A city flood prediction method based on bayesian convolutional neural network

Abstract

The application discloses a kind of urban flood prediction methods based on bayesian convolutional neural network, comprising: collecting historical rainfall events of study area, using hydrodynamic simulation software to simulate different rainfall events to obtain maximum submerged water depth;Select the characteristic variable that influences waterlogging water depth, including 10 rainfall characteristic variables and 10 spatial characteristic variables;Considering uncertainty, a bayesian convolutional neural network prediction model is constructed;Based on loss function MAE, the model is trained;The data in the verification set are input into the trained model, and the mean of the output approximate posterior distribution is taken as the predicted value of water depth.The relationship between the characteristic variable and the target variable is calculated and analyzed, the different data are effectively fused, and the possible uncertainty source is considered.The method not only realizes the prediction of the size and range of the submerged water depth in the study area, but also quantifies the uncertainty of the prediction, providing support for real-time flood disaster management.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of flood forecasting, in particular to a city flood prediction method based on Bayesian convolutional neural network. BACKGROUND

[0002] The essence of flood forecasting is to predict the flood inundation map of the urban area, measured by flood depth. In recent years, data-driven models based on deep learning have been gradually applied to the prediction of urban stormwaterlogging by domestic and foreign researchers. For example, the existing literature: Dai Mengqi. City stormwaterlogging water depth prediction method based on deep learning, Nanjing Normal University, which generates water depth prediction feature factors as model input for spatiotemporal prediction of water depth, including rainfall, pipe network density, slope, road network density, water system density and land use type. However, the selection of this feature factor is not comprehensive enough, and the influence of hydrological conditions and surface elevation on waterlogging water depth is not considered. Among them, the slope can only reflect the local topographic changes, while the surface elevation can directly reflect the overall undulating changes of the ground surface in space, affecting the generation process of urban surface runoff. At the same time, the formation and development of flood are extremely complex, affected by meteorological and geographical factors, and the sources of its uncertainty are very complex and inevitable. This literature does not consider the uncertainty of the prediction results. SUMMARY

[0003] To solve the problems of the existing technology, such as insufficient comprehensive selection of feature factors and not considering the uncertainty of the prediction results, a city flood prediction method based on Bayesian convolutional neural network is proposed.

[0004] The present application adopts the following technical solutions:

[0005] A city flood prediction method based on Bayesian convolutional neural network, comprising the following steps:

[0006] Step 1, collect historical rainfall events in the study area, and simulate the maximum inundation water depth by water dynamics simulation software under different rainfall events;

[0007] Step 2, select feature variables affecting waterlogging water depth, including 10 rainfall feature variables and 10 spatial feature variables, and perform data preprocessing;

[0008] Step 3, consider the uncertainty to construct a Bayesian convolutional neural network prediction model

[0009] The historical rainfall events in step 1 are divided into a training set and a validation set, the 20 feature variables described in step 2 are used as inputs of the model in the training set, the maximum inundation depth values corresponding to the rainfall events obtained in step 1 are used as outputs of the model in the training set, a random Gaussian noise is added to the output item to reflect accidental uncertainty, a Student's prior distribution is set for the filter weight of each convolutional layer to reflect cognitive uncertainty, and 20 parameter values are randomly extracted as initial values of the filter weight by using the Monte Carlo sampling method;

[0010] In step 4, the model in step 3 is trained based on the loss function MAE, the MAE value between the maximum inundation depth value predicted by the Bayesian convolutional neural network and the maximum inundation depth value generated by the two-dimensional hydrodynamic model is used for back propagation training of the model, and the training is automatically terminated when the loss function no longer decreases;

[0011] In step 5, the data in the validation set are input into the model trained in step 4, the mean value of the approximate posterior distribution of the output is calculated as the predicted value of the waterlogging depth.

[0012] Further, the variance of the approximate posterior distribution of the output in step 5 is calculated, the variance is used to quantify the uncertainty and construct a confidence interval, and the interval prediction value of the waterlogging depth in the study area is obtained.

