Rainfall-runoff interval prediction method based on spatio-temporal graph convolution

Abstract

This invention discloses a rainfall-runoff interval prediction method based on spatiotemporal graph convolution. It uses physical mechanisms to divide the research object into different homogeneous objects to simulate the watershed. Simultaneously, it considers watershed boundaries and feature alignment issues during the construction process. A TCN temporal convolutional network and graph convolution methods are used to extract and encode temporal and spatial information during construction, respectively, enabling hydrological extrapolation of the rainfall-runoff process. Specifically, the temporal convolution operation incorporates an attention mechanism to better extract temporal features, while the spatial graph convolution operation is based on the homogeneous graph and graph convolution method constructed in this method. The output layer introduces the LUBE interval prediction method to estimate the prediction results, thereby achieving rainfall-runoff interval prediction. This invention integrates the spatial and temporal information features of the watershed, achieving a spatiotemporally consistent data organization mechanism. The introduction of interval prediction methods in the output prediction values ​​improves the accuracy of rainfall-runoff forecasts.

Description

Technical Field

[0001] This invention belongs to the field of data-driven rainfall-runoff prediction in small and medium-sized watersheds, and specifically relates to a rainfall-runoff interval prediction method based on spatiotemporal graph convolution. Background Technology

[0002] As water conservancy enters a new stage of development, various industries, represented by water conservancy, have built or are building industry-specific big data infrastructures, showing a trend of using data mining to achieve domain-specific tasks. Domestic and international scholars are actively conducting research on intelligent rainfall-runoff prediction using long-term accumulated hydrological observation and practical data. However, because most current models do not fully consider domain knowledge, the low reliability and short lead time of forecast results still hinder the performance improvement and widespread application of intelligent models. As a dynamic system with spatiotemporal evolution, how to fully and rationally utilize available information such as underlying surface, temperature, wind speed, and rainfall within a watershed is a key focus and challenge in current intelligent rainfall-runoff prediction research. Therefore, it is necessary to explore and invent a new rainfall-runoff interval prediction method based on spatiotemporal graph convolution, study spatiotemporally consistent data organization mechanisms for multi-scale water conservancy objects, and mine the correlation between water conservancy objects and water cycle processes in the rainfall-runoff process to solve the technical challenges of applying spatiotemporal graph convolutional networks in the field of water conservancy. Deterministic forecasting methods are simple, direct, and relatively easy to implement, and most existing forecasting methods employ deterministic prediction. However, the exceptional complexity of precipitation-runoff processes and the limited human understanding of these processes make uncertainty in deterministic forecasts unavoidable. Deterministic forecasts can only predict a single value of a variable at a future time, failing to provide the inherent degree of uncertainty associated with that prediction. Interval forecasting, on the other hand, not only provides a possible forecast interval for the variable but also offers the probability confidence level; therefore, research on interval forecasting is necessary. Summary of the Invention

[0003] Purpose of the invention: The purpose of this invention is to provide a rainfall-runoff interval prediction method based on spatiotemporal graph convolution, thereby solving the aforementioned problems existing in the prior art.

[0004] Technical solution: This invention provides a method for predicting rainfall-runoff intervals based on spatiotemporal graph convolution, comprising the following steps:

[0005] (1) Store the hydrological data collected in advance from each station in the study basin into the hydrological historical database;

[0006] (2) Preprocess the historical hydrological data, and then divide the preprocessed data into training set and test set according to the hold-out method;

[0007] (3) Construct a spatiotemporal graph convolutional rainfall-runoff interval prediction model and train it using a training set. Adjust the prediction model parameters to make the prediction model converge. The prediction model construction includes four processes: homogeneous graph generation, temporal attention convolution, spatial graph convolution, and interval prediction. By constructing a homogeneous graph based on physical mechanisms, the temporal attention convolution and spatial graph convolution methods are used to simulate the watershed state change process according to the monitored sub-basin characteristics from a spatiotemporal perspective, thereby realizing interval prediction.

[0008] (4) Use the test set to evaluate the performance of the spatiotemporal graph convolutional rainfall-runoff interval prediction model;

[0009] (5) The preprocessed current hydrological data is used as the input of the spatiotemporal map convolutional rainfall-runoff interval prediction model, and the flow rate at the outlet section of the basin at the k-th time in the future is the output of the model, that is, the flow rate at the k-th hour in the future.

