An urban waterlogging prediction method based on a quadratic isomorphic modal decomposition GRU model

Abstract

The application provides a city waterlogging prediction method based on a quadratic isomorphism modal decomposition GRU model, uses the EMD-GRU model which has relatively strong nonlinear feature extraction capability and sequence modeling capability, so that the nonlinear and non-stationary data can be better processed, and therefore the prediction accuracy and stability are improved. Meanwhile, the rainfall data used in the city waterlogging prediction usually contains certain randomness and uncertainty, therefore, the stationary treatment is carried out on the rainfall data, so that the random error and uncertainty can be reduced to the minimum, and therefore the accuracy and reliability of the prediction result are improved.

Description

Technical Field

[0001] This invention relates to the field of urban flooding forecasting technology, and in particular to an urban flooding forecasting method based on a quadratic isomorphic mode decomposition (GRU) model. Background Technology

[0002] With increasing urbanization and expanding urban areas, asphalt and concrete roads are becoming more prevalent. Large areas of concrete pavement have poor permeability, and are frequently affected by rainfall, leading to urban flooding. To prevent urban flooding from endangering people's lives and property, it is essential to predict and warn of urban floodwater depth. Current urban floodwater depth prediction technologies primarily employ mechanistic models.

[0003] There are many traditional urban stormwater mechanism models, such as SWMM, STORM, DR3M-QUAL, MOUSE, InfoWorks, SUSTAIN, SWC and other models. As for the SWMM model, it can simulate the operation of urban drainage system under rainfall conditions and predict parameters such as rainwater flow, sewage flow, and water level.

[0004] Existing technical solutions have various drawbacks. In the process of constructing the mechanism model, data such as pipeline network data, GIS data, and historical water depth and rainfall are required. Moreover, pipeline network data and GIS data are difficult to obtain, which affects the promotion and use of these models. Summary of the Invention

[0005] In view of this, the purpose of this invention is to provide an urban flooding forecasting method based on the quadratic isomorphic mode decomposition GRU model, which only requires historical water depth and rainfall data, and has strong nonlinear feature extraction capabilities and flooding time series data modeling capabilities. It can better handle nonlinear and nonstationary data, and improve prediction accuracy and stability.

[0006] To achieve the above objectives, the present invention adopts the following technical solution: a method for predicting urban flooding based on a quadratic isomorphic mode decomposition (GRU) model, comprising the following steps:

[0007] Step 1: Obtain rainfall and water depth data at the monitoring station using sensors installed at the monitoring station;

[0008] Step 2: First, perform correlation analysis on the rainfall and water level data in the data, select the feature set with high correlation, and then use the isolated forest algorithm to find outliers in the data.

[0009] Step 3: Handle missing and outlier values ​​in the data, and then divide the data into training and test sets;

[0010] Step 4: Use the EMD method to perform mode decomposition on the rainfall data. Empirical mode decomposition technology can stabilize non-stationary rainfall data.

[0011] Step 5: Lasso feature selection and quadratic isomorphic mode decomposition;

[0012] Step 6: Data normalization;

[0013] Step 7: Build and train the GRU model;

[0014] Step 8: Predict future water levels using future rainfall data.

[0015] Step 9: GRU model evaluation.

[0016] In a preferred embodiment, step 2 specifically comprises:

[0017] Step 21, data correlation analysis; organize the station's water level data and rainfall data into the same table, and perform correlation analysis on the integrated data using the Pearson correlation coefficient.

[0018] The Pearson correlation coefficient is defined as:

[0019]

[0020] Where cov is the covariance, σ is the standard deviation, X represents the independent variable, Y represents the dependent variable, X represents rainfall, and Y represents water level;

[0021] The equation for calculating the Pearson correlation coefficient is shown below:

[0022]

[0023]

[0024]

[0025] Substituting the above formula into the definition, we get...

[0026]

[0027] Where n is the sample size and r is the correlation coefficient;

[0028] This allows us to calculate the correlation coefficient between station rainfall data or areal rainfall data and water level data, and select a feature set with high correlation.