[0013] Further, the 10 rainfall feature variables described in step 2 include: rainfall time, maximum rainfall, total rainfall, the ratio of the cumulative rainfall from the start of rainfall to the peak of rainfall to the cumulative rainfall from the peak of rainfall to the end of rainfall, the ratio of the maximum rainfall change per unit time to the total rainfall, the ratio of the cumulative rainfall from the start of rainfall to 0.33T to the total rainfall, the ratio of the cumulative rainfall from the start of rainfall to 0.3T to the total rainfall, the ratio of the cumulative rainfall from the start of rainfall to 0.5T to the total rainfall, the position of the center of gravity of the rainfall process line and the position of the maximum rainfall change.

[0014] Further, the 10 spatial feature variables described in step 2 include: surface elevation, slope, slope direction, plan curvature, terrain moisture index, impervious rate, distance to drainage network, flow accumulation value, runoff accumulation value and unit slope flow accumulation value.

[0015] Further, in step 1, a one-dimensional sewer network model and a two-dimensional surface model of the study area are respectively built by using a hydrodynamic software, then the sewer network model and the surface model are coupled by using a MIKE FLOOD module to establish a coupled model, and the historical rainfall events of the study area are input into the coupled model to obtain the maximum inundation depth corresponding to different events.

[0016] Further, a convolutional attention mechanism module is introduced in the Bayesian convolutional neural network in step 3, and the convolutional attention mechanism module comprises a channel attention module and a spatial attention module, wherein the channel attention module compresses a feature map in a spatial dimension to obtain a one-dimensional vector, and the spatial attention module identifies a region with high flood risk, especially a low-lying area lower than the surrounding area, and the water depth value of the region will be focused on and extracted for repeated training.

[0017] The present application has the following advantages:

[0018] The method calculates and analyzes the relationship between the characteristic variable and the target variable, effectively fuses different data, and considers the possible sources of uncertainty, and proposes a method for predicting urban floods by using a Bayesian convolutional neural network model, which not only realizes the prediction of the size and range of the submerged water depth in the study area, but also quantifies the uncertainty of the prediction, and provides support for real-time flood disaster management. BRIEF DESCRIPTION OF DRAWINGS

[0019] Figure 1 The Bayesian convolutional neural network is used for submerged water depth prediction framework.

[0020] Figure 2 The Spearman rank correlation coefficient diagram of the spatial characteristic variable;

[0021] Figure 3 The data structure type of the spatial characteristic, wherein 1567x1834 represents the number of grid in the study area, and 10 represents the number of channels, i.e., the number of spatial characteristic variables.

[0022] Figure 4 The structure diagram of the Bayesian convolutional neural network, wherein HxW represents the resolution size, and a one-dimensional data is converted into a two-dimensional data through a fully connected layer with a size of 4096, and N f The number of convolution kernels;

[0023] Figure 5 The study area is divided into a plurality of patches with the same size.

[0024] Figure 6 The submergence map of the "20080815" rainfall event in the validation set obtained by the two-dimensional water dynamic model and the BCNN model is shown.

[0025] Figure 7 The submergence map of the "20050803" rainfall event in the validation set obtained by the two-dimensional water dynamic model and the BCNN model is shown.

[0026] Figure 8The flooding inundation map of the "19960715" rainfall event in the validation set obtained by the two-dimensional hydrodynamic model and the BCNN model is shown;

[0027] Figure 9 The scatter plot of the predicted value and the target value of the maximum inundation water depth of all grids in the study area in the "20050803" rainfall event in the validation set is shown;

[0028] Figure 10 The scatter plot of the predicted value and the target value of the maximum inundation water depth of all grids in the study area in the "20050803" rainfall event in the validation set is shown;

[0029] Figure 11 The scatter plot of the predicted value and the target value of the maximum inundation water depth of all grids in the study area in the "19960715" rainfall event in the validation set is shown;

[0030] Figure 12 The local area prediction of one of the patches in the study area is shown;

[0031] Figure 13 The local area prediction of another patch in the study area is shown;

[0032] Figure 14 The prediction water depth error and variance of one of the patches A in the study area in the rainfall event "19960715" are shown;

[0033] Figure 15 The prediction water depth error and variance of one of the patches B in the study area in the rainfall event "19960715" are shown;

[0034] Figure 16 The prediction water depth error and variance of one of the patches C in the study area in the rainfall event "19960715" are shown;

[0035] Figure 17 The prediction water depth error and variance of one of the patches D in the study area in the rainfall event "19960715" are shown;

[0036] Figure 18 The water depth prediction box plot of each checkpoint in the 95% confidence interval is shown. DETAILED DESCRIPTION

[0037] In order to make the purpose, technical scheme and technical effects of the present application clearer, the present application is further described in detail below in combination with the drawings and examples of the specification.

