical runoff increments is calculated, and candidate features that meet the information-theoretic correlation requirements are selected, including: For any candidate feature in the statistically significant feature set Calculate its relationship with each prediction step size. h Corresponding historical runoff increment series The information-theoretic correlation between them is used, and the average, weighted, or maximum of these information-theoretic correlations is used as the candidate feature. The comprehensive information theory relevance; When candidate features When the overall information theory relevance is not less than the preset relevance threshold, it is considered to meet the information theory relevance requirement.

7. The runoff prediction method based on statistical significance constraints as described in claim 6, characterized in that, Based on the redundancy among candidate features in the relevant feature set, candidate features that meet the redundancy requirements are selected to form a feature subset, including: The candidate features with the highest comprehensive information theory relevance from the relevant feature set are placed into the feature subset; The remaining candidate features in the relevant feature set are traversed sequentially, and the redundancy between the current candidate feature and each candidate feature in the feature subset is calculated. If the redundancy between the current candidate feature and all candidate features in the feature subset is not greater than the preset redundancy threshold, the current candidate feature is placed into the feature subset. After the traversal is completed, the final feature subset is obtained.

8. The runoff prediction method based on statistical significance constraints as described in any one of claims 1-7, characterized in that, The runoff prediction model was trained and validated several times, including: After training the runoff prediction model once, calculate the error evaluation index. If the error evaluation index does not meet the preset verification threshold, update at least one parameter in the parameter set and train the runoff prediction model again until the error evaluation index meets the preset verification threshold, and obtain the final trained runoff prediction model. The parameter set includes network structure parameters, training parameters, and feature engineering configuration parameters of the runoff prediction model. The feature engineering configuration parameters include candidate feature generation parameters and candidate feature selection parameters. When updating parameters, network structure parameters or training parameters are adjusted and updated first. If the preset verification threshold is still not met after a preset number of adjustments, the feature engineering configuration parameters are then updated.

9. The runoff prediction method based on statistical significance constraints as described in claim 8, characterized in that, The error evaluation indicators include full-sample error evaluation indicators and flood peak section error evaluation indicators. The full-sample error evaluation indicators include normalized root mean square error, mean absolute error, Nash efficiency coefficient, and mean absolute percentage error. The flood peak section error evaluation indicators include flood peak qualification rate, flood peak mean relative error, and flood peak underestimation rate. These flood peak section error evaluation indicators are calculated on the flood peak sample set, which refers to the sample set where the measured runoff at the target prediction section is not less than the flood peak threshold.

10. A runoff prediction system based on statistical significance constraints, characterized in that, Includes a processor for executing the runoff prediction method based on statistical significance constraints as described in any one of claims 1-9.

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