[0029] Step 22, find outliers; use the Isolation Forest algorithm to detect whether outliers exist;

[0030] First, the rainfall and water depth datasets are randomly divided into datasets X1, X2, ..., Xn. The model builds decision trees Y1, Y2, ..., Yn based on the randomly divided datasets. Then, the model randomly selects the maximum and minimum values ​​in the rainfall or water level feature set as split values ​​to isolate outliers, making the paths of abnormal data points in the tree shorter, thus separating them from other normal data. Using ensemble learning, the above steps are repeated multiple times to complete the construction of the isolation forest. Based on the anomaly score, it is determined whether a point is an outlier, and finally, the outlier values ​​are obtained.

[0031] The parameters of the isolated forest model are set as follows: the number of trees n_estimators is 100, the outlier contamination rate is 0.01, and the seed random_state of the random number generator is 0. The model is then trained to obtain the isolated forest model. The isolated forest model is then used to detect outliers: the data is input into the model for prediction, and if the value is -1, it is an outlier. Finally, all outliers are output.

[0032] In a preferred embodiment, step 3 specifically comprises:

[0033] Step 31: If missing values ​​occur for several consecutive days, delete the missing values;

[0034] Step 32, outlier handling; The outliers found in Step 2 using the Isolation Forest algorithm are handled as follows: Locate the outlier and delete it; Sum the two values ​​before and after the outlier and average them to fill the position.

[0035] Step 33, Dataset Splitting; the first 70% of the example data is used as the training set, and the last 30% is used as the test set.

[0036] In a preferred embodiment, step 4 specifically involves:

[0037] Step 41: Find all the maximum and minimum points of the original rainfall time series x(t), and fit the upper envelope U(t) and lower envelope L(t) for all extreme points using cubic spline interpolation.

[0038] Step 42, calculate the mean M(t) of the upper and lower envelopes;

[0039] M(t)=(U(t)+L(t)) / 2 (6)

[0040] Step 43: Subtract the mean envelope from the original sequence to obtain the intermediate sequence h(t);

[0041] h(t)=x(t)-M(t) (7)

[0042] Step 44: Determine whether h(t) satisfies the two constraints of the IMF. If it does, it is an IMF component. If it does not, return to step 1 and iterate repeatedly.

[0043] Step 45: Assuming h(t) is an IMF component and is denoted as IMF1, repeat steps 1-4 to decompose M(t) as the original sequence to obtain the next IMF component IMF2, until the residual component is a monotonic function or a constant, then stop the decomposition.

[0044] After decomposition, the original sequence x(t) is represented as:

[0045] x(t)=∑IMF(i)+res (8)

[0046] After EMD processing, the obtained modal feature data is added to the dataset, and the original rainfall data and the decomposed IMF map are plotted. The last component after decomposition is the residual component, denoted as res.

[0047] In a preferred embodiment, step 5 specifically comprises:

[0048] Lasso Feature Selection: The IMF components after EMD decomposition are subjected to Lasso selection to obtain multiple selected IMF components. The rainfall IMF components after EMD decomposition are used as a set of features to be selected. Each feature is standardized, and the data is trained using the Lasso model. The complexity of the model is penalized by adding an L1 regularization term to the objective function to obtain the feature coefficients corresponding to each feature. If the feature coefficient is 0, the feature is discarded. Features are selected in descending order of their feature coefficients.

[0049] rt1, rt2, ..., rt9 are used as a set of features to be selected and then fed into the Lasso model for filtering. Finally, the rt6 component is selected.

[0050] Two EMD decompositions: The preprocessed rainfall and water level data are subjected to EMD decomposition. After the important feature rt6 is screened out by Lasso, rt6 is subjected to EMD decomposition again to obtain the modal data of rt6. Then, Lasso screening is performed on it to finally obtain the important features of rt6.

[0051] This step yields two sets of data: feature data obtained from the original data after EMD decomposition and Lasso filtering, and feature data obtained from rt6 after EMD decomposition and Lasso filtering.

[0052] In a preferred embodiment, step 6 specifically involves: normalizing the preprocessed data and the two sets of features processed in steps 4 and 5 using the min-max normalization method for subsequent model training; the normalization formula is as follows:

[0053]

[0054] x refers to the value of the data before normalization, x' refers to the value of the data after normalization, max(X) is the maximum value of the data, and min(X) is the minimum value of the data.