[0038] Example 1

[0039] The urban flood prediction method based on the Bayesian convolutional neural network is described by taking a historical rainfall event in Rushan City as an example. Figure 1 , the method comprises:

[0040] Step 1, simulate different rainfall events by hydrodynamic simulation software to obtain waterlogging inundation map, maximum inundation water depth and average inundation water depth;

[0041] A one-dimensional sewer pipe network model and a two-dimensional surface model of the research area are respectively built, and then the MIKE FLOOD module is used to couple the sewer pipe network model and the surface model to establish a coupled model, and the water exchange between the sewer system and the surface system is reflected through the coupled model.

[0042] The 5m resolution DEM elevation is obtained from the terrain TIFF raster data. In order to reflect the true elevation of the urban surface, the buildings and roads in the research area are superimposed on the basis of DEM, the buildings are raised by 5m on the original terrain, and the roads are lowered by 0.15m on the original terrain. The processed DEM data (including the building data raised by 5m on the original terrain and the road data lowered by 0.15m on the original terrain) will be input into the MIKE URBAN CS module and the MIKE 21FM module as terrain data, respectively. In the MIKE URBAN CS module, the DEM data is used to obtain the surface elevation of the inspection well; in the MIKE 21FM module, the DEM data is divided into 1567x1834 rectangular grids, and the length of the grid is consistent with the resolution of the DEM, that is, 5m.

[0043] MIKE URBAN is an independent urban drainage and integrated watershed simulation software, and the MIKE URBAN CS module in it is mainly used to simulate urban runoff and sewage discharge process. MIKE 21FM belongs to MIKE 21 software, which is mainly used for hydrodynamic simulation. The MIKE URBAN CS module and the MIKE 21FM module both need to input the data of buildings raised by 5m on the original terrain and roads lowered by 0.15m on the original terrain.

[0044] After the processed DEM data is input into the MIKE URBAN CS module and the MIKE 21FM module as terrain data, one-dimensional sewer pipe network model and two-dimensional surface model are obtained, and pipe flow process simulation and urban surface, river, lake and other free surface flow water body flow direction simulation are carried out respectively. The MIKE FLOOD module is used to dynamically couple the one-dimensional sewer pipe network and the two-dimensional surface model, and the mutual influence between the ground water and the urban pipe network is reflected through the manhole connection mode. When the pipe network node overflows, the water enters the two-dimensional overland flow model to calculate the inundation condition, and when the full pipe flow state ends, the water quantity of the two-dimensional model returns to the pipe network for calculation.

[0045] This embodiment collects the rainstorm event set in the past thirty years in the history of Rushan City, a total of 33 rainfall events are selected, the rainfall events are input into the coupling model to obtain the waterlogging inundation map corresponding to different events, and the maximum inundation water depth and the average inundation water depth are shown in Table 1. The maximum inundation water depth and the average inundation water depth in Table 1 are obtained from the waterlogging inundation map, and the remaining data in Table 1 is the measured record of the meteorological bureau.

[0046] Table 1: Strong rainfall events in Rushan City from 1992 to 2022

[0047]

[0048]

[0049] Step 2, analyze the characteristic variables affecting the water depth of waterlogging;

[0050] Step 2.1, spatial distribution correlation of waterlogging water depth

[0051] In order to verify the spatial correlation of the waterlogging distribution in the study area, the global Moran's I index is used to analyze the global spatial autocorrelation of the waterlogging water depth, i.e. the maximum inundation water depth, simulated in step 1.

