Urban flood prediction method based on Bayesian convolutional neural network

Abstract

The invention discloses an urban flood prediction method based on a Bayesian convolutional neural network, and the method comprises the steps: collecting historical rainfall events of a research region, simulating different rainfall events through hydrodynamic simulation software, and obtaining the maximum submerging water depth; selecting characteristic variables influencing waterlogging water depth, wherein the characteristic variables comprise 10 rainfall characteristic variables and 10 spatial characteristic variables; considering uncertainty to construct a Bayesian convolutional neural network prediction model; training the model based on a loss function MAE; and inputting the data in the verification set into the trained model, and calculating the mean value of the output approximate posteriori distribution as the predicted value of the water depth. The method is proposed on the basis of calculating and analyzing the relationship between the characteristic variables and the target variables, effectively fusing different data and considering possible uncertainty sources, not only realizes the prediction of the size and range of the submerged water depth of the research area, but also quantifies the prediction uncertainty, so that the prediction accuracy is improved. And support is provided for real-time flood disaster management.

Description

Technical Field

[0001] The present invention relates to the technical field of flood forecasting, and in particular to an urban flood forecasting method based on a Bayesian convolutional neural network. Background Art

[0002] The essence of flood forecasting is the prediction of flood inundation maps of urban areas, measured by flood depth. In recent years, data-driven models based on deep learning have gradually been applied by domestic and foreign researchers to the prediction of urban rainstorm waterlogging, such as the existing literature: Dai Mengqi. Research on urban rainstorm waterlogging depth prediction method based on deep learning, Nanjing Normal University. In this literature, water depth prediction characteristic factors are generated as model inputs 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 characteristic factor is not comprehensive enough, lacking consideration of the influence of hydrological conditions and surface elevation on water depth. The slope can only reflect local terrain changes, while the surface elevation can directly reflect the overall fluctuation of the surface in space, affecting the generation process of urban surface runoff. At the same time, the formation and development of floods are extremely complex, affected by meteorological and geographical factors, and the sources of uncertainty are very complex and inevitable. This literature does not consider the uncertainty of the prediction results. Summary of the invention

[0003] In order to solve the problems of insufficient comprehensiveness of characteristic factor selection in existing technologies and failure to consider the uncertainty of prediction results, a method for urban flood prediction based on Bayesian convolutional neural network was proposed.

[0004] The present invention adopts the following technical solution:

[0005] A method for urban flood prediction based on Bayesian convolutional neural network includes the following steps:

[0006] Step 1: Collect historical rainfall events in the study area and simulate different rainfall events using hydrodynamic simulation software to obtain the maximum flooding depth;

[0007] Step 2, select characteristic variables that affect water depth, including 10 rainfall characteristic variables and 10 spatial characteristic variables, and perform data preprocessing;

[0008] Step 3: Construct a Bayesian convolutional neural network prediction model considering uncertainty

[0009] The historical rainfall events in step 1 are divided into a training set and a validation set. The 20 characteristic variables in step 2 of the training set are used as the input of the model. The maximum flooding depth value of the corresponding rainfall event obtained in step 1 of the training set is used as the output of the model. 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. 20 parameter values ​​are randomly selected as the initial value of the filter weight by using Monte Carlo sampling.

[0010] Step 4, training the model in step 3 based on the loss function MAE, back-propagating the MAE value between the maximum flooding depth value predicted by the Bayesian convolutional neural network and the maximum flooding depth value generated by the two-dimensional hydrodynamic model to train the model, and when the loss function no longer decreases, the training automatically terminates;

[0011] Step 5: Input the data in the validation set into the model trained in step 4, and calculate the mean of the approximate posterior distribution of the output as the predicted value of the water depth of the urban flooding.

[0012] Furthermore, in step 5, the variance of the output approximate posterior distribution is calculated, and the variance is used to quantify uncertainty and construct confidence intervals to obtain interval prediction values ​​of water depth in the study area.

[0013] Furthermore, the 10 rainfall characteristic variables in step 2 include: rainfall time, maximum rainfall, total rainfall, the ratio of the cumulative rainfall from the start of rainfall to the peak rainfall to the cumulative rainfall from the peak 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 of the rainfall process line and the location of the maximum rainfall change.

[0014] Furthermore, the 10 spatial characteristic variables in step 2 include: surface elevation, slope, slope aspect, plane curvature, terrain moisture index, impermeability, distance to the drainage network, flow accumulation value, runoff accumulation value and unit slope flow accumulation value.