[0010] Furthermore, the hydrological data in step (1) includes historical rainfall data, historical flow data of the river outlet section, historical evaporation data of the basin, historical temperature data of the basin, and historical wind speed data of the basin.

[0011] Furthermore, the preprocessing of hydrological historical data in step (2) includes data missing completion, data anomaly correction, and data normalization; wherein data missing completion adopts Kriging interpolation; data anomaly correction refers to replacing single abnormal data with the average value of the same station before and after the time, and replacing continuous abnormal data with the average value of adjacent stations at the same time; data normalization is Min-max standardization.

[0012] Furthermore, the temporal attention convolution described in step (3) introduces the attention mechanism into the temporal convolutional network (TCN) model.

[0013] Furthermore, in step (3), the homogeneous graph generation infers the local or global state of the spatial graph based on the state of the nodes and the connectivity relationships, and uses prior knowledge to constrain the estimation of the system:

[0014]

[0015] in, This represents the connectivity between various site objects within a homogeneous graph. Characteristics representing simple objects; Indicates that it has been selected for estimation. A collection of objects.

[0016] Furthermore, the spatial graph convolution in step (3) employs a Chebyshev polynomial first-order approximation method to simplify the calculation, and the calculation process is as follows:

[0017]

[0018] Among them, the largest eigenvalue ; ;in, For ease of calculation, let's take the vector of polynomial coefficients. For a node in the graph at a certain moment, a certain feature and adjacency matrix Obtain the Laplace matrix ,in The degree matrix can be obtained by calculation using the formula:

[0019]

[0020] Where K=1; after activation function After processing, a spatiotemporal feature matrix processed by spatiotemporal graph convolution can be obtained. :

[0021]

[0022] in, These represent ReLU activation operations. ; This represents the hidden state obtained after temporal convolution; after spatiotemporal graph convolution, information from the input features in different dimensions is fused into the spatiotemporal hidden state. In this process, the output layer can utilize a fully connected network with strong fitting capabilities to predict the output.

[0023] Furthermore, the interval prediction in step (3) quantifies the uncertainty of the prediction result and provides the probability confidence that the predicted object may appear within the prediction interval, as shown in the following formula:

[0024]

[0025] The ADAM optimization method is applied to the interval prediction method, based on ADAM. The optimization algorithm is as follows:

[0026] Input high-dimensional meteorological factor data, including rainfall data, flow rate data, temperature data, wind speed data, evapotranspiration data, and geographic data; initialize X. The data is preprocessed to X using a sliding window and forward chain cross-validation method; the preprocessed data is then input into the model for training. The parameters of the LUBE fully connected layer in the network are iteratively updated using the ADAM optimization method. and Until now At that time, take Training ends thereafter; based on the criterion of effective prediction coverage width. .

[0027] Furthermore, the implementation process of step (4) is as follows:

[0028] Root Mean Square Error (RMSE):

[0029]

[0030] absolute median difference MedAE:

[0031]

[0032] Interval Forecasting Indicator (CWC):

[0033]

[0034] in: This represents the flow rate observation of the i-th sample. This represents the predicted flow rate value for the i-th sample. This represents the number of test samples, where n represents the nth sample in the test set. , These represent the flow observations for the 1st and nth samples, respectively. , Let represent the predicted flow values ​​for the 1st and nth samples, respectively. PINAW represents the width of the confidence interval for the interval prediction, and PICP represents the probability that the confidence interval for the interval prediction covers the observed value. This is a hyperparameter.

[0035] Beneficial effects: Compared with the prior art, the beneficial effects of the present invention are as follows: The present invention uses homogeneous graphs to extract hydrological knowledge such as watershed information in a visible manner, and utilizes the ability of TCN to capture effective long-term time features to achieve a spatiotemporally consistent data organization mechanism. In addition, the LUBE interval prediction method introduced improves the prediction accuracy, which is superior to traditional machine models such as support vector machines, and provides technical support for subsequent dynamic flood forecasting modeling and prediction based on heterogeneous graphs. Attached Figure Description

[0036] Figure 1 This is a flowchart of the present invention. Detailed Implementation

[0037] The present invention will now be described in further detail with reference to the accompanying drawings.