[0052] From the 33 rainfall events, 5 events are randomly selected, and the maximum inundation water depth in the grid is taken as the waterlogging water depth value. The global Moran's I index is calculated respectively to explore the spatial distribution pattern of waterlogging, and the results are shown in Table 2.

[0053] Table 2: Calculation results of global Moran's I index of different rainstorm events

[0054] Moran's index I z value p value 20080817 0.214 3.15 0 20070719 0.041 2.68 0 20120705 0.582 4.74 0 19960715 0.384 8.75 0 20202723 0.284 2.32 0

[0055] From Table 2, it can be seen that the Moran index I of the 5 rainstorm events in the study area is greater than 0 and the z value passes the significance test, which proves that the waterlogging water depth in the study area has significant spatial autocorrelation, and the spatial distribution is characterized by high value aggregation.

[0056] The z value is a statistical quantity obtained by standardization, which measures the difference between the spatial pattern of actual observation data and the random distribution pattern. The larger the z value, the higher the spatial autocorrelation. The p value is the value of hypothesis testing. The null hypothesis is that there is no spatial autocorrelation in the study content, and p<0.01 means that the null hypothesis is rejected at a 99% confidence interval.

[0057] The study of step 2.1 proves that urban waterlogging has obvious spatial aggregation effect. According to the research of relevant scholars, the distribution pattern of urban flood is mainly affected by topographic conditions (such as surface roughness, relative elevation, slope), climate conditions (such as extreme rainfall), landscape pattern (such as land cover type, three-dimensional building pattern) and human activities (such as drainage system, urban planning).

[0058] Step 2.2 selection of characteristic variables affecting water depth of waterlogging

[0059] According to the previous relevant literature and the difficulty of data acquisition, the characteristic variables affecting the water depth of waterlogging are selected from the following five aspects: rainfall, topographic factors, hydrological conditions, drainage capacity and land use type.

[0060] The rainfall characteristic variables are selected as the rainfall time, the maximum rainfall and the total rainfall to measure the intensity. In order to distinguish the time variability of different rainfall events, the ratio of the cumulative rainfall from the beginning of rainfall to the peak of rainfall to the cumulative rainfall from the peak of rainfall to the end of rainfall, the ratio of the maximum rainfall change per unit time to the total rainfall, the ratio of the cumulative rainfall from the beginning of rainfall to 0.33T to the total rainfall, the ratio of the cumulative rainfall from the beginning of rainfall to 0.3T to the total rainfall, the ratio of the cumulative rainfall from the beginning of rainfall to 0.5T to the total rainfall are constructed according to the research results of Wartalska et al. In addition, the center of gravity position of the rainfall process line and the position of the maximum rainfall change are selected to measure the uneven change of rainfall with time.

[0061] The topographic factors, hydrological conditions, drainage capacity and land use type have spatial variability, so they are collectively referred to as spatial characteristics, and the rationality of the selection of spatial characteristic variables needs to be verified.

[0062] Step 2.3 correlation test of spatial characteristic variables

[0063] The Spearman rank correlation coefficient is used to measure the strength of the monotonic relationship between the characteristic variables and the predicted variables, and to verify the rationality of the variable selection. This method is the prior art and will not be described here.

[0064] Finally, the spatial characteristic variables are determined as the surface elevation, slope, slope direction, plane curvature, terrain humidity index, impervious rate, distance to drainage pipe network, flow cumulative value, runoff cumulative value and unit slope flow cumulative value by the Spearman rank correlation coefficient. The Spearman rank correlation coefficient between the spatial characteristic variables and the corresponding maximum water depth is shown in Figure 2 , in which the slope direction is quantitatively represented by sine and cosine functions, respectively, which are ASP1 and ASP2.

[0065] The terrain factors include surface elevation, slope, aspect and plan curvature, the hydrological condition factors include topographic wetness index, flow accumulation value, runoff accumulation value and flow accumulation value per unit slope, the drainage capacity factors include the distance to drainage network, and the land use type variables include impervious rate.