[0015] Furthermore, in step 1, hydrodynamic software was used to build a one-dimensional sewer network model and a two-dimensional surface model of the study area. Then, the MIKE FLOOD module was used to couple the sewer network model and the surface model to establish a coupling model. The historical rainfall events in the study area were input into the coupling model to obtain the maximum flooding depth corresponding to different events.

[0016] Furthermore, in step 3, a convolutional attention mechanism module is introduced into the Bayesian convolutional neural network. The convolutional attention mechanism module includes a channel attention module and a spatial attention module. The channel attention module compresses the feature map in the spatial dimension to obtain a one-dimensional vector. The spatial attention module is used to identify areas with high flood risk, especially those low-lying areas with lower terrain than the surrounding areas. The water depth values ​​of these areas will be focused on and extracted for repeated training.

[0017] The beneficial effects of the present invention are:

[0018] This method calculates and analyzes the relationship between characteristic variables and target variables, effectively integrates different data, and considers possible sources of uncertainty. It proposes a method for predicting urban floods using a Bayesian convolutional neural network model. It not only predicts the size and range of the flood depth in the study area, but also quantifies the uncertainty of the prediction, providing support for real-time flood disaster management. BRIEF DESCRIPTION OF THE DRAWINGS

[0019] Figure 1 A framework for flood depth prediction based on Bayesian convolutional neural network;

[0020] Figure 2 is the Spearman rank correlation coefficient diagram of the spatial characteristic variables;

[0021] Figure 3 It is the data structure type of spatial characteristics. In the figure, 1567×1834 represents the number of grids in the study area, and 10 represents the number of channels, that is, the number of spatial characteristic variables;

[0022] Figure 4 Schematic diagram of the Bayesian convolutional neural network structure, where H×W represents the resolution size, and the one-dimensional data is converted into two-dimensional data through a fully connected layer of size 4096. f is the number of convolution kernels;

[0023] Figure 5 To divide the study area into several patches of equal size;

[0024] Figure 6 The waterlogging inundation map obtained by the two-dimensional hydrodynamic model and the BCNN model for the “20080815” rainfall event in the validation set is shown;

[0025] Figure 7 The waterlogging inundation map obtained by the two-dimensional hydrodynamic model and the BCNN model for the "20050803" rainfall event in the validation set is shown;

[0026] Figure 8The waterlogging inundation map obtained by the two-dimensional hydrodynamic model and the BCNN model for the “19960715” rainfall event in the validation set is shown;

[0027] Fig. 9 The scatter plot of the predicted and target values ​​of the maximum flooding depth of all grids in the study area in the "20080815" rainfall event in the validation set is shown;

[0028] Fig.10 The scatter plot of the predicted and target values ​​of the maximum flooding depth of all grids in the study area in the "20050803" rainfall event in the validation set is shown;

[0029] Fig.11 The scatter plot of the predicted and target values ​​of the maximum flooding depth of all grids in the study area in the "19960715" rainfall event in the validation set is shown;

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

[0031] Fig.13 The local area prediction for another patch within the study area is shown;

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

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

[0034] Fig.16 The predicted water depth error and variance of one of the patches C in the study area during the rainfall event “19960715” are shown;

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

[0036] Fig.18 Box plots of water depth prediction for each checkpoint with 95% confidence intervals are shown. DETAILED DESCRIPTION

[0037] In order to make the purpose, technical scheme and technical effect of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments.

[0038] Example 1

[0039] The urban flood prediction method based on Bayesian convolutional neural network of the present invention is illustrated by taking the historical rainfall events in Rushan City as an example. Figure 1 , methods include:

[0040] Step 1: Use hydrodynamic simulation software to simulate different rainfall events to obtain waterlogging inundation maps and maximum inundation depth and average inundation depth;

[0041] A one-dimensional sewer network model and a two-dimensional surface model of the study area were built respectively. Then the MIKE FLOOD module was used to couple the sewer network model and the surface model to establish a coupling model. The coupling model reflects the water flow exchange between the sewer system and the surface system.

[0042] The 5m resolution DEM elevation is obtained from the terrain TIFF raster data. In order to reflect the real elevation of the urban surface, the buildings and roads in the study area are superimposed on the 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 after being raised by 5m on the original terrain and the road data after being 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. In the MIKE URBAN CS module, the DEM data is used to obtain the surface elevation of the inspection well; in the MIKE21FM module, the DEM data is divided into 1567×1834 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, in which the MIKE URBAN CS module is mainly used to simulate urban runoff and sewage discharge processes. MIKE 21FM belongs to the MIKE 21 software, which is mainly used for hydrodynamic simulation. Both the MIKE URBAN CS module and the MIKE 21FM module need to input data after the building is raised by 5m on the original terrain and the road is lowered by 0.15m on the original terrain.