[0038] This invention provides a rainfall-runoff interval prediction method based on spatiotemporal graph convolution. It simulates a watershed by dividing the research object into different homogeneous simple objects according to physical mechanisms. Simultaneously, the watershed boundary and feature alignment issues are considered during the construction process. Ordinary convolution and graph convolution methods are used to extract and encode temporal and spatial information respectively, enabling the deduction of the rainfall-runoff process. The temporal convolution operation is a standard convolution operation, while the spatial graph convolution operation is based on the homogeneous graph and (spectral domain) graph convolution methods constructed in this method. Leveraging the simulation and decoding capabilities of a typical fully connected neural network, the system state is estimated by decoding spatiotemporal information, thereby achieving flood forecasting. Figure 1 As shown, it includes the following steps:

[0039] Step 1: First, collect hydrological data from various stations in the study basin, and then store the collected hydrological data in a historical hydrological database.

[0040] Hydrological data for the target watershed (Qijiang River Basin) from 1979 to 2019 were collected at a granularity of 1 data point per day, and then stored in a historical database. The hydrological data included historical rainfall data, historical flow data at the river outlet section, historical evaporation data, historical temperature data, and historical wind speed data.

[0041] Step 2: Preprocess the historical hydrological data. Missing data is filled using linear interpolation over time. Data anomalies refer to data that is not normal. For a single anomalous data point, the average value of the time before and after the same station is used as the replacement. For consecutive anomalous data points, the average value of adjacent stations at the same time is used as the replacement.

[0042] The data normalization method, wherein the normalization method is Min-max standardization, is defined by the following formula: in, The data is after normalization. The raw data to be processed. The minimum value in the original data. The maximum value in the original data represents the value of the normalized data, which is between 0 and 1. The normalized data is divided into a training set and a test set, which are two mutually exclusive sets. The partitioning method is the hold-out method, and the ratio of the training set to the test set is 8:2. The training set contains data from 1979 to 2011, and the test set contains data from 2011 to 2019.

[0043] Step 3: Construct a spatiotemporal graph convolutional rainfall-runoff interval prediction model and train it using a training set. Adjust the prediction model parameters to make the prediction model converge. The construction of the prediction model includes four modeling operations: homogeneous graph generation, temporal attention convolution, spatial graph convolution, and interval prediction. By constructing object connection relationships (homogeneous graph) based on physical mechanisms, the model simulates the watershed state change process from a spatiotemporal perspective based on the monitored sub-basin characteristics using temporal attention convolution and spatial (spectral domain) graph convolution methods, thereby achieving rainfall-runoff forecasting.

[0044] Homogeneous graphs can infer the local or global state of a system based on the state of nodes and their connectivity. The result of generating a homogeneous graph is stored as an adjacency matrix, denoted as A, whose dimension is usually related to the number of nodes N in the graph.

[0045]

[0046] in, This represents the connectivity between objects within a homogeneous graph; Characteristics representing simple objects; Indicates the quantity being estimated; Indicates that it has been selected for estimation. The set of objects. By explicitly constraining relationships, the modeling method based on homogeneous graphs can utilize prior knowledge to constrain the estimation of the system, thus explicitly expressing domain knowledge into the data mining model to a certain extent.

[0047] Temporal Attention Convolutional Network (TCN) extracts features only from the temporal dimension of the data and incorporates an attention mechanism during input to better capture relevant features. The specific structure of TCN is as follows: In the case of a univariate sequence, given a one-dimensional hydrological variable sequence X and a filter function of size k... The full dilated causal convolution operation f on a continuous layer is defined on a sequence s as follows:

[0048]

[0049] Where s is the element of the sequence, d is the expansion parameter, and The past direction is described. *d is referred to as the dilated convolution operation to distinguish it from the normal convolution operation. The normal convolution operator (*) is a specific version of dilated convolution (when d=1). The receptive field of the causal network is increased in two ways: one is by increasing the filter size k; the other is by increasing the dilation factor d. In this study, d is determined based on the network depth. The index is increased to ensure effective coverage of long-term history; specifically, Used for the i-th level of the network.