[0055] In a preferred embodiment, step 7 specifically involves: setting up a GRU model with two GRU layers, the first GRU layer having 250 GRU neurons and the second GRU layer having 200 GRU neurons. During training, the GRU neurons learn how to process the input data and generate a hidden state vector h. The cell state c, along with the hidden state vector h, is transmitted to the next layer. Each GRU unit contains multiple gating units for controlling the flow and updating of data. The sigmoid function is set as the activation function to control the on / off state of the gating units. The training process of the GRU model will involve 100 iterations, with each result being Yi. The Adam optimization function is set, and the Adam algorithm is used to update the weight parameters. The fully connected layer has only one neuron, which receives all inputs from the previous layer and calculates a single output value. The three sets of data obtained in step 6 are used for training, resulting in three prediction models.

[0056] In a preferred embodiment, step 8 specifically comprises:

[0057] Step 81: Insert the collected future rainfall data into the last row of the original data and perform EMD decomposition together with the original data;

[0058] Step 82: Perform Lasso filtering on the decomposed data to filter out important features;

[0059] Step 83: Perform EMD decomposition on the selected features again, and then perform Lasso screening to further screen important features.

[0060] Step 84, the same method as in step 6, normalizes the selected features for subsequent prediction;

[0061] Step 85: Input the processed rainfall characteristics and the original rainfall data into the urban flooding prediction model for prediction, and then perform inverse normalization on the predicted values. The predicted data in the last row is a predicted value of the future water level.

[0062] In a preferred embodiment, step 9 specifically involves: using the three models obtained in step 7 to predict the data in the test set, visualizing the prediction results, comparing them with the true values, and plotting the fitting curves; plotting the MSE-loss curves of the three models, and using the mean absolute error of MAE, mean squared error of MSE, mean absolute percentage error of MAPE, and R2 as evaluation indicators to select the model with the best fitting effect.

[0063] The calculation formulas for each evaluation indicator are as follows:

[0064]

[0065]

[0066]

[0067]

[0068] Where y i and t i Let S1 and S2 represent the predicted value and true label of the i-th sample, respectively, n represent the total number of samples in the test set, SSR represent the regression sum of squares, and SST represent the total sum of squares.

[0069] Compared with the prior art, the present invention has the following beneficial effects:

[0070] 1. The EMD-GRU model can extract features from nonlinear and nonstationary data, and has a stronger ability to extract nonlinear features. It can better capture the causes of urban flooding and improve prediction accuracy and stability.

[0071] 2. The EMD-GRU model has high accuracy and stability, and can more accurately predict the time and location of urban flooding, providing a more precise basis for decision-making in urban flood prevention and control. Attached Figure Description

[0072] Figure 1 This is a detailed flowchart of a preferred embodiment of the present invention;

[0073] Figure 2 This is a flowchart of an isolated forest outlier detection according to a preferred embodiment of the present invention;

[0074] Figure 3 This is a water level-rainfall distribution diagram before pretreatment, according to a preferred embodiment of the present invention.

[0075] Figure 4 This is an index of water level anomalies after missing value processing in a preferred embodiment of the present invention.

[0076] Figure 5This is a distribution diagram of outlier values ​​in water level data after missing value processing, according to a preferred embodiment of the present invention.

[0077] Figure 6 This is a pre-processed water level-rainfall distribution map of a preferred embodiment of the present invention;

[0078] Figure 7 This is an in-depth modal component diagram of a preferred embodiment of the present invention;

[0079] Figure 8 This is a description diagram of Lasso feature selection in a preferred embodiment of the present invention;

[0080] Figure 9 This is a flowchart of the two-stage EMD decomposition process according to a preferred embodiment of the present invention;

[0081] Figure 10 This is a preferred embodiment of the GRU model of the present invention;

[0082] Figure 11 This is a flowchart of a preferred embodiment of the present invention for predicting urban flooding;

[0083] Figure 12 This is a GRU model fitting diagram of the original data in a preferred embodiment of the present invention;

[0084] Figure 13 This is a GRU model fitting diagram of the EMD decomposition features in a preferred embodiment of the present invention.

[0085] Figure 14 This is a fitting diagram of the GRU model for the secondary EMD decomposition features of a preferred embodiment of the present invention;

[0086] Figure 15 This is a graph showing the mse-loss curve of the original data GRU model in a preferred embodiment of the present invention.

[0087] Figure 16 This is a graph of the mse-loss curve of the GRU model for EMD decomposition features in a preferred embodiment of the present invention.