[0044] The processed DEM data is input into the MIKE URBAN CS module and the MIKE21FM module as terrain data to obtain a one-dimensional sewer network model and a two-dimensional surface model, and the pipe flow process simulation and the flow velocity and direction simulation of free surface flowing water bodies such as urban surface, rivers, and lakes are respectively performed. The MIKE FLOOD module is used to dynamically couple the one-dimensional sewer 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. When the pipe network node overflows, the water volume enters the two-dimensional overflow model to calculate the flooding situation. When the full pipe flow state ends, the water volume of the two-dimensional model returns to the pipe network for calculation.

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

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

[0047]

[0048]

[0049] Step 2: Analyze the characteristic variables that affect the water depth of urban flooding;

[0050] Step 2.1: Spatial distribution correlation of waterlogging depth

[0051] In order to verify the existence of spatial correlation in the distribution of waterlogging in the study area, the global Moran's I index was used to conduct global spatial autocorrelation analysis on the waterlogging depth, i.e., the maximum flooding depth, simulated in step 1.

[0052] Five rainfall events were randomly selected from the 33 rainfall events, and the maximum flooding depth in the grid was used as the water depth value of the waterlogging. Their global Moran's I index was calculated to explore the spatial distribution pattern of waterlogging. The results are shown in Table 2.

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

[0054] Moran 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] It can be seen from Table 2 that the Moran index I of the five rainstorm events in the study area are all greater than 0 and the z values ​​all pass the significance test, which proves that the urban waterlogging depth in the study area has significant spatial autocorrelation, which is specifically manifested in the characteristics of high-value clustering in space.

[0056] The z value is a standardized statistic that measures the difference between the spatial pattern of the actual observed data and the random distribution pattern. The larger the z value, the higher the degree of spatial autocorrelation. The p value is the value of the hypothesis test. The null hypothesis is: there is no spatial autocorrelation in the research content, and p < 0.01 means that the null hypothesis is rejected at a 99% confidence interval.

[0057] The study in step 2.1 proved that urban waterlogging has obvious spatial aggregation effect. According to the research of relevant scholars, the distribution pattern of urban floods is mainly affected by terrain 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

[0059] According to previous relevant literature and the difficulty of data acquisition, five aspects including rainfall, topographic factors, hydrological conditions, drainage capacity, and land use type were considered to select characteristic variables that affect the depth of urban waterlogging.

[0060] The rainfall characteristic variables selected rainfall time, maximum rainfall and total rainfall as characteristic variables to measure the intensity. In order to distinguish the temporal variability of different rainfall events, referring to the research results of Wartalska et al., five characteristics were constructed, namely, the ratio of the cumulative rainfall from the beginning of rainfall to the peak rainfall to the cumulative rainfall from the peak 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, and the ratio of the cumulative rainfall from the beginning of rainfall to 0.5T to the total rainfall. In addition, the centroid position of the rainfall process line and the location of the maximum rainfall change were selected to measure the uneven change of precipitation over time.

[0061] However, topographic factors, hydrological conditions, drainage capacity, and land use types are spatially variable and are therefore collectively referred to as spatial characteristics. 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 Spear rank correlation coefficient is used for the spatial characteristic variables to measure the strength of the monotonic relationship between the characteristic variables and the variables to be predicted, and to verify the rationality of the variable selection. This method is a prior art and will not be described in detail here.

[0064] Finally, through the Spearman rank correlation coefficient, the spatial characteristic variables were determined to be surface elevation, slope, slope aspect, plane curvature, terrain moisture index, impermeability, drainage network distance, flow accumulation value, runoff accumulation value and unit slope flow accumulation value. The Spearman rank correlation coefficient between the spatial characteristic variables and the corresponding maximum flooding depth is shown in Figure 1. Figure 2 ,The slope aspects in the figure are quantitatively represented by sine and cosine functions, which are ASP1 and ASP2 respectively.

[0065] Topographic factors include surface elevation, slope, aspect and plane curvature; hydrological condition factors include terrain wetness index, flow accumulation value, runoff accumulation value and unit slope flow accumulation value; drainage capacity factors include the distance to the drainage network; and land use type variables include imperviousness.