[0050] Spatial graph convolution operations build upon the results of temporal convolution operations by utilizing the adjacency matrix generated from the model's homogeneous graph. To implement the spectral domain graph convolution operation, the calculation process in the spatial graph convolution module adopts the Chebyshev polynomial first-order approximation method to simplify the calculation. The calculation process is shown in the following formula:

[0051]

[0052] Among them, the largest eigenvalue ; ;in, For ease of calculation, let's take the vector of polynomial coefficients. For a node in the graph at a certain moment, a certain feature... and adjacency matrix The Laplace matrix can be obtained. ,in The degree matrix can be obtained by calculation using the formula:

[0053]

[0054] Typically, a K-order polynomial can be used for computational simplification, and the value of K plays a crucial role. In this invention, we generally only consider the influence of upstream and downstream nodes on a single node, and considering both computational complexity and interpretability, we choose K=1. Furthermore, after activation function processing, we obtain the spatiotemporal feature matrix processed by the spatiotemporal graph convolution operation, which can be represented by the following formula:

[0055]

[0056] in, Indicates ReLU activation. ; This represents the hidden state obtained after the temporal convolution operation. After the spatiotemporal graph convolution operation, information from the input features in different dimensions is fused into the spatiotemporal hidden state. In this process, the output layer can utilize a fully connected network with strong fitting capabilities to predict the output.

[0057] Interval forecasting primarily quantifies the uncertainty of the forecast results and provides the confidence level of the probability that the predicted object may appear within the forecast interval. Its formula is as follows:

[0058]

[0059] Since the lower and upper bound estimation (LUBE) method cannot be trained using gradient descent, the ADAM optimization method is adopted. Its training is as follows: ADAM-based... The optimization algorithm is shown below:

[0060] 1) Input high-dimensional meteorological factor data, including rainfall data, flow rate data, temperature data, wind speed data, evapotranspiration data, and geographic data; initialize X. .

[0061] 2) Randomly select 80% of the data as the training set and 20% as the test set.

[0062] 3) Use a sliding window and day-to-day cross-validation method to preprocess the data into X.

[0063] 4) Input the preprocessed data into the model for training. .

[0064] 5) Iteratively update the parameters of the LUBE fully connected layer of the network using the ADAM optimization method. and Until now At that time, take The training then ended.

[0065] 6) Criteria based on effective prediction of coverage width .

[0066] The above algorithm trains the model for interval prediction by introducing the CWC index, a method for predicting upper and lower boundary intervals.

[0067] Step 4: Use the test set to evaluate the performance of the spatiotemporal graph-based convolutional rainfall-runoff interval prediction model.

[0068] The model performance was evaluated using two evaluation criteria: root mean square error (RMSE) and median absolute error (MedAE).

[0069] The evaluation criteria formula is as follows:

[0070] Root Mean Square Error (RMSE):

[0071]

[0072] absolute median difference MedAE:

[0073]

[0074] Interval Forecasting Indicator (CWC):

[0075]

[0076] in: This represents the flow rate observation of the i-th sample. This represents the predicted flow rate value for the i-th sample. This represents the number of test samples, where n represents the nth sample in the test set. , These represent the flow observations for the 1st and nth samples, respectively. , Let represent the predicted flow values ​​for the 1st and nth samples, respectively. PINAW represents the width of the confidence interval for the interval prediction, and PICP represents the probability that the confidence interval for the interval prediction covers the observed value. This is a hyperparameter.

[0077] Step 5: Input the preprocessed current hydrological data into the spatiotemporal graph convolutional rainfall-runoff interval prediction model, and output the flow rate at the watershed outlet section at the k-th time in the future, which is the flow rate at the k-th hour in the future.

[0078] In the actual prediction process, the newly arrived hydrological data also needs to be preprocessed. The processed data is then used as the input to the prediction model, and the flow rate at the outlet section of the basin at time k is the model output. That is, the flow rate that this method can predict for the next k hours is the flow rate.