[0088] Figure 17 The image shows the mse-loss curve of the GRU model for the secondary EMD decomposition feature in a preferred embodiment of the present invention. Detailed Implementation

[0089] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0090] It should be noted that the following detailed descriptions are illustrative and intended to provide further explanation of this application. Unless otherwise specified, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application pertains.

[0091] It should be noted that the terminology used herein is for the purpose of describing particular implementations only and is not intended to limit the exemplary implementations according to this application; as used herein, the singular form is intended to include the plural form as well, unless the context clearly indicates otherwise; furthermore, it should be understood that when the terms “comprising” and / or “including” are used in this specification, they indicate the presence of features, steps, operations, devices, components and / or combinations thereof.

[0092] This invention provides an urban flooding forecasting method based on a quadratic isomorphic mode decomposition (GRU) model, offering predictive and early warning capabilities for urban flooding depth. The detailed process is as follows: Figure 1 As shown;

[0093] Step 1: Obtain Data

[0094] The rainfall and water depth data at the monitoring station are obtained by sensors installed at the waterlogging monitoring station.

[0095] Step 2: Exploratory Data Analysis

[0096] First, a correlation analysis was performed on the rainfall (divided into station rainfall and areal rainfall) and water level data in the data to select the feature set with high correlation. Then, the isolated forest algorithm was used to find outliers in the data.

[0097] Step 2.1 Data Correlation Analysis

[0098] The water level data and rainfall data of the stations are organized into the same table, and correlation analysis is performed on the integrated data. In this invention, the Pearson correlation coefficient is used for correlation analysis.

[0099] The Pearson correlation coefficient is defined as:

[0100]

[0101] Where cov is the covariance, σ is the standard deviation, X represents the independent variable, and Y represents the dependent variable. Here, X represents rainfall and Y represents water level.

[0102] The equation for calculating the Pearson correlation coefficient is shown below:

[0103]

[0104]

[0105]

[0106] Substituting the above formula into the definition, we get...

[0107]

[0108] Where n is the sample size and r is the correlation coefficient.

[0109] This allows us to calculate the correlation coefficient between station rainfall data or areal rainfall data and water level data, and select feature sets with high correlation.

[0110] Step 2.2 Find outliers

[0111] The process of detecting outliers using the Isolation Forest algorithm is as follows: Figure 2 As shown;

[0112] This invention first randomly divides the rainfall and water depth datasets into datasets X1, X2, ..., Xn. The model then builds decision trees Y1, Y2, ..., Yn based on these random divisions. Next, the model randomly selects the maximum and minimum values ​​from the rainfall or water level feature sets as split points to isolate outliers, shortening the paths of abnormal data points within the tree and thus separating them from other normal data. Using ensemble learning, the above steps are repeated multiple times to construct an isolated forest. Finally, anomaly scores are used to determine whether a point is an outlier, ultimately identifying the outlier values.

[0113] In the case of this invention, the parameter values ​​of the isolated forest model are set as follows: n_estimators (number of trees) is 100, contamination (percentage of outliers) is 0.01, and random_state (seed of the random number generator) is 0. The model is then trained to obtain the isolated forest model. The isolated forest model is then used to detect outliers: the data is input into the model for prediction, and if the value is -1, it is an outlier. Finally, all outliers are output.

[0114] Step 3 Data Preprocessing

[0115] Missing and outlier values ​​in the data are handled, and then the training and test sets are divided.

[0116] Step 3.1 Missing Value Handling

[0117] Since rainfall and water level data come from sensors at monitoring stations, they are easily affected by the surrounding environment within the city, resulting in poor data quality. In cases where there are missing values ​​for several consecutive days, the missing values ​​are deleted.

[0118] Step 3.2 Outlier Handling

[0119] The outliers identified using the Isolation Forest algorithm in step 2.2 are handled as follows:

[0120] 1. Locate the outlier and delete it.

[0121] 2. Sum the two values ​​before and after the outlier and fill the average into the position.

[0122] For example, the distribution of water level and rainfall before and after pretreatment are shown in the figure. Figure 3-6 As shown.

[0123] Step 3.3 Dataset partitioning

[0124] In this invention, the first 70% of the data is used as the training set, and the last 30% is used as the test set.