[0066] The existence of a large number of impervious surfaces in urban areas will prevent the process of rainwater infiltration, thus forming runoff on the ground surface quickly; while other different land use types represent different impervious rates and vegetation cover conditions, which also affect the runoff and confluence processes of the ground surface to a certain extent, leading to different degrees of waterlogging. In order to reflect the influence of different land use types on the runoff generation process, the impervious rate is used to measure the land use type.

[0067] Step 3, considering uncertainty, constructing a Bayesian convolutional neural network prediction model;

[0068] First, the structure type of the data is unified, and the rainfall characteristic variable is converted into a two-dimensional data type. The spatial characteristic variable and the converted rainfall characteristic variable are used as the input of the model. The data is normalized, and all the data is scaled to 0-1 or -1 to 1.

[0069] The target data set (the maximum submerged water depth in Table 1) is truncated, and the water depth less than 0.05 m is truncated. Then, the sample set is divided, and the three rainfall events of 20080815, 20050803 and 19960715 are selected as the validation set, and the remaining events are used as the training set.

[0070] In order to limit the size of the model input, the study area is divided into multiple patches of the same size, and the proportion of different patches is selected. In order to generate enough sample data, a method similar to "data enhancement" is adopted. The study area is divided into multiple patches of the same size, and the input of the Bayesian convolutional neural network prediction can only be a square, as shown in Figure 5 The patch with yellow line in the figure is the area outside the study area, and the patch with blue line is located in the study area. After excluding those patches whose entire area is outside the study area, the remaining patches are processed as follows:

[0071] · If the blue area accounts for more than 60% of the total area, it is included in this study, and the remaining patches are not processed.

[0072] Consider;

[0073] · All data in the yellow area of the patch are set to 0.

[0074] As shown in Figure 4The Bayesian convolutional neural network structure mainly includes an input layer, a convolutional layer, an activation layer, a pooling layer, and a fully connected layer. The hyperparameters involved in the network mainly include the input layer size, the convolution kernel size, the number of convolution kernels, the learning rate, the optimizer, the initial learning rate, the training batch, the loss function, and the number of iterations.

[0075] A convolutional attention mechanism module is introduced into the Bayesian convolutional neural network, which includes a channel attention module (CAM) and a spatial attention module (SAM). The CAM compresses a feature map in the spatial dimension to obtain a one-dimensional vector, as shown in FIG. 2, and then uses the SAM to identify areas at high risk of flood risk, especially low-lying areas lower than the surrounding areas. The water depth values of these parts will be focused on and extracted for repeated training. Figure 3

[0076] The convolutional layer does not highlight the features of the key areas when extracting features from the input data. The convolutional attention mechanism module can calculate attention weights based on the extracted feature map, that is, the feature map obtained by convolution is input into the transformation to output an attention weight matrix corresponding to the feature map. Each element of the weight matrix corresponds to the importance degree of the corresponding position in the original feature map, that is, a higher attention weight is given to important areas. The weight value is not simply determined as a fixed value, but is described as the possibility of the weight based on a probability distribution. In addition, the attention weight matrix calculated is multiplied with the feature map obtained by the previous convolution to perform a weighting operation on the feature map, so that the features of the key attention areas in the original feature map are strengthened. The addition of the convolutional attention mechanism module significantly improves the feature extraction capability of the model without increasing the amount of calculation.

[0077] The training set is input into the model for training, and random Gaussian noise is added to the output item to reflect accidental uncertainty. The input item is an image corresponding to different feature variables, which contains the numerical value of a certain feature variable in the study area. The output item is the maximum submerged water depth.

[0078] A Student's prior distribution is set for the filter weight of each convolutional layer to reflect cognitive uncertainty. Monte Carlo sampling is used to randomly extract 20 parameter values as the initial values of the filter weights, and the uncertainty of the model is forward propagated.

[0079] Here, the initial value refers to the initial weight of the convolution kernel, that is, the specific numerical value in the convolution kernel used to extract different feature variables. The number of parameter values corresponds to the number of feature variables, which is 20, that is, 10 rainfall feature variables and 10 spatial feature variables determined in step 2.