[0066] The existence of a large number of impervious surfaces in urban areas will prevent rainwater from infiltrating, thereby quickly forming runoff on the surface; other different land use types represent different impervious rates and vegetation coverage conditions, which also affect the surface runoff generation and convergence process to a certain extent, leading to varying degrees of waterlogging. In order to reflect the impact of different land use types on the runoff generation process, impervious rate is used to measure land use types.

[0067] Step 3: Consider uncertainty to build a Bayesian convolutional neural network prediction model;

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

[0069] The target data set (maximum flooding depth in Table 1) is truncated, and the water depth less than 0.05m is partially 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. At the same time, 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. The input predicted by the Bayesian convolutional neural network can only be square, such as Figure 5 As shown in the figure. The patches with yellow lines are outside the study area, while the patches with blue lines are within the study area. After excluding those patches that are entirely outside the study area, the remaining patches are processed as follows:

[0071] If the blue line area accounts for more than 60% of the total area, it will be included in this study, and the remaining patches will not be included.

[0072] consider;

[0073] All data within the yellow line area of ​​the patch are set to 0.

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

[0075] The convolutional attention mechanism module is introduced into the Bayesian convolutional neural network, which includes the channel attention module (Channel Attention Module, CAM) and the spatial attention module (Spatial Attention Module, SAM). The CAM compresses the feature map in the spatial dimension to obtain a one-dimensional vector, such as Figure 3 As shown, SAM is then used to identify areas with high flood risk, especially those low-lying areas with lower terrain than the surrounding areas. The water depth values ​​in these areas will be focused on, extracted and repeatedly trained.

[0076] When the convolution layer extracts features from the input data, the features of the key areas are not highlighted. Adding the convolutional attention mechanism module can calculate the attention weight based on the extracted feature map, that is, the feature map obtained by convolution is used as input and transformed to output the attention weight matrix corresponding to the feature map. Each element of this weight matrix corresponds to the importance of the corresponding position in the original feature map, that is, a higher attention weight is given to the important area. The weight value is not simply determined as a fixed value, but the possibility of describing the weight based on the probability distribution. In addition, the calculated attention weight matrix is ​​multiplied by the feature map obtained by the previous convolution, and the feature map is weighted, so that the features of the key focus area in the original feature map can be strengthened. Adding 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 the image corresponding to different feature variables, and the image contains the value of a certain feature variable in the study area. The output item is the maximum flooding depth.

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

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

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

[0081] Step 3: Train BCNN. During training, the characteristic variables of the training set are used as input items, and the maximum flooding depth is submitted to BCNN as the output item to train the corresponding relationship. The purpose of training is to enable BCNN to establish a suitable input-output relationship. The ultimate goal is to obtain the output item maximum flooding depth through the input of the validation set and compare it with the maximum flooding depth obtained by the hydrodynamic model simulation.

[0082] Step 4: Verify and analyze the prediction model and prediction results.

[0083] The mean and variance of the output approximate posterior distribution are calculated respectively, where the mean is used as the predicted value of the water depth in this application, and the variance is used to quantify 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, the water depth prediction result with uncertainty can be obtained to measure uncertainty.

[0084] The trained model was verified using the validation set, and the validation data was input into the trained model to obtain the predicted water depth and uncertainty of the flooding, and the prediction results were evaluated.

[0085] By comparing the flooded area in the study area predicted by the BCNN model with the flooded area generated by the hydrodynamic model software, the predicted and target values ​​of the maximum flooded depth of all grids in the study area under different rainfall scenarios, and the time required for the prediction results, the accuracy and performance of the BCNN model are evaluated from three aspects: the prediction of the flooded area, the prediction of the maximum flooded depth, and the computational efficiency. This application selects the mean absolute error (MAE), the root mean square error (RMSE), and the Nash efficiency coefficient (NSE) as evaluation indicators to evaluate the ability of the BCNN model, directly compares the maximum flooded depth prediction results of the BCNN model with the maximum flooded depth simulation results of the two-dimensional hydrodynamic model, and quantifies the prediction error.

[0086] The study area is divided into several non-overlapping 256×256 patches, the maximum flooding depth in different patches is obtained, and all patches are spliced ​​together to obtain the waterlogging inundation map in the study area. Figure 6 , 7, 8 show the flooding maps obtained by the two-dimensional hydrodynamic model and the BCNN model for three heavy rainfall events in the validation set. Considering that the water depth less than 5 cm has little impact on the normal operation of the city, this application truncates all water depth values ​​less than 5 cm and does not show them in the figure. The corresponding flooded areas of the study area under these three rainfall scenarios were calculated respectively, and only the areas with the maximum water depth greater than 0.05 m were considered, and the ratio of the flooded area to the total area was counted, see Table 3.