[0125] Step 4: EMD decomposition

[0126] The EMD method is used to perform mode decomposition on rainfall data. Empirical mode decomposition technology can stabilize non-stationary rainfall data.

[0127] The EMD algorithm process is as follows:

[0128] 1. Find all the maximum and minimum points of the original rainfall time series x(t), and fit the upper envelope U(t) and lower envelope L(t) for all extreme points using cubic spline interpolation.

[0129] 2. Find the mean value M(t) of the upper and lower envelopes.

[0130] M(t)=(U(t)+L(t)) / 2 (6)

[0131] 3. Subtract the mean envelope from the original sequence to obtain the intermediate sequence h(t).

[0132] h(t)=x(t)-M(t) (7)

[0133] 4. Determine whether h(t) satisfies the two constraints of the IMF. If it does, it is an IMF component. If it does not, return to step 1 and iterate repeatedly.

[0134] 5. Assuming h(t) is an IMF component and is denoted as IMF1, repeat steps 1-4 to decompose M(t) as the original sequence to obtain the next IMF component IMF2, until the residual component is a monotonic function or a constant, then stop the decomposition.

[0135] After decomposition, the original sequence x(t) can be represented as:

[0136] x(t)=∑IMF(i)+res (8)

[0137] After EMD processing, the obtained modal feature data is added to the dataset, and the original rainfall data and the decomposed IMF map are plotted. The last component after decomposition is the residual component, denoted as res.

[0138] The intrinsic modal component diagram of the present invention is as follows: Figure 7 As shown;

[0139] Step 5: Lasso Feature Selection and Quadratic Isomorphic Mode Decomposition

[0140] The Lasso feature selection process is as follows: Figure 8 As shown;

[0141] The IMF components derived from the EMD decomposition are then subjected to Lasso filtering to obtain multiple filtered IMF components. These rainfall IMF components are used as a set of potential features. Each feature is standardized, and the data is trained using a Lasso model. An L1 regularization term is added to the objective function to penalize the model's complexity, resulting in feature coefficients for each feature. If a feature coefficient is 0, that feature is discarded. Features are then selected sequentially from largest to smallest based on their coefficients.

[0142] In this case, we put rt1, rt2, ..., rt9 into the Lasso model as a set of features to be selected, and finally selected the rt6 component.

[0143] This invention proposes a two-stage isomorphic mode decomposition, i.e., performing two EMD decompositions, the process of which is as follows: Figure 9 As shown:

[0144] The preprocessed rainfall and water level data were decomposed using EMD. After Lasso filtering to identify the important feature rt6, rt6 was decomposed again using EMD to obtain the modal data of rt6. Lasso filtering was then performed on rt6 to finally obtain the important features of rt6.

[0145] After this step, we obtained two sets of data: feature data obtained from the original data after EMD decomposition and Lasso filtering, and feature data obtained from rt6 after EMD decomposition and Lasso filtering.

[0146] Step 6: Data Normalization

[0147] The min-max normalization method is used to normalize the preprocessed data and the two sets of features processed in steps 4 and 5, for subsequent model training. The normalization formula is as follows:

[0148]

[0149] x refers to the value of the data before normalization, x' refers to the value of the data after normalization, max(X) is the maximum value of the data, and min(X) is the minimum value of the data.

[0150] Step 7: Build and train the model

[0151] Establish a GRU model, the structure of which is as follows: Figure 10 As shown:

[0152] This model employs two GRU layers: the first layer has 250 GRU neurons, and the second layer has 200 GRU neurons. During training, the GRU neurons learn how to process the input data and generate a hidden state vector h. The cell state c, along with the hidden state vector h, is transmitted to the next layer. Each GRU unit contains multiple gating units to control the flow and updates of data. A sigmoid function is used to control the on / off state of the gating units. Due to the larger number of neurons in the first GRU layer, its expressive power is stronger. Simultaneously, the smaller number of neurons in the second GRU layer results in relatively lower computational complexity. This setup balances the model's expressive power and computational efficiency to some extent, improving model performance. The GRU model training process involves 100 iterations, with each iteration producing the result Y. i Set up the Adam optimization function and use the Adam algorithm to update the weight parameters; the fully connected layer has only one neuron, which will receive all the inputs from the previous layer and compute a single output value.