[0080] ​The model is trained based on the loss function MAE, and the MAE value between the maximum submerged water depth value predicted by the Bayesian convolutional neural network and the maximum submerged water depth value generated by the two-dimensional hydrodynamic model is back-propagated to train the model. After each round of training, a test is performed, and the accuracy of the training set and the validation set is calculated. Due to the use of an automatic stopping mechanism, when the loss function no longer decreases, the training is automatically terminated, at which time the optimal value of each variational parameter and the approximate posterior distribution of the waterlogging depth are obtained.

[0081] Step three trains the BCNN. During training, the feature variables of the training set are used as input items, and the maximum submerged water depth is used as an output item to submit to the BCNN for further training of the corresponding relationship. The purpose of training is to enable the BCNN to establish a suitable input-output relationship. Ultimately, the input of the validation set is used to obtain the output item of the maximum submerged water depth, which is compared with the maximum submerged water depth simulated by the hydrodynamic model.

[0082] Step 4, verify and analyze the prediction model and the prediction results.

[0083] The mean and variance of the output approximate posterior distribution are calculated, where the mean is used as the prediction value of the waterlogging depth in this application, and the variance is used to quantify the uncertainty and construct a confidence interval to obtain the interval prediction value of the water depth in the study area. By constructing a 95% confidence interval, a water depth prediction result with uncertainty can be obtained to measure the uncertainty.

[0084] The trained model is verified using the validation set. The validation data is input into the trained model to obtain the predicted waterlogging depth value and uncertainty, and the prediction results are evaluated.

[0085] By comparing the waterlogging submerged area in the study area predicted by the BCNN model with the waterlogging submerged area generated by the hydrodynamic model software, the predicted values and target values of the maximum submerged water depth of all grids in the study area under different rainfall scenarios, and the time required for the prediction, the maximum submerged water depth prediction, and the calculation efficiency of the waterlogging area, the accuracy and performance of the BCNN model are evaluated. The mean absolute error (MAE), root mean square error (RMSE), and Nash efficiency coefficient (NSE) are selected as evaluation indicators to evaluate the ability of the BCNN model. The maximum submerged water depth prediction results of the BCNN model are directly compared with the maximum submerged water depth simulation results of the two-dimensional hydrodynamic model, and the prediction error is quantified.

[0086] The study area is divided into several non-intersecting 256x256 patches, and the maximum submerged water depth in different patches is obtained. The waterlogging submerged map in the study area can be obtained by splicing all the patches. Figure 6 、 7Figures 8 respectively show the inundation maps of the three heavy rainfall events in the validation set, which are obtained by the two-dimensional hydrodynamic model and the BCNN model. Considering that the water depth less than 5 cm has little effect on the normal operation of the city, all water depth values less than 5 cm are truncated and not shown in the figures. The corresponding inundation areas of the study area under the three rainfall scenarios are calculated, and only the areas with a maximum water depth greater than 0.05 m are considered. The ratio of the inundation area to the total area is calculated and shown in Table 3.

[0087] Table 3 Ratio of inundation area obtained by the hydrodynamic model and the BCNN model

[0088]

[0089] The results show that under different rainfall scenarios, the inundation distribution of the study area predicted by the BCNN model constructed in this application is basically consistent with the inundation distribution generated by the hydrodynamic model, indicating that this method can successfully learn the spatial distribution pattern of waterlogging and accurately identify most of the areas that produce waterlogging. At the same time, the model can also correctly distinguish areas that will not produce waterlogging.

[0090] To illustrate the accuracy of the model in predicting water depth, the predicted and target values of waterlogging water depth of all grids in the study area under different rainfall scenarios are plotted into scatter plots, as shown in Figures 11. Figure 9 、 10 、11. In the figure, the X-axis represents the target value, i.e. the maximum inundation water depth value simulated by the two-dimensional hydrodynamic model; while the Y-axis represents the predicted value of waterlogging water depth, i.e. the maximum inundation water depth value predicted by the BCNN model. The black line in the figure is the 45-degree reference line, which means that the predicted value and the target value are completely consistent, representing the most ideal result. N in the figure represents the total number of grids, and MAE and RMSE represent the mean absolute error and the mean square error of the predicted water depth, respectively. From the figure, it can be seen that the fitting effect of the predicted water depth value and the target value of most grids is good, and most of the scatter points are gathered around the black line. In the three rainfall events, the RMSE value is less than 0.05 m, and the MAE value is less than 0.02 m. The prediction error of water depth in most grids is controlled within -0.1 m and 0.1 m, and the error distribution in different regions is relatively uniform, and there is no region with significant difference.