[0087] Table 3. Percentage of flooded area obtained by hydrodynamic model and BCNN model

[0088]

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

[0090] In order to illustrate the accuracy of the model in predicting water depth, this application plotted the predicted values ​​and target values ​​of waterlogging depth of all grids in the study area under different rainfall scenarios into a scatter plot. The results are as follows: Fig. 9 , 10 , as shown in Figure 11. In the figure, the X-axis represents the target value, that is, the maximum flooding depth value obtained by the two-dimensional hydrodynamic model simulation; and the Y-axis represents the predicted value of the water depth of the waterlogging, that is, the maximum flooding depth value predicted by the BCNN model. The black line in the figure is the 45-degree baseline. At this time, the predicted value and the target value are completely consistent, representing the most ideal result. In the figure, N represents the total number of grids, and MAE and RMSE represent the mean absolute error and mean square error of the predicted water depth, respectively. It can be seen from the figure that the predicted water depth values ​​of most grids have a good fit with the target value, and most of the scattered points are concentrated around the black line. The RMSE values ​​in the three rainfall events are all less than 0.05m, and the MAE values ​​are all less than 0.02m. The predicted error values ​​of the water depth in most grids are controlled between -0.1m and 0.1m. At the same time, the error distribution in different regions is relatively uniform, and there is no obvious area with huge differences.

[0091] Due to the large number of data samples, the existence of a large number of points with water depth values ​​of 0 makes the MAE and RMSE values ​​low, and cannot fully and truly show the error between the maximum flooded water depth value and the target value. In order to reflect the performance of the model in predicting high water depth values ​​and reflect the details of its prediction, this application selects two patches in the study area to show the prediction of the model in the local area, such as Fig.12 , 13As shown. For each grid with a maximum flooding depth value exceeding 0.5m, its NSE index is calculated separately and plotted on the graph. The size of the NSE value reflects the prediction effect of the 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 water depth prediction value on the grid is to the observed value, which is specifically shown in red in the figure. The NSE value of the grid with poor prediction effect is close to 0, which is shown in blue in the figure.

[0092] like Fig.12 , 13 As shown in the figure, the NSE values ​​of most waterlogged areas are greater than 0.8, which indicates that the model can not only identify the "hotspot" areas where floods occur, but also accurately predict the water depths in these areas. However, it should also be noted that although the model has achieved good prediction results in the central area of ​​the flood, it cannot accurately predict shallow floods extending along the runoff path, and its performance is poor in the periphery of the flood. This also explains why the model's predictions for the flooded area are generally lower than the target value, and there are points in the scatter plot where the water depth is insufficiently predicted. Since the data-driven model does not rely on any physical theorem, this part of the error is inevitable.

[0093] Table 4 shows the calculation time of the two-dimensional hydrodynamic model and the BCNN model for the three rainfall events, where the calculation time of the BCNN model only considers the time required for prediction using the trained model. All calculations of the two-dimensional hydrodynamic model and the BCNN model are completed on the same computer, and a high-performance professional-grade GPU is used throughout the process to accelerate the calculation process. The GPU model is NVIDIA RTX A4000 with 16GB of video memory.

[0094] Table 4 Comparison of calculation time

[0095]

[0096] In summary, the predicted flooding inundation map generated by the BCNN prediction model proposed in this application is quite consistent with the flooding inundation map generated by the hydrodynamic model. The BCNN model shows good prediction performance for both the scope and depth of flooding, and the error is within an acceptable range. At the same time, the BCNN model is significantly superior to the hydrodynamic model in terms of computational efficiency, and can make early forecasts of urban flood disasters, providing support for 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 estimate of the uncertainty expressed as the prediction variance at each spatial location. This application uses variance as the uncertainty measurement indicator. Figure 14-17The figure shows the predicted water depth error and variance in four random different areas under the rainfall event "19960715". Figure 14-17 The first row of images is the predicted water depth value, the second row of images is the predicted error, and the third row of images is the predicted variance, that is, the uncertainty of the model prediction results.