[0079] The above description is only a preferred embodiment of the present invention. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the principle of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A method for predicting rainfall-runoff intervals based on spatiotemporal graph convolution, characterized in that, Includes the following steps: (1) Store the hydrological data collected in advance from each station in the study watershed into the hydrological history database; (2) Preprocess the historical hydrological data, and then divide the preprocessed data into training set and test set according to the hold-out method; (3) Construct a spatiotemporal graph convolutional rainfall-runoff interval prediction model and train it using a training set. Adjust the prediction model parameters to make the prediction model converge. The prediction model construction includes four processes: homogeneous graph generation, temporal attention convolution, spatial graph convolution, and interval prediction. By constructing a homogeneous graph based on physical mechanisms, the temporal attention convolution and spatial graph convolution methods are used to simulate the watershed state change process according to the monitored sub-basin characteristics from a spatiotemporal perspective, thereby realizing interval prediction. (4) Use the test set to evaluate the performance of the spatiotemporal graph convolutional rainfall-runoff interval prediction model; (5) The preprocessed current hydrological data is used as the input to the spatiotemporal map convolutional rainfall-runoff interval prediction model, and the flow rate at the watershed outlet section at the k-th time in the future is the model output, that is, the flow rate at the k-th hour in the future; Step (3) involves generating a homogeneous graph by inferring the local or global state of the spatial graph based on the state of the nodes and their connectivity, and using prior knowledge to constrain the estimation of the system. ； in, This represents the connectivity between various site objects within a homogeneous graph. Characteristics representing simple objects; Indicates that it has been selected for estimation. A collection of objects; The interval prediction in step (3) is used to quantify the uncertainty of the prediction result and provide the probability confidence that the predicted object may appear within the prediction interval. The formula is as follows: ； Wherein, PINAW represents the width of the confidence interval for interval prediction, and PICP represents the probability that the confidence interval for interval prediction covers the observed value. For hyperparameters; The ADAM optimization method is applied to the interval prediction method, based on ADAM. The optimization algorithm is as follows: Input high-dimensional meteorological factor data, including rainfall data, flow rate data, temperature data, wind speed data, evapotranspiration data, and geographic data; initialize X. The data is preprocessed to X using a sliding window and forward chain cross-validation method; the preprocessed data is then input into the model for training. The parameters of the LUBE fully connected layer in the network are iteratively updated using the ADAM optimization method. and Until now At that time, take The training then ended.

2. The method for predicting rainfall-runoff intervals based on spatiotemporal graph convolution as described in claim 1, characterized in that, The hydrological data mentioned in step (1) includes historical rainfall data, historical flow data of river outlet sections, historical evaporation data of the basin, historical temperature data of the basin, and historical wind speed data of the basin.

3. The method for predicting rainfall-runoff intervals based on spatiotemporal graph convolution as described in claim 1, characterized in that, Step (2) involves preprocessing historical hydrological data, including data completion, anomaly correction, and data normalization. Data completion uses Kriging interpolation. Anomaly correction replaces individual anomalous data with the average of the time before and after the same station, and consecutive anomalous data replaces the average of adjacent stations at the same time. Data normalization is Min-max standardization.

4. The method for predicting rainfall-runoff intervals based on spatiotemporal graph convolution as described in claim 1, characterized in that, The temporal attention convolution mentioned in step (3) introduces the attention mechanism into the temporal convolutional network (TCN) model.

5. The method for predicting rainfall-runoff intervals based on spatiotemporal graph convolution as described in claim 1, characterized in that, The spatial graph convolution in step (3) uses the Chebyshev polynomial first-order approximation method to simplify the calculation. The calculation process is as follows: ； Among them, the largest eigenvalue ; ;in, Let be a vector of polynomial coefficients. For ease of calculation, take . For a node in the graph at a certain moment, a certain feature and adjacency matrix Obtain the Laplace matrix ,in The degree matrix is ​​obtained by the following formula: ； Where K=1; after activation function After processing, a spatiotemporal feature matrix processed by spatiotemporal graph convolution can be obtained. : ； in, This indicates a ReLU activation operation. ; This represents the hidden state obtained after temporal convolution; after spatiotemporal graph convolution, information from the input features in different dimensions is fused into the spatiotemporal feature matrix. In this process, the output layer utilizes a fully connected network to predict the output.

6. The method for predicting rainfall-runoff intervals based on spatiotemporal graph convolution as described in claim 1, characterized in that, The implementation process of step (4) is as follows: Root Mean Square Error (RMSE): ； absolute median difference MedAE: ； Interval Forecasting Indicator (CWC): ； in: This represents the flow rate observation of the i-th sample. This represents the predicted flow rate value for the i-th sample. This represents the number of test samples, where n represents the nth sample in the test set. , These represent the flow observations for the 1st and nth samples, respectively. , Let represent the predicted flow values ​​for the 1st and nth samples, respectively. PINAW represents the width of the confidence interval for the interval prediction, and PICP represents the probability that the confidence interval for the interval prediction covers the observed value. This is a hyperparameter.

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