[0091] Due to the large number of data samples, the existence of a large number of water depth values of 0 makes the MAE and RMSE values low, and cannot fully reflect the error between the maximum inundation water depth value and the target value. To reflect the performance of the model in predicting high water depth values and to reflect the details of the prediction, this application selects two patches in the study area to show the prediction of the model in local areas, as shown in Figures 12. Figure 12 、 13As shown in the figure. For each grid with a maximum flooding depth exceeding 0.5m, the NSE index is calculated and plotted on the graph. The NSE value reflects the prediction performance of that grid on the validation set, taking into account the prediction errors under all rainfall events. The closer the NSE value is to 1, the closer the predicted water depth at that grid is to the observed value, as shown in red in the figure. Grids with poor prediction performance have NSE values ​​close to 0 and are shown in blue.

[0092] like Figure 12 、 13 As shown, the NSE values ​​for most flooded areas are greater than 0.8, indicating that the model not only identifies flood "hotspots" but also accurately predicts the water depths in these areas. However, it should also be noted that while the model achieves good prediction results in the central flood zone, it cannot accurately predict shallow flooding along the runoff path and performs poorly in the periphery of the flood zone. This explains why the model's predictions for flooded areas are generally lower than the target value, as well as the points in the scatter plot where water depths are underpredicted. Because data-driven models do not rely on any physical theorems, these errors are unavoidable.

[0093] Table 4 shows the computation time for the two-dimensional hydrodynamic model and the BCNN model for the three rainfall events. The BCNN model computation time only considers the time required to make predictions using the trained model. All computations for the two-dimensional hydrodynamic model and the BCNN model were performed on the same computer, using a high-performance professional-grade NVIDIA RTX A4000 GPU with 16GB of video memory for acceleration.

[0094] Table 4 Comparison of calculation time

[0095]

[0096] In summary, the predicted urban flooding inundation maps generated by the proposed BCNN prediction model are highly consistent with those generated by the hydrodynamic model. The BCNN model demonstrates excellent prediction performance for both the extent and depth of urban flooding, with acceptable errors. Furthermore, the BCNN model significantly outperforms the hydrodynamic model in computational efficiency, enabling early forecasting of urban flooding disasters and supporting real-time flood disaster management.

[0097] In addition to predicting the maximum flooding depth, the BCNN model can also quantify the uncertainty of the depth prediction results and provide an uncertainty estimate expressed as prediction variance at each spatial location. This application uses variance as the uncertainty metric. Figures 14-17The predicted water depth error and variance size in four different areas are shown under the rainfall event "19960715". Figures 14-17 The image in the first row is the predicted water depth value, the image in the second row is the predicted error, and the image in the third row is the predicted variance size, i.e., the uncertainty size of the model prediction result.

[0098] As can be seen from the figure, the area with uncertainty in the predicted water depth is roughly consistent with the area with waterlogging, and through comparison of the second row error and the third row variance, it can be concluded that the area with larger prediction error also has larger uncertainty. Since the model established in the present application is completely based on data driving and does not rely on any physical theorem, it is inevitable that there will be incomplete cognition, and in addition, the noise existing in the original data will make the model prediction have uncertainty, which will cause deviation between the predicted water depth value and the observed value. Quantifying the uncertainty of the result can well compensate for the error caused by the above sources of uncertainty.

[0099] In addition, the confidence interval of the water depth can also be constructed through the predicted value and the variance. The present application randomly selects 9 checkpoints in the study area. Figure 18 The predicted interval of each checkpoint in the 95% confidence interval is shown, and the observed value of the checkpoint is shown by a dot.