[0098] As can be seen from the figure, the areas where the predicted water depth is uncertain roughly coincide with the areas where waterlogging occurs. At the same time, by comparing the second row error and the third row variance, it is concluded that the areas with large prediction errors also have large uncertainties. Since the model established in this application is completely data-driven and does not rely on any physical theorem, there will inevitably be cognitive incompleteness, coupled with the noise in the original data, which will make the model's predictions uncertain and cause deviations between the predicted and observed values ​​of the water depth. Quantifying the uncertainty of the results can well compensate for the errors caused by the above sources of uncertainty.

[0099] In addition, the confidence interval of water depth can be constructed by using the predicted value and variance. This application randomly selected 9 checkpoints in the study area. Fig.18 The prediction intervals for each checkpoint with a 95% confidence interval are shown, and the observed values ​​for the checkpoints are shown as dots.

[0100] like Fig.18 As shown, 5 of the maximum water depths of the 9 checkpoints are within the 95% confidence interval predicted by the BCNN model. By setting different confidence levels, water depth confidence intervals at different significance levels can be obtained. Although ordinary deep neural networks also have powerful 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 this application takes into account the impact of local uncertainty on the results and produces a wider and safer confidence area around the predicted flood.

[0101] It should be understood that parts not described in detail in this specification belong to the prior art.

[0102] The above combined with the accompanying drawings are only specific implementation methods and processes of the present invention, but the protection scope of the present invention is not limited to this. Any technician familiar with the field should understand that this is only an example, and various changes and substitutions can be made to this implementation method without departing from the essential content of the present invention.

Claims

1. A method for urban flood prediction based on Bayesian convolutional neural network, characterized in that: The steps include: Step 1: Collect historical rainfall events in the study area and simulate different rainfall events using hydrodynamic simulation software to obtain the maximum flooding depth; Step 2, select characteristic variables that affect water depth, including 10 rainfall characteristic variables and 10 spatial characteristic variables, and perform data preprocessing; Step 3, consider the uncertainty to build a Bayesian convolutional neural network prediction model; The historical rainfall events in step 1 are divided into a training set and a validation set. The 20 characteristic variables in step 2 of the training set are used as the input of the model. The maximum flooding depth value of the corresponding rainfall event obtained in step 1 of the training set is used as the output of the model. 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. 20 parameter values ​​are randomly selected as the initial value of the filter weight by using Monte Carlo sampling. Step 4, training the model in step 3 based on the loss function MAE, back-propagating the MAE value between the maximum flooding depth value predicted by the Bayesian convolutional neural network and the maximum flooding depth value generated by the two-dimensional hydrodynamic model to train the model, and when the loss function no longer decreases, the training automatically terminates; Step 5: Input the data in the validation set into the model trained in step 4, and calculate the mean of the approximate posterior distribution of the output as the predicted value of the water depth of the urban flooding.

2. The urban flood prediction method based on Bayesian convolutional neural network according to claim 1 is characterized in that: In step 5, the variance of the output approximate posterior distribution is calculated. The variance is used to quantify uncertainty and construct confidence intervals to obtain interval prediction values ​​of water depth in the study area.

3. The urban flood prediction method based on Bayesian convolutional neural network according to claim 1 is characterized in that: The 10 rainfall characteristic 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 rainfall to the cumulative rainfall from the peak 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 of the rainfall process line and the location of the maximum rainfall change.

4. The urban flood prediction method based on Bayesian convolutional neural network according to claim 1 is characterized in that: The 10 spatial characteristic variables described in step 2 include: surface elevation, slope, slope aspect, plane curvature, terrain moisture index, impermeability, distance to the drainage network, flow accumulation value, runoff accumulation value and unit slope flow accumulation value.

5. The urban flood prediction method based on Bayesian convolutional neural network according to claim 1 is characterized in that: In step 1, hydrodynamic software is used to build a one-dimensional sewer network model and a two-dimensional surface model of the study area. Then, the MIKE FLOOD module is used to couple the sewer network model and the surface model to establish a coupling model. The historical rainfall events in the study area are input into the coupling model to obtain the maximum flooding depth corresponding to different events.

6. The urban flood prediction method based on Bayesian convolutional neural network according to claim 1 is characterized in that: In step 3, a convolutional attention mechanism module is introduced into the Bayesian convolutional neural network. The convolutional attention mechanism module includes a channel attention module and a spatial attention module. The channel attention module compresses the feature map in the spatial dimension to obtain a one-dimensional vector. The spatial attention module is used to identify areas with high flood risk, especially those low-lying areas with lower terrain than the surrounding areas. The water depth values ​​of these areas will be paid special attention and extracted for repeated training.

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