[0153] The parameter settings for the model are shown in the table below:

[0154] Table 1 GRU model parameters

[0155]

[0156] This example uses the three sets of data obtained in step 6 to train three prediction models.

[0157] Step 8: Flooding Forecast

[0158] The general process of using future rainfall data to predict future water levels is as follows: Figure 11 As shown;

[0159] 1. Insert the collected future rainfall data into the last row of the original data and perform EMD decomposition together with the original data. The insertion method is shown in the table below:

[0160] Table 2. Illustration of where to insert future rainfall and water level data.

[0161]

[0162] The decomposed EMD table is shown below:

[0163] Table 3. Schematic diagram of future rainfall data after EMD decomposition.

[0164]

[0165] 2. Perform Lasso filtering on the decomposed data to filter out important features.

[0166] 3. Perform EMD decomposition on the selected features again, and then perform Lasso screening to further filter important features.

[0167] 4. Similar to step 6, normalize the selected features for subsequent prediction.

[0168] 5. Input the processed rainfall characteristics and the original rainfall data into the urban flooding prediction model for prediction, and then inversely normalize the predicted values. The predicted data in the last row is a predicted value of the future water level.

[0169] Step 9: Model Evaluation

[0170] The three models obtained in step 7 are used to predict the data on the test set. The prediction results are visualized and compared with the true values ​​to plot the fitting curves. The MSE-loss curves of the three models are plotted, and the mean absolute error (MAE), mean squared error (MSE), mean absolute percentage error (MAPE), and R² are used as evaluation metrics to select the model with the best fit.

[0171] The calculation formulas for each evaluation indicator are as follows:

[0172]

[0173]

[0174]

[0175]

[0176] Where y i and t i Let S1 and S2 represent the predicted value and true label of the i-th sample, respectively, n represent the total number of samples in the test set, SSR represent the regression sum of squares, and SST represent the total sum of squares.

[0177] Step 10 Results Display

[0178] After normalizing the preprocessed data, a model is built and trained. The model's fitting effect is plotted, as shown in the following figure:

[0179] 1. The original data GRU model fitting graph is shown below. Figure 12 As shown;

[0180] 2. EMD decomposition feature GRU model fitting plot;

[0181] The preprocessed rainfall data was decomposed using EMD, and the decomposed features were filtered using Lasso. The data was then normalized, and the model was rebuilt and trained. The resulting fitting effect is shown in the figure below. Figure 13 As shown;

[0182] 3. Fitting plot of GRU model for secondary EMD decomposition features

[0183] The previously selected features are then subjected to EMD decomposition, lasso filtering, data normalization, and added to the GRU model to obtain a new fitted plot, as shown below. Figure 14 As shown;

[0184] Test set prediction evaluation metrics such as Figure 15 As shown;

[0185] 1. Evaluation metrics for the GRU model based on raw data

[0186] Table 4. Evaluation Indicators for the GRU Model Based on Original Data

[0187] Indicator values 0.000002 0.001306 4.916584 0.984553

[0188] 2. Evaluation metrics for the EMD decomposition feature GRU model, such as Figure 16 As shown;

[0189] Table 5 Evaluation Indicators of EMD Decomposition Feature GRU Model

[0190] Indicator values 0.000001 0.000771 3.01216 0.994226

[0191] 3. Evaluation metrics for the secondary EMD decomposition feature GRU model, such as... Figure 17 As shown;

[0192] Table 6 Evaluation Indicators of the GRU Model for Secondary EMD Decomposition Characteristics

[0193] Indicator values 0.0000007 0.0004212 1.1075086 0.9974895

[0194] The evaluation metrics for the three models are compared in the table below:

[0195] Table 7 Comparison of Model Indicators

[0196]

[0197]

[0198] This invention uses the EMD model to perform a stabilization process on rainfall data. Based on the frequency and amplitude of the rainfall data, the rainfall data is adaptively decomposed into a series of intrinsic mode functions (IMF1, IMF2, ..., IMFn) with the characteristics of the original rainfall data. By processing these intrinsic mode functions, useless information is filtered out, thereby achieving the purpose of noise reduction.

[0199] This invention introduces the EMD decomposition method. It decomposes the time series into multiple intrinsic mode functions (IMFs), each IMF representing a different frequency component. The introduction of the EMD decomposition method enables the EMD-GRU model to handle nonlinear and non-stationary time series.

[0200] After the first EMD decomposition, this invention uses lasso filtering to identify rt6 as a more important feature compared to other modal features. However, extracting the lasso-filtered features for modeling did not significantly improve the fitting effect. Therefore, a second EMD decomposition and lasso filtering were performed on rt6. The selected features were then used to build the model again, resulting in the best fitting effect. These two EMD decompositions further improved the accuracy and stability of the features, avoiding interference from noise and redundant features, thereby improving the model's predictive performance.

Claims

1. A method for predicting urban flooding based on a quadratic isomorphic mode decomposition (GRU) model, characterized in that, Includes the following steps: Step 1: Obtain rainfall and water level data for the monitoring station by using sensors installed at the monitoring station; Step 2: First, perform correlation analysis on the rainfall and water level data in the data, select the feature set with high correlation, and then use the isolated forest algorithm to find outliers in the data. Step 3: Handle missing and outlier values ​​in the data, and then divide the data into training and test sets; Step 4: Use the EMD method to perform mode decomposition on the rainfall data. Empirical mode decomposition technology can stabilize non-stationary rainfall data. Step 5: Lasso feature selection and quadratic isomorphic mode decomposition; Step 6: Data normalization; Step 7: Build and train the GRU model; Step 8: Use future rainfall data to predict future water levels; Step 9: GRU model evaluation; Step 5 specifically involves: Lasso Feature Selection: The IMF components after EMD decomposition are subjected to Lasso selection to obtain multiple selected IMF components. The rainfall IMF components after EMD decomposition are used as a set of features to be selected. Each feature is standardized, and the data is trained using the Lasso model. The complexity of the model is penalized by adding an L1 regularization term to the objective function to obtain the feature coefficients corresponding to each feature. If the feature coefficient is 0, the feature is discarded. Features are selected in descending order of their feature coefficients. rt1, rt2, ..., rt9 are used as a set of features to be selected and then fed into the Lasso model for filtering. Finally, the rt6 component is selected. Two EMD decompositions: The preprocessed rainfall and water level data are subjected to EMD decomposition. After the important feature rt6 is screened out by Lasso, rt6 is subjected to EMD decomposition again to obtain the modal data of rt6. Then, Lasso screening is performed on it to finally obtain the important features of rt6. After this step, two sets of data are obtained: feature data obtained from the original data after EMD decomposition and Lasso filtering, and feature data obtained from rt6 after EMD decomposition and Lasso filtering. Step 8 specifically involves: Step 81: Insert the collected future rainfall data into the last row of the original data and perform EMD decomposition together with the original data; Step 82: Perform Lasso filtering on the decomposed data to filter out important features; Step 83: Perform EMD decomposition on the selected features again, and then perform Lasso screening to further screen important features. Step 84, the same method as in step 6, normalizes the selected features for subsequent prediction; Step 85: Input the processed rainfall characteristics and the original rainfall data into the urban flooding prediction model for prediction, and then perform inverse normalization on the predicted values. The predicted data in the last row is a predicted value of the future water level.

2. The urban flooding forecasting method based on a quadratic isomorphic mode decomposition (GRU) model according to claim 1, characterized in that, Step 2 specifically involves: Step 21, data correlation analysis; organize the station's water level data and rainfall data into the same table, and perform correlation analysis on the integrated data using the Pearson correlation coefficient. The Pearson correlation coefficient is defined as: （1） in For covariance, Let X be the standard deviation, X be the independent variable, and Y be the dependent variable. X represents rainfall, and Y represents water level. The equation for calculating the Pearson correlation coefficient is shown below: （2） （3） （4） Substituting the above formulas (2)-(4) into the definition, we get: （5） in For the sample size, The correlation coefficient; This allows us to calculate the correlation coefficient between station rainfall data or areal rainfall data and water level data, and select a feature set with high correlation. Step 22, find outliers; use the Isolation Forest algorithm to detect whether outliers exist; First, the rainfall dataset and water level dataset are randomly divided into datasets X1, X2, ..., Xn. The model builds decision trees Y1, Y2, ..., Yn based on the randomly divided datasets. Then, the model randomly selects the maximum and minimum values ​​in the rainfall or water level feature set as split values ​​to isolate outliers, making the path of abnormal data points generated in the tree shorter, thereby separating them from other normal data. By using ensemble learning, the steps of randomly partitioning the dataset, building decision trees, and randomly selecting split values ​​are repeated multiple times to complete the construction of an isolated forest. The outlier score is used to determine whether a point is an outlier, and finally, outlier values ​​are obtained. The parameters of the isolated forest model are set as follows: the number of trees n_estimators is 100, the outlier contamination rate is 0.01, and the seed random_state of the random number generator is 0. The model is then trained to obtain the isolated forest model. The isolated forest model is then used to detect outliers: the data is input into the model for prediction, and if the value is -1, it is an outlier. Finally, all outliers are output.

3. The urban flooding forecasting method based on a quadratic isomorphic mode decomposition (GRU) model according to claim 1, characterized in that, Step 3 specifically involves: Step 31: If missing values ​​occur for several consecutive days, delete the missing values; Step 32, outlier handling; The outliers found in Step 2 using the Isolation Forest algorithm are handled as follows: Locate the outlier and delete it; Sum the two values ​​before and after the outlier and average them to fill the position. Step 33: Split the dataset; the first 70% of the data is used as the training set, and the last 30% is used as the test set.

4. The urban flooding forecasting method based on a quadratic isomorphic mode decomposition (GRU) model according to claim 1, characterized in that, Step 4 specifically involves: Step 41, find the original rainfall time series. For all maxima and minima, fit the upper envelope using cubic spline interpolation for all extreme points. and lower envelope ; Step 42, calculate the mean of the upper and lower envelopes. ; （6） Step 43: Subtract the mean envelope from the original sequence to obtain the intermediate sequence. ; （7） Step 44, Determine If the two constraints of the IMF are satisfied, it is an IMF component; otherwise, return to step 41 and iterate repeatedly. Step 45, assuming If M(t) is an IMF component and is denoted as IMF1, then repeat steps 41-44 to continue decomposing M(t) as the original sequence to obtain the next IMF component IMF2, until the residual component is a monotonic function or a constant, then stop the decomposition. After decomposition, the original sequence Represented as: （8） After EMD processing, the obtained modal feature data is added to the dataset, and the original rainfall data and the decomposed IMF plot are drawn. The last component after decomposition is the residual component, denoted as... .

5. The urban flooding forecasting method based on a quadratic isomorphic mode decomposition (GRU) model according to claim 1, characterized in that, Step 6 specifically involves: normalizing the preprocessed data and the two sets of features processed in steps 4 and 5 using the min-max normalization method, for use in subsequent model training; the normalization formula is as follows: （9） Refers to the value of the data before normalization. Refers to the value of the data after normalization. For the maximum value of the data, This represents the minimum value of the data.

6. The urban flooding forecasting method based on a quadratic isomorphic mode decomposition (GRU) model according to claim 1, characterized in that, Step 7 specifically involves: setting up a GRU model with two GRU layers. The first GRU layer has 250 GRU neurons, and the second GRU layer has 200 GRU neurons. During training, the GRU neurons learn how to process the input data and generate a hidden state vector h. The cell state c, along with the hidden state vector h, is transmitted to the next layer. Each GRU unit contains multiple gating units to control the flow and updating of data. The sigmoid function is set as the activation function to control the on / off state of the gating units. The training process of the GRU model will involve 100 iterations, with each result being Yi. The Adam optimization function is set, and the Adam algorithm is used to update the weight parameters. The fully connected layer has only one neuron, which will receive all inputs from the previous layer and calculate a single output value. The three sets of data obtained in step 6 were used to train the three prediction models, resulting in three prediction models.

7. The urban flooding forecasting method based on a quadratic isomorphic mode decomposition (GRU) model according to claim 6, characterized in that, Step 9 specifically involves: using the three models obtained in step 7 to predict the data in the test set, visualizing the prediction results, comparing them with the true values, and plotting the fitting curves; drawing the MSE-loss curves of the three models, and using the mean absolute error of MAE, mean square error of MSE, mean absolute percentage error of MAPE, and R2 as evaluation indicators to select the model with the best fitting effect. The calculation formulas for each evaluation indicator are as follows: （10） （11） （12） （13） in and Let S1 and S2 represent the predicted value and true label of the i-th sample, respectively, n represent the total number of samples in the test set, SSR represent the regression sum of squares, and SST represent the total sum of squares.

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