[0100] As Figure 18 shown, the maximum water depth of the 9 checkpoints has 5 located in the 95% confidence interval predicted by the BCNN model. By setting different confidence levels, the water depth confidence interval under different significance levels can be obtained. Although ordinary deep neural networks also have strong nonlinear regression and fitting capabilities, they can only predict an average value in their standard state and do not provide any guidance on how much trust can be placed in the predicted value. The BCNN model constructed in the present application considers the influence of local uncertainty on the result, and generates a wider and safer confidence area around the predicted flood.

[0101] It should be understood that parts not described in detail in the present application are all prior art.

[0102] The above, combined with the drawings, is only a specific implementation method and process of the present application, but the protection scope of the present application is not limited thereto, and any person skilled in the art should understand that this is only an example for illustration, and various changes and substitutions can be made to the implementation method without departing from the essential content of the present application.

Claims

1. A method for urban flood forecasting based on Bayesian convolutional neural network, characterized in that, It comprises the following steps: Step 1, collect historical rainfall events in the study area, simulate the maximum inundation water depth under different rainfall events through hydrodynamic simulation software; Step 2, select characteristic variables affecting waterlogging water depth, including 10 rainfall characteristic variables and 10 spatial characteristic variables, and perform data preprocessing; The 10 rainfall characteristic variables include: rainfall time, maximum rainfall, total rainfall, the ratio of the cumulative rainfall from the start of rainfall to the peak of rainfall to the cumulative rainfall from the peak of rainfall to the end of rainfall, the ratio of the maximum rainfall change per unit time to the total rainfall, the ratio of the cumulative rainfall from the start of rainfall to 0.33T to the total rainfall, the ratio of the cumulative rainfall from the start of rainfall to 0.3T to the total rainfall, the ratio of the cumulative rainfall from the start of rainfall to 0.5T to the total rainfall, the center of gravity position of the rainfall process line and the position of the maximum rainfall change; The 10 spatial characteristic variables include: surface elevation, slope, slope direction, plan curvature, terrain moisture index, impervious rate, distance to drainage network, flow accumulation value, runoff accumulation value and unit slope flow accumulation value; Step 3, consider uncertainty and construct a Bayesian convolutional neural network prediction model; In step 1, the historical rainfall events are divided into training set and validation set, the 20 characteristic variables in step 2 are used as the input of the model in the training set, the maximum inundation water depth value corresponding to the rainfall event in step 1 in the training set is used as the output of the model, and random Gaussian noise is added to the output item to reflect accidental uncertainty, the student's prior distribution is set for the filter weight of each convolutional layer to reflect cognitive uncertainty, and 20 parameter values are randomly extracted as the initial value of the filter weight by using Monte Carlo sampling method; A convolutional attention mechanism module is introduced in the Bayesian convolutional neural network, which includes a channel attention module and a spatial attention module, wherein the channel attention module compresses the feature map in the spatial dimension to obtain a one-dimensional vector, and the spatial attention module identifies areas with high flood risk, such as low-lying areas with lower terrain than the surrounding areas, and the water depth value of these parts is paid attention to and extracted for repeated training; Step 4, train the model in step 3 based on the loss function MAE, and train the model by inversely propagating the MAE value between the maximum inundation water depth value predicted by the Bayesian convolutional neural network and the maximum inundation water depth value generated by the two-dimensional hydrodynamic model, and the training is automatically terminated when the loss function no longer decreases; Step 5, input the data in the validation set into the model trained in step 4, calculate the mean value of the approximate posterior distribution as the prediction value of the waterlogging water depth.

2. The urban flood forecasting method based on Bayesian convolutional neural network according to claim 1, characterized in that, In step 5, the variance of the approximate posterior distribution is calculated, which is used to quantify uncertainty and construct a confidence interval to obtain the interval prediction value of the waterlogging depth in the study area.

3. The urban flood forecasting method based on Bayesian convolutional neural network according to claim 1, characterized in that, The water power software is selected in step 1 to build a one-dimensional sewer pipe network model and a two-dimensional surface model of the research area, and then the MIKE FLOOD module is used to couple the sewer pipe network model and the surface model to build a coupled model. The historical rainfall events of the research area are input into the coupled model to obtain the maximum flooded water depth corresponding to different